TANGLI • TANGLI • TANGLI •
SeriesSeriesSeries ISSN:ISSN: ISSN: 2160-47112160-4711 2160-4711 YNTHEYNTHEYNTHESSSIIISSS ECTUREECTUREECTURESSSONONON SSS LLL MORGANMORGANMORGAN&&&CLAYPOOLCLAYPOOLCLAYPOOL PUBLISHERSPUBLISHERSPUBLISHERS TTTHEHEHE SSSEMANTICEMANTICEMANTIC W WWEBEBEB::: T TTHEORYHEORYHEORY ANDANDAND T TTECHNOECHNOECHNOLLLOGYOGYOGY
SeriesSeriesSeries Editors: Editors:Editors: Ying YingYing Ding, Ding,Ding, Indiana IndianaIndiana University UniversityUniversity & && Paul PaulPaul Groth, Groth,Groth, VU VUVU University UniversityUniversity Amsterdam AmsterdamAmsterdam FoundingFoundingFounding Editor EditorEditor Emeritus: Emeritus:Emeritus: James JamesJames Hendler, Hendler,Hendler, Rensselaer RensselaerRensselaer Polytechic PolytechicPolytechic Institute InstituteInstitute SemanticSemanticSemantic MiningMiningMining ofofof SocialSocialSocial NetworksNetworksNetworks SemanticSemanticSemantic MiningMiningMining ofofof JieJieJie TangTang Tang and andand Juanzi JuanziJuanzi Li, Li,Li, Tsinghua TsinghuaTsinghua University UniversityUniversity SocialSocialSocial NetworksNetworksNetworks OnlineOnlineOnline socialsocial social networksnetworks networks havehave have alreadyalready already becomebecome become aa a bridgebridge bridge connectingconnecting connecting ourour our physicalphysical physical dailydaily daily lifelife life withwith with thethe the (web-based)(web-based) (web-based) inforinfor infor---
mationmationmation space.space. space. This This This connectionconnection connection producesproduces produces aa a hugehuge huge volumevolume volume ofof of data,data, data, notnot not onlyonly only aboutabout about thethe the informationinformation information itself,itself, itself, butbut but alsoalso also aboutabout about SEMANTIC OFMINING SOCIAL NETWORKS SEMANTIC OFMINING SOCIAL NETWORKS SEMANTIC OFMINING SOCIAL NETWORKS useruseruser behavior.behavior. behavior. The The The ubiquityubiquity ubiquity ofof of thethe the socialsocial social WebWeb Web andand and thethe the wealthwealth wealth ofof of socialsocial social datadata data oo offfererer usus us unprecedentedunprecedented unprecedented opportunitiesopportunities opportunities forfor for studyingstudyingstudying the thethe interaction interactioninteraction patterns patternspatterns among amongamong users usersusers so soso as asas to toto understand understandunderstand the thethe dynamic dynamicdynamic mechanisms mechanismsmechanisms underlying underlyingunderlying di didiffferenterenterent networks,networks,networks, something somethingsomething that thatthat was waswas previously previouslypreviously di didifffcultcultcult to toto explore exploreexplore due duedue to toto the thethe lack lacklack of ofof available availableavailable data. data.data. InInIn this thisthis book, book,book, we wewe present presentpresent the thethe architecture architecturearchitecture of ofof the thethe research researchresearch for forfor social socialsocial network networknetwork mining, mining,mining, from fromfrom a aa microscopic microscopicmicroscopic point pointpoint of ofof view.view.view. We WeWe focus focusfocus on onon investigating investigatinginvestigating several severalseveral key keykey issues issuesissues in inin social socialsocial networks. networks.networks. Speci SpeciSpecifffcally,cally,cally, we wewe begin beginbegin with withwith analytics analyticsanalytics of ofof social socialsocial interactionsinteractionsinteractions between betweenbetween users. users.users. The TheThe f ffrstrstrst kinds kindskinds of ofof questions questionsquestions we wewe try trytry to toto answer answeranswer are: are:are: What WhatWhat are areare the thethe fundamental fundamentalfundamental factors factorsfactors thatthatthat form formform the thethe di didiffferenterenterent categories categoriescategories of ofof social socialsocial ties? ties?ties? How HowHow have havehave reciprocal reciprocalreciprocal relationships relationshipsrelationships been beenbeen developed developeddeveloped from fromfrom parasocial parasocialparasocial relationships?relationships?relationships? How HowHow do dodo connected connectedconnected users usersusers further furtherfurther form formform groups? groups?groups? AnotherAnotherAnother theme themetheme addressed addressedaddressed in inin this thisthis book bookbook is isis the thethe study studystudy of ofof social socialsocial in ininfffuence.uence.uence. Social SocialSocial in ininfffuenceuenceuence occurs occursoccurs when whenwhen one’s one’sone’s opin opinopin--- ions,ions,ions, emotions, emotions,emotions, or oror behaviors behaviorsbehaviors are areare a afaffectedectedected by byby others, others,others, intentionally intentionallyintentionally or oror unintentionally. unintentionally.unintentionally. Considerable ConsiderableConsiderable research researchresearch has hashas been beenbeen conductedconductedconducted to toto verify verifyverify the thethe existence existenceexistence of ofof social socialsocial in ininfffuenceuenceuence in inin various variousvarious networks. networks.networks. However, However,However, few fewfew literature literatureliterature studies studiesstudies address addressaddress howhowhow to toto quantify quantifyquantify the thethe strength strengthstrength of ofof in ininfffuenceuenceuence between betweenbetween users usersusers from fromfrom di didiffferenterenterent aspects. aspects.aspects. In InIn Chapter ChapterChapter 4 44 and andand in inin [138], [138],[138], we wewe have havehave studiedstudiedstudied how howhow to toto model modelmodel and andand predict predictpredict user useruser behaviors. behaviors.behaviors. One OneOne fundamental fundamentalfundamental problem problemproblem is isis distinguishing distinguishingdistinguishing the thethe e efeffectsectsects of ofof di didifffererer--- ententent social socialsocial factors factorsfactors such suchsuch as asas social socialsocial in ininfffuence,uence,uence, homophily, homophily,homophily, and andand individual’s individual’sindividual’s characteristics. characteristics.characteristics. We WeWe introduce introduceintroduce a a a probabilistic probabilisticprobabilistic modelmodelmodel to toto address addressaddress this thisthis problem. problem.problem. Finally,Finally,Finally, we wewe use useuse an anan academic academicacademic social socialsocial network, network,network, ArnetMiner, ArnetMiner,ArnetMiner, as asas an anan example exampleexample to toto demonstrate demonstratedemonstrate how howhow we wewe apply applyapply the thethe intro introintro--- JieJieJie Tang TangTang ducedducedduced technologies technologiestechnologies for forfor mining miningmining real realreal social socialsocial networks. networks.networks. In InIn this thisthis system, system,system, we wewe try trytry to toto mine minemine knowledge knowledgeknowledge from fromfrom both bothboth the thethe infor inforinfor--- mativemativemative (publication)(publication) (publication) networknetwork network andand and thethe the socialsocial social (collaboration)(collaboration) (collaboration) network,network, network, andand and toto to understandunderstand understand thethe the interactioninteraction interaction mechanismsmechanisms mechanisms JuanziJuanziJuanzi LiLiLi betweenbetweenbetween the thethe two twotwo networks. networks.networks. TheThe The system systemsystem has hashas been beenbeen in inin operation operationoperation since sincesince 2006 20062006 and andand has hashas already alreadyalready attracted attractedattracted millions millionsmillions of ofof users usersusers fromfromfrom more moremore than thanthan 220 220220 countries/regions. countries/regions.countries/regions. OGN CLAYPOOL CLAYPOOLMORGAN& MORGAN& CLAYPOOL MORGAN& ABOUTABOUTABOUT SYNTHESIS SYNTHESISSYNTHESIS ThisThisThis volume volumevolume is isis a aa printed printedprinted version versionversion of ofof a aa work workwork that thatthat appears appearsappears in inin the thethe Synthesis SynthesisSynthesis Digital DigitalDigital LibraryLibrary Library ofof of EngineeringEngineering Engineering andand and ComputerComputerComputer Science Science Science.. Synthesis.Synthesis Synthesis LecturesLectures Lectures provideprovide provide concise, concise, concise, original original original presentations presentations presentations of of of important important important research research research and and and development development development topics,topics,topics, published publishedpublished quickly, quickly,quickly, in inin digital digitaldigital and andand print printprint formats. formats.formats. For ForFor more moremore information informationinformation visit visitvisit www.morganclaypool.com www.morganclaypool.comwww.morganclaypool.com
ISBN:ISBN:ISBN: 978-1-60845-857-8978-1-60845-857-8978-1-60845-857-8 SSSYNTHEYNTHEYNTHESSSIIISSS LLLECTUREECTUREECTURESSS ONONON MORGANMORGANMORGAN&&&CLAYPOOLCLAYPOOLCLAYPOOL PUBLISHERS PUBLISHERSPUBLISHERS 999000000000000 TTTHEHEHE SSSEMANTICEMANTICEMANTIC W WWEBEBEB::: T TTHEORYHEORYHEORY ANDANDAND T TTECHNOECHNOECHNOLLLOGYOGYOGY www.morganclaypool.comwww.morganclaypool.comwww.morganclaypool.com YingYingYing Ding DingDing and andand Paul PaulPaul Groth, Groth,Groth, Series SeriesSeries Editors EditorsEditors 999777888111666000888444555888555777888
4FNBOUJD .JOJOH PG 4PDJBM /FUXPSLT 4ZOUIFTJT -FDUVSFT PO UIF 4FNBOUJD 8FC DzFPSZ BOE 5FDIOPMPHZ
&EJUPST :JOH %JOH *OEJBOB 6OJWFSTJUZ 1BVM (SPUI &MTFWJFS -BCT 'PVOEJOH &EJUPS &NFSJUVT +BNFT )FOEMFS 3FOTTFMBFS 1PMZUFDIOJD *OTUJUVUF
4ZOUIFTJT -FDUVSFT PO UIF 4FNBOUJD 8FC ɩFPSZ BOE "QQMJDBUJPO JT FEJUFE CZ :JOH %JOH PG *OEJBOB 6OJWFSTJUZ BOE 1BVM (SPUI PG &MTFWJFS -BCT 8IFUIFS ZPV DBMM JU UIF 4FNBOUJD 8FC -JOLFE %BUB PS 8FC B OFX HFOFSBUJPO PG 8FC UFDIOPMPHJFT JT PĊFSJOH NBKPS BEWBODFT JO UIF FWPMVUJPO PG UIF 8PSME 8JEF 8FC "T UIF mSTU HFOFSBUJPO PG UIJT UFDIOPMPHZ USBOTJUJPOT PVU PG UIF MBCPSBUPSZ OFX SFTFBSDI JT FYQMPSJOH IPX UIF HSPXJOH 8FC PG %BUB XJMM DIBOHF PVS XPSME 8IJMF UPQJDT TVDI BT POUPMPHZCVJMEJOH BOE MPHJDT SFNBJO WJUBM OFX BSFBT TVDI BT UIF VTF PG TFNBOUJDT JO 8FC TFBSDI UIF MJOLJOH BOE VTF PG PQFO EBUB PO UIF 8FC BOE GVUVSF BQQMJDBUJPOT UIBU XJMM CF TVQQPSUFE CZ UIFTF UFDIOPMPHJFT BSF CFDPNJOH JNQPSUBOU SFTFBSDI BSFBT JO UIFJS PXO SJHIU 8IFUIFS UIFZ CF TDJFOUJTUT FOHJOFFST PS QSBDUJUJPOFST 8FC VTFST JODSFBTJOHMZ OFFE UP VOEFSTUBOE OPU KVTU UIF OFX UFDIOPMPHJFT PG UIF 4FNBOUJD 8FC CVU UP VOEFSTUBOE UIF QSJODJQMFT CZ XIJDI UIPTF UFDIOPMPHJFT XPSL BOE UIF CFTU QSBDUJDFT GPS BTTFNCMJOH TZTUFNT UIBU JOUFHSBUF UIF EJĊFSFOU MBOHVBHFT SFTPVSDFT BOE GVODUJPOBMJUJFT UIBU XJMM CF JNQPSUBOU JO LFFQJOH UIF 8FC UIF SBQJEMZ FYQBOEJOH BOE DPOTUBOUMZ DIBOHJOH JOGPSNBUJPO TQBDF UIBU IBT DIBOHFE PVS MJWFT 5PQJDT UP CF JODMVEFE t 4FNBOUJD 8FC 1SJODJQMFT GSPN MJOLFEEBUB UP POUPMPHZ EFTJHO t ,FZ 4FNBOUJD 8FC UFDIOPMPHJFT BOE BMHPSJUINT t 4FNBOUJD 4FBSDI BOE MBOHVBHF UFDIOPMPHJFT t ɩF &NFSHJOH w8FC PG %BUBw BOE JUT VTF JO JOEVTUSZ HPWFSONFOU BOE VOJWFSTJUZ BQQMJDBUJPOT t 5SVTU 4PDJBM OFUXPSLJOH BOE DPMMBCPSBUJPO UFDIOPMPHJFT GPS UIF 4FNBOUJD 8FC t ɩF FDPOPNJDT PG 4FNBOUJD 8FC BQQMJDBUJPO BEPQUJPO BOE VTF t 1VCMJTIJOH BOE 4DJFODF PO UIF 4FNBOUJD 8FC t 4FNBOUJD 8FC JO IFBMUI DBSF BOE MJGF TDJFODFT JJJ
4FNBOUJD .JOJOH PG 4PDJBM /FUXPSLT +JF 5BOH BOE +VBO[J -J 4PDJBM 4FNBOUJD 8FC .JOJOH 5PQF 0NJUPMB 4FCBTUJÈO " 3ÓPT BOE +PIO ( #SFTMJO 4FNBOUJD #SFBLUISPVHI JO %SVH %JTDPWFSZ #JO $IFO )VJKVO 8BOH :JOH %JOH BOE %BWJE 8JME 4FNBOUJDT JO .PCJMF 4FOTJOH ;IJYJBO :BO BOE %JQBOKBO $IBLSBCPSUZ 1SPWFOBODF "O *OUSPEVDUJPO UP 1307 -VD .PSFBV BOE 1BVM (SPUI 3FTPVSDF0SJFOUFE "SDIJUFDUVSF 1BUUFSOT GPS 8FCT PG %BUB #SJBO 4MFUUFO "BSPO 4XBSU[T " 1SPHSBNNBCMF 8FC "O 6OmOJTIFE 8PSL "BSPO 4XBSU[ *ODFOUJWF$FOUSJD 4FNBOUJD 8FC "QQMJDBUJPO &OHJOFFSJOH &MFOB 4JNQFSM 3PCFSUB $VFM BOE .BSUJO 4UFJO 1VCMJTIJOH BOE 6TJOH $VMUVSBM )FSJUBHF -JOLFE %BUB PO UIF 4FNBOUJD 8FC &FSP )ZWÚOFO 7*70 " 4FNBOUJD "QQSPBDI UP 4DIPMBSMZ /FUXPSLJOH BOE %JTDPWFSZ ,BUZ #ÚSOFS .JDIBFM $POMPO +PO $PSTPO3JLFSU BOE :JOH %JOH -JOLFE %BUB &WPMWJOH UIF 8FC JOUP B (MPCBM %BUB 4QBDF 5PN )FBUI BOE $ISJTUJBO #J[FS $PQZSJHIU ª CZ .PSHBO $MBZQPPM
"MM SJHIUT SFTFSWFE /P QBSU PG UIJT QVCMJDBUJPO NBZ CF SFQSPEVDFE TUPSFE JO B SFUSJFWBM TZTUFN PS USBOTNJUUFE JO BOZ GPSN PS CZ BOZ NFBOTFMFDUSPOJD NFDIBOJDBM QIPUPDPQZ SFDPSEJOH PS BOZ PUIFS FYDFQU GPS CSJFG RVPUBUJPOT JO QSJOUFE SFWJFXT XJUIPVU UIF QSJPS QFSNJTTJPO PG UIF QVCMJTIFS
4FNBOUJD .JOJOH PG 4PDJBM /FUXPSLT +JF 5BOH BOE +VBO[J -J rrrXKQ`; M+H vTQQHX+QK
*4#/ QBQFSCBDL *4#/ FCPPL
%0* 4&%7:8#&
" 1VCMJDBUJPO JO UIF .PSHBO $MBZQPPM 1VCMJTIFST TFSJFT 4:/5)&4*4 -&$563&4 0/ 5)& 4&."/5*$ 8&# 5)&03: "/% 5&$)/0-0(:
-FDUVSF 4FSJFT &EJUPST :JOH %JOH *OEJBOB 6OJWFSTJUZ 1BVM (SPUI &MTFWJFS -BCT 'PVOEJOH &EJUPS &NFSJUVT +BNFT )FOEMFS 3FOTTFMBFS 1PMZUFDIOJD *OTUJUVUF 4FSJFT *44/ 1SJOU &MFDUSPOJD 9 4FNBOUJD .JOJOH PG 4PDJBM /FUXPSLT
+JF 5BOH BOE +VBO[J -J 5TJOHIVB 6OJWFSTJUZ
4:/5)&4*4 -&$563&4 0/ 5)& 4&."/5*$ 8&# 5)&03: "/% 5&$)/0-0(:
M &C Morgan& cLaypool publishers "#453"$5 0OMJOF TPDJBM OFUXPSLT IBWF BMSFBEZ CFDPNF B CSJEHF DPOOFDUJOH PVS QIZTJDBM EBJMZ MJGF XJUI UIF XFCCBTFE JOGPSNBUJPO TQBDF ɩJT DPOOFDUJPO QSPEVDFT B IVHF WPMVNF PG EBUB OPU POMZ BCPVU UIF JOGPSNBUJPO JUTFMG CVU BMTP BCPVU VTFS CFIBWJPS ɩF VCJRVJUZ PG UIF TPDJBM 8FC BOE UIF XFBMUI PG TPDJBM EBUB PĊFS VT VOQSFDFEFOUFE PQQPSUVOJUJFT GPS TUVEZJOH UIF JOUFSBDUJPO QBUUFSOT BNPOH VTFST TP BT UP VOEFSTUBOE UIF EZOBNJD NFDIBOJTNT VOEFSMZJOH EJĊFSFOU OFUXPSLT TPNFUIJOH UIBU XBT QSFWJPVTMZ EJċDVMU UP FYQMPSF EVF UP UIF MBDL PG BWBJMBCMF EBUB *O UIJT CPPL XF QSFTFOU UIF BSDIJUFDUVSF PG UIF SFTFBSDI GPS TPDJBM OFUXPSL NJOJOH GSPN B NJDSPTDPQJD QPJOU PG WJFX 8F GPDVT PO JOWFTUJHBUJOH TFWFSBM LFZ JTTVFT JO TPDJBM OFUXPSLT 4QFDJG JDBMMZ XF CFHJO XJUI BOBMZUJDT PG TPDJBM JOUFSBDUJPOT CFUXFFO VTFST ɩF mSTU LJOET PG RVFTUJPOT XF USZ UP BOTXFS BSF 8IBU BSF UIF GVOEBNFOUBM GBDUPST UIBU GPSN UIF EJĊFSFOU DBUFHPSJFT PG TPDJBM UJFT )PX IBWF SFDJQSPDBM SFMBUJPOTIJQT CFFO EFWFMPQFE GSPN QBSBTPDJBM SFMBUJPOTIJQT )PX EP DPOOFDUFE VTFST GVSUIFS GPSN HSPVQT "OPUIFS UIFNF BEESFTTFE JO UIJT CPPL JT UIF TUVEZ PG TPDJBM JOnVFODF 4PDJBM JOnVFODF PDDVST XIFO POFT PQJOJPOT FNPUJPOT PS CFIBWJPST BSF BĊFDUFE CZ PUIFST JOUFOUJPOBMMZ PS VOJO UFOUJPOBMMZ $POTJEFSBCMF SFTFBSDI IBT CFFO DPOEVDUFE UP WFSJGZ UIF FYJTUFODF PG TPDJBM JOnVFODF JO WBSJPVT OFUXPSLT )PXFWFS GFX MJUFSBUVSF TUVEJFT BEESFTT IPX UP RVBOUJGZ UIF TUSFOHUI PG JO nVFODF CFUXFFO VTFST GSPN EJĊFSFOU BTQFDUT *O $IBQUFS BOE JO <> XF IBWF TUVEJFE IPX UP NPEFM BOE QSFEJDU VTFS CFIBWJPST 0OF GVOEBNFOUBM QSPCMFN JT EJTUJOHVJTIJOH UIF FĊFDUT PG EJĊFSFOU TPDJBM GBDUPST TVDI BT TPDJBM JOnVFODF IPNPQIJMZ BOE JOEJWJEVBMT DIBSBDUFSJTUJDT 8F JOUSPEVDF B QSPCBCJMJTUJD NPEFM UP BEESFTT UIJT QSPCMFN 'JOBMMZ XF VTF BO BDBEFNJD TPDJBM OFUXPSL "SOFU.JOFS BT BO FYBNQMF UP EFNPOTUSBUF IPX XF BQQMZ UIF JOUSPEVDFE UFDIOPMPHJFT GPS NJOJOH SFBM TPDJBM OFUXPSLT *O UIJT TZTUFN XF USZ UP NJOF LOPXMFEHF GSPN CPUI UIF JOGPSNBUJWF QVCMJDBUJPO OFUXPSL BOE UIF TPDJBM DPMMBCPSBUJPO OFUXPSL BOE UP VOEFSTUBOE UIF JOUFSBDUJPO NFDIBOJTNT CFUXFFO UIF UXP OFUXPSLT ɩF TZTUFN IBT CFFO JO PQFSBUJPO TJODF BOE IBT BMSFBEZ BUUSBDUFE NJMMJPOT PG VTFST GSPN NPSF UIBO DPVOUSJFTSFHJPOT
,&:803%4 TPDJBM UJF TUSPOHXFBL UJFT QBSBTPDJBM JOUFSBDUJPOT SFDJQSPDJUZ TPDJBM JOnVFODF DPM MFDUJWF DMBTTJmDBUJPO HSBQIJDBM NPEFM TPDJBM OFUXPSL BOBMZTJT TPDJBM SFMBUJPOTIJQ SFMBUJPOTIJQ NJOJOH MJOL QSFEJDUJPO JOnVFODF NBYJNJ[BUJPO OFUXPSL DFOUSBMJUZ VTFS NPEFMJOH TPDJBM BDUJPO TPDJBM UIFPSJFT TPDJBM CBMBODF TPDJBM TUBUVT USJBEJD DMP TVSF GBDUPS HSBQI JOnVFODF QSPQBHBUJPO DPOTFSWBUJWF JOnVFODF QSPQBHBUJPO OPO DPOTFSWBUJWF JOnVFODF QSPQBHBUJPO VTFS CFIBWJPVS QSFEJDUJPO QSPmMF FYUSBDUJPO FY QFSU mOEJOH OBNF EJTBNCJHVBUJPO "SOFU.JOFS WJJ
$POUFOUT
"DLOPXMFEHNFOUT YJ
*OUSPEVDUJPO #BDLHSPVOE 4PDJBM ɩFPSJFT 4PDJBM 5JF "OBMZTJT 4PDJBM *OnVFODF "OBMZTJT 6TFS .PEFMJOH BOE "DUJPOT (SBQIJDBM .PEFMT #PPL 0VUMJOF 4PDJBM 5JF "OBMZTJT 0WFSWJFX 1SFEJDUJOH .JTTJOH -JOLT 4JNJMBSJUZ .FUSJDT .BUSJY 'BDUPSJ[BUJPO *OGFSSJOH 4PDJBM 5JFT 1SPCMFN 'PSNVMBUJPO 6OTVQFSWJTFE -FBSOJOH UP *OGFS 4PDJBM 5JFT 4VQFSWJTFE -FBSOJOH UP *OGFS 4PDJBM 5JFT "DUJWFMZ -FBSOJOH UP *OGFS 4PDJBM 5JFT *OGFSSJOH 4PDJBM 5JFT BDSPTT )FUFSPHFOFPVT /FUXPSLT $PODMVTJPOT 4PDJBM *OnVFODF "OBMZTJT 0WFSWJFX .JOJOH 5PQJDMFWFM 4PDJBM *OnVFODF BOBMZTJT 5PQJDBM "ċOJUZ 1SPQBHBUJPO %ZOBNJD 4PDJBM *OnVFODF "OBMZTJT .PEFM "QQMJDBUJPO &YQFSJNFOUBM 3FTVMUT 4VNNBSZ WJJJ .JOJOH 5PQJDMFWFM *OnVFODF GSPN )FUFSPHFOFPVT /FUXPSLT ɩF "QQSPBDI 'SBNFXPSL *OnVFODF 1SPQBHBUJPO BOE "HHSFHBUJPO $POTFSWBUJWF BOE /PODPOTFSWBUJWF 1SPQBHBUJPO 6TFS #FIBWJPS 1SFEJDUJPO &WBMVBUJPO 4VNNBSZ $PODMVTJPOT 6TFS #FIBWJPS .PEFMJOH BOE 1SFEJDUJPO 0WFSWJFX "QQSPBDI 'SBNFXPSL GPS 4PDJBM "DUJPO 1SFEJDUJPO .PEFM -FBSOJOH &WBMVBUJPO &WBMVBUJPO .FUSJDT 1SFEJDUJPO 1FSGPSNBODF &ċDJFODZ 1FSGPSNBODF 2VBMJUBUJWF $BTF 4UVEZ 4VNNBSZ "SOFU.JOFS %FFQ .JOJOH GPS "DBEFNJD 4PDJBM /FUXPSLT 0WFSWJFX 3FTFBSDIFS 1SPmMF &YUSBDUJPO " 6OJmFE "QQSPBDI UP 1SPmMJOH 1SPmMF &YUSBDUJPO 1FSGPSNBODF /BNF %JTBNCJHVBUJPO " 6OJmFE 1SPCBCJMJTUJD 'SBNFXPSL /BNF %JTBNCJHVBUJPO 1FSGPSNBODF 5PQJD .PEFMJOH 0VS 1SPQPTFE 5PQJD .PEFMT &YQFSUJTF 4FBSDI %BUB 4FUT BOE &WBMVBUJPO .FBTVSFT 3FTVMUT "DBEFNJD 4PDJBM /FUXPSL .JOJOH .JOJOH "EWJTPS"EWJTFF 3FMBUJPOTIJQT .FBTVSJOH "DBEFNJD *OnVFODF .PEFMJOH 3FTFBSDIFS *OUFSFTUT $PODMVTJPOT JY 3FTFBSDI 'SPOUJFST " 3FTPVSDFT " 4PGUXBSF " %BUB 4FUT
#JCMJPHSBQIZ
"VUIPST #JPHSBQIJFT
YJ
"DLOPXMFEHNFOUT
ɩJT XPSL JT TVQQPSUFE CZ UIF /BUJPOBM )JHI5FDI 3% 1SPHSBN /P "" /B UJPOBM #BTJD 3FTFBSDI 1SPHSBN PG $IJOB /P $# /P $# /BUVSBM 4DJFODF 'PVOEBUJPO PG $IJOB /P /P UIF 5TJOHIVB 6OJWFSTJUZ *OJUJB UJWF 4DJFOUJmD 3FTFBSDI 1SPHSBN B SFTFBSDI GVOE TVQQPSUFE CZ )VBXFJ *OD BOE #FJKJOH LFZ MBC PG OFUXPSLFE NVMUJNFEJB
+JF 5BOH BOE +VBO[J -J "QSJM
$ )"15&3 *OUSPEVDUJPO
" TPDJBM OFUXPSL JT B TPDJBM TUSVDUVSF NBEF VQ PG B TFU PG BDUPST TVDI BT JOEJWJEVBMT PS PSHBOJ[B UJPOT BOE B DPNQMFY TFU PG UIF EZBEJD UJFT CFUXFFO UIFTF BDUPST 4PDJBM OFUXPSL NJOJOH BJNT UP QSPWJEF B DPNQSFIFOTJWF VOEFSTUBOEJOH PG HMPCBM BOE MPDBM QBUUFSOT NFDIBOJTN PG UIF OFUXPSL GPSNBUJPO BOE EZOBNJDT PG VTFS CFIBWJPST 4PDJBM OFUXPSL BOBMZTJT BOE NJOJOH JT BO JOIFSFOUMZ JOUFSEJTDJQMJOBSZ BDBEFNJD mFME XIJDI FNFSHFE GSPN TPDJPMPHZ QTZDIPMPHZ TUBUJTUJDT BOE HSBQI UIFPSZ )PXFWFS EVF UP UIF MBDL PG FċDJFOU DPNQVUBUJPOBM NPEFMT BOE UIF OPOBWBJMBCJMJUZ PG MBSHFTDBMF TPDJBM OFUXPSLJOH EBUB USBEJUJPOBM SFTFBSDI PO TPDJBM OFUXPSLT IBT NBJOMZ GPDVTFE PO RVBMJUBUJWF TUVEZ JO TNBMMTDBMF OFUXPSLT 'PS FYBNQMF .JMHSBN TQFOU NBOZ ZFBST WBMJEBUFOH UIF FYJTUFODF PG TNBMMXPSME QIFOPNFOPO BMTP SFGFSSFE UP BT TJYEFHSFFT PG TFQBSBUJPO CZ TFOEJOH NBJM UP UIPVTBOET PG QFPQMF <> *O UIF T (FPSH 4JNNFM QSPQPTFE UIF DPODFQU PG TUSVD UVSBM UIFPSJFT JO TPDJPMPHZ XIJDI GPDVTFT PO UIF EZOBNJD GPSNBUJPO PG USJBET <> BOE JO UIF T +BDPC .PSFOP XBT UIF mSTU UP EFWFMPQ TPDJPHSBNT UP BOBMZ[F QFPQMFT JOUFSSFMBUJPOTIJQT -BUFS GPS RVBOUJUBUJWFMZ BOBMZ[JOH TPDJBM OFUXPSLT SFTFBSDIFST HBWF NBUIFNBUJDBM GPSNVMBUJPOT GPS TPDJBM OFUXPSL BOBMZTJT BOE EFWFMPQFE DPNQVUBUJPOBM NFUIPET <> )PXFWFS NPTU TPDJBM OFUXPSL SFTFBSDI XBT TUJMM DPOEVDUFE CZ JOUFSWJFXJOH UIF QBSUJDJQBOUT XJUI TNBMMTDBMF TPDJBM OFU XPSLT .PSF SFDFOUMZ XJUI UIF FNFSHFODF BOE SBQJE QSPMJGFSBUJPO PG POMJOF TPDJBM BQQMJDBUJPOT BOE NFEJBTVDI BT JOTUBOU NFTTBHJOH FH *3$ "*. .4/ +BCCFS 4LZQF TIBSJOH TJUFT FH 'MJDLS 1JDBTTB :PV5VCF 1MBYP CMPHT FH #MPHHFS 8PSE1SFTT -JWF+PVSOBM XJLJT FH 8JLJQFEJB 1#8JLJ NJDSPCMPHT FH 5XJUUFS +BJLV 8FJCP TPDJBM OFUXPSLT FH 'BDFCPPL .Z4QBDF /JOH DPMMBCPSBUJPO OFUXPSLT FH %#-1 "SOFU.JOFS UP NFOUJPO B GFXUIFTF POMJOF TFSWJDFT CSJOH NBOZ PQQPSUVOJUJFT GPS TUVEZJOH TPDJBM OFUXPSLT XIJMF BMTP QPTJOH B OVN CFS PG OFX DIBMMFOHFT 'JSTU UIF POMJOF TPDJBM OFUXPSL JT NVDI MBSHFS UIBO UIF QIZTJDBM TPDJBM OFUXPSLT JO USBEJUJPOBM SFTFBSDI 'BDFCPPL IBE NPSF UIBO CJMMJPO VTFST JO BOE 5FODFOU UIF MBSHFTU TPDJBM OFUXPSLJOH TFSWJDF JO $IJOB BUUSBDUFE NJMMJPO VTFST JO 5XJUUFS UIF MBSHFTU NJDSPCMPHHJOH TFSWJDF IBT IJU IBMG B CJMMJPO UXFFUT B EBZ "MM UIFTF CJH OVNCFST CSJOH OFX DIBMMFOHFT BOE BMTP UIF SFRVJSFNFOUT GPS EFWFMPQJOH OFX NFUIPET UP TUPSF TFBSDI BOBMZ[F BOE NJOF UIF iCJH TPDJBM EBUBw 4FDPOE GSPN B NJDSPTDPQJD WJFXQPJOU XIBU BSF UIF TVCUMF DIBOHFT PG CFIBWJPST XIFO VTFST HP POMJOF GSPN UIF PČJOF QIZTJDBM OFUXPSLT "SF UIF USBEJUJPOBM TPDJBM UIFPSJFT TUJMM BQQMJDBCMF &YJTUJOH SFTFBSDI SFMBUFE UP TPDJBM OFUXPSL NJOJOH DBO CF DBUFHPSJ[FE JOUP NJDSPMFWFM NFTPMFWFM BOE NBDSPMFWFM BMUIPVHI UIF MFWFMT PG NJOJOH BSF OPU OFDFTTBSJMZ NVUVBMMZ FYDMV */530%6$5*0/
Application Information Prediction Search Diffusion Advertise
Macro Meso Micro
Social Small-worldS Community Erd Power-law Structural modeling Influence Social tie behavior Action Network Group Triad User User ő hole Analysis s-Rényi
Theory Algorithmic Social Theories Foundations
BIG Social Data
'JHVSF 3FTFBSDI SPBENBQ GPS TPDJBM OFUXPSL NJOJOH
TJWF "U UIF NJDSPMFWFM TPDJBM OFUXPSL NJOJOH JT NBJOMZ DPODFSOFE XJUI NPEFMJOH JOEJWJEVBMT CFIBWJPST BOE JOUFSBDUJPOT CFUXFFO VTFST BU UIF NBDSPMFWFM JU GPDVTFT PO TUVEZJOH UIF HMPCBM QBUUFSOT PG UIF TPDJBM OFUXPSLT GPS FYBNQMF OFUXPSL UPQPMPHZ <> BOE OFUXPSL HFOFSBUJWF NPE FMT < > BOE BU UIF NJDSPMFWFM TPDJBM OFUXPSL NJOJOH JT NBJOMZ DPODFSOFE XJUI NPEFMJOH JOEJWJEVBMT CFIBWJPST BOE JOUFSBDUJPOT CFUXFFO VTFST GPS FYBNQMF TPDJBM BDUJPO UIFPSZ <> TP DJBM UJFT <> TPDJBM JOnVFODF < > BOE VTFS NPEFMJOH <> ɩF NFTPMFWFM SFTFBSDI GBMMT CFUXFFO UIF NJDSP BOE NBDSPMFWFMT GPS FYBNQMF DPNNVOJUZ EFUFDUJPO < > TUSVD UVSBM IPMF < > BOE HSPVQ CFIBWJPS BOBMZTJT < > 'JHVSF HJWFT UIF SFTFBSDI SPBENBQ GPS TPDJBM OFUXPSL NJOJOH 0O UPQ PG TPDJBM OFUXPSL NJOJOH XF DBO DPOTJEFS NBOZ BQQMJDBUJPOT TVDI BT TPDJBM QSFEJDUJPO <> TPDJBM TFBSDI < > JOGPSNBUJPO EJĊVTJPO <> BOE TPDJBM BE WFSUJTFNFOU <> ɩF VOEFSMZJOH UIFPSJFT GPS TPDJBM OFUXPSL NJOJOH JODMVEF UIFPSJFT GSPN TPDJBM TDJFODF BOE BMHPSJUINJD GPVOEBUJPOT GSPN DPNQVUFS TDJFODF *O UIJT CPPL XF TUVEZ TPDJBM OFUXPSL NJOJOH GSPN B NJDSPTDPQJD WJFXQPJOU 8F GPDVT PO NPEFMJOH VTFST CFIBWJPST BOE UIFJS JOUFSBDUJPOT CFUXFFO FBDI PUIFS *O QBSUJDVMBS XF QSFTFOU LFZ UFDIOPMPHJFT GPS TPDJBM UJF BOBMZTJT TPDJBM JOnVFODF BOBMZTJT BOE VTFS CFIBWJPS NPEFMJOH
#"$,(306/% 8F JOUSPEVDF TFWFSBM SFMBUFE TPDJBM UIFPSJFT BOE UIFO CSJFnZ SFWJFX FYJTUJOH MJUFSBUVSFT PO TPDJBM UJF BOBMZTJT TPDJBM JOnVFODF BOBMZTJT BOE VTFS CFIBWJPS NPEFMJOH #"$,(306/%
'JHVSF *MMVTUSBUJPO PG TUSVDUVSBM CBMBODF UIFPSZ " BOE # BSF CBMBODFE XIJMF $ BOE % BSF OPU CBMBODFE
'JHVSF *MMVTUSBUJPO PG TUBUVT UIFPSZ " BOE # TBUJTGZ UIF TUBUVT UIFPSZ XIJMF $ BOE % EP OPU TBUJTGZ UIF TUBUVT UIFPSZ )FSF QPTJUJWF i w EFOPUFT UIF UBSHFU OPEF IBT B IJHIFS TUBUVT UIBO UIF TPVSDF OPEF BOE OFHBUJWF iw EFOPUFT UIF UBSHFU OPEF IBT B MPXFS TUBUVT UIBO UIF TPVSDF OPEF *O UPUBM UIFSF BSF EJĊFSFOU DBTFT
40$*"- 5)&03*&4 " CBTJD QSJODJQMF GPS NJOJOH TPDJBM OFUXPSLT JO UIJT CPPL JT UP JODPSQPSBUF TPDJBM UIFPSJFT JOUP EBUB NJOJOH PS NBDIJOF MFBSOJOH NPEFM 'PS TPDJBM UIFPSJFT XF NBJOMZ DPOTJEFS TPDJBM CBMBODF <> TPDJBM TUBUVT <> TUSVDUVSBM IPMF <> UXPTUFQ JOGPSNBUJPOnPX <> BOE TUSPOHXFBL UJF IZ QPUIFTJT < > 4PDJBM CBMBODF UIFPSZ TVHHFTUT UIBU QFPQMF JO B TPDJBM OFUXPSL UFOE UP GPSN JOUP B CBMBODFE OFUXPSL TUSVDUVSF 'JHVSF TIPXT TVDI BO FYBNQMF UP JMMVTUSBUF UIF TUSVDUVSBM CBMBODF UIFPSZ PWFS USJBET XIJDI JT UIF TJNQMFTU HSPVQ TUSVDUVSF UP XIJDI CBMBODF UIFPSZ BQQMJFT 'PS B USJBE UIF CBMBODF UIFPSZ JNQMJFT UIBU FJUIFS BMM UISFF PG UIFTF VTFST BSF GSJFOETiUIF GSJFOE PG NZ GSJFOE JT NZ GSJFOEw PS POMZ POF QBJS PG UIFN BSF GSJFOETiUIF FOFNZ PG NZ FOFNZ JT NZ GSJFOEw "OPUIFS TPDJBM QTZDIPMPHJDBM UIFPSZ JT UIF UIFPSZ PG TUBUVT < > ɩJT UIFPSZ JT CBTFE PO UIF EJSFDUFE SFMBUJPOTIJQ OFUXPSL 4VQQPTF FBDI EJSFDUFE SFMBUJPOTIJQ JT MBCFMFE CZ B QPTJUJWF TJHO i w PS B OFHBUJWF TJHO iw XIFSF TJHO i wiw EFOPUFT UIF UBSHFU OPEF IBT B IJHIFSMPXFS TUBUVT UIBO UIF TPVSDF OPEF ɩFO TUBUVT UIFPSZ QPTJUT UIBU JG JO B USJBOHMF PO UISFF OPEFT BMTP DBMMFE USJBE XF UBLF FBDI OFHBUJWF FEHF SFWFSTF JUT EJSFDUJPO BOE nJQ JUT TJHO UP QPTJUJWF UIFO UIF SFTVMUJOH USJBOHMF XJUI BMM QPTJUJWF FEHF TJHOT TIPVME CF BDZDMJD 'JHVSF JMMVTUSBUFT GPVS FYBNQMFT ɩF mSTU UXP USJBOHMFT TBUJTGZ UIF TUBUVT PSEFSJOH BOE UIF MBUUFS UXP EP OPU TBUJTGZ JU 3PVHIMZ TQFBLJOH B VTFS JT TBJE UP TQBO B TUSVDUVSBM IPMF JO B TPDJBM OFUXPSL JG TIF JT MJOLFE UP QFPQMF JO QBSUT PG UIF OFUXPSL UIBU BSF PUIFSXJTF OPU XFMM DPOOFDUFE UP POF BOPUIFS <> 4VDI B VTFS JT BMTP SFGFSSFE UP BT TUSVDUVSBM IPMF TQBOOFS <> "SHVNFOUT CBTFE PO TUSVDUVSBM IPMFT TVHHFTU UIBU UIFSF JT BO JOGPSNBUJPOBM BEWBOUBHF UP IBWF GSJFOET JO B OFUXPSL XIP EP OPU LOPX */530%6$5*0/
'JHVSF "O FYBNQMF PG JOGFSSJOH TPDJBM UJFT JO B NPCJMF DPNNVOJDBUJPO OFUXPSL ɩF MFGU mHVSF JT UIF JOQVU PG UIF UBTL BOE UIF SJHIU mHVSF JT UIF PVUQVU PG UIF UBTL PG JOGFSSJOH TPDJBM UJFT
FBDI PUIFS " TBMFT NBOBHFS XJUI B EJWFSTF SBOHF PG DPOOFDUJPOT DBO CF DPOTJEFSFE BT B TUSVDUVSBM IPMF TQBOOFS XJUI B OVNCFS PG QPUFOUJBMMZ XFBL UJFT <> UP JOEJWJEVBMT JO EJĊFSFOU DPNNVOJUJFT .PSF HFOFSBMMZ XF DBO UIJOL BCPVU XFCTJUFT TVDI BT F#BZ BT TQBOOJOH TUSVDUVSBM IPMFT JO UIBU UIFZ GBDJMJUBUF FDPOPNJD JOUFSBDUJPOT CFUXFFO QFPQMF XIP XPVME PUIFSXJTF OPU CF BCMF UP mOE FBDI PUIFS ɩF UXPTUFQ JOGPSNBUJPOnPX UIFPSZ JT mSTU JOUSPEVDFE JO <> BOE GVSUIFS FMBCPSBUFE JO MJUFSBUVSF < > ɩF UIFPSZ TVHHFTUT UIBU JEFBT JOOPWBUJPOT VTVBMMZ nPX mSTU UP PQJOJPO MFBEFST BOE UIFO GSPN UIFN UP B XJEFS QPQVMBUJPO *O UIF FOUFSQSJTF FNBJM OFUXPSL GPS FYBNQMF NBOBHFST NBZ BDU BT PQJOJPO MFBEFST UP IFMQ TQSFBE JOGPSNBUJPO UP TVCPSEJOBUFT *OUFSQFSTPOBM UJFT HFOFSBMMZ DPNF JO UISFF WBSJFUJFT TUSPOH XFBL PS BCTFOU 4USPOH UJF IZ QPUIFTJT JNQMJFT UIBU POFT DMPTF GSJFOET UFOE UP NPWF JO UIF TBNF DJSDMFT UIBU TIFIF EPFT XIJMF XFBL UJF IZQPUIFTJT BSHVFT UIBU XFBL UJFT BSF SFTQPOTJCMF GPS UIF NBKPSJUZ PG UIF FNCFEEFEOFTT BOE TUSVDUVSF PG TPDJBM OFUXPSLT JO TPDJFUZ BT XFMM BT UIF USBOTNJTTJPO PG JOGPSNBUJPO UISPVHI UIFTF OFUXPSLT <>
40$*"- 5*& "/"-:4*4 .JOJOH TPDJBM UJFT JT BO JNQPSUBOU QSPCMFN JO TPDJBM OFUXPSL BOBMZTJT #BTFE PO UIF TUSPOHXFBL UJF IZQPUIFTJT UIFSF JT B CVODI PG SFTFBSDI DPOEVDUFE JO SFDFOU ZFBST ɩF HPBM PG TPDJBM UJF BOBMZTJT JT UP BVUPNBUJDBMMZ SFDPHOJ[F UIF TFNBOUJDT BTTPDJBUFE XJUI FBDI TPDJBM SFMBUJPOTIJQ "XBSFOFTT PG UIF TFNBOUJDT PG TPDJBM SFMBUJPOTIJQT DBO CFOFmU NBOZ BQQMJDBUJPOT 'PS FYBNQMF JG XF DPVME IBWF FYUSBDUFE GSJFOETIJQT CFUXFFO VTFST GSPN UIF NPCJMF DPNNVOJDBUJPO OFUXPSL UIFO XF DBO MFWFSBHF UIF GSJFOETIJQT GPS B iXPSEPGNPVUIw QSPNPUJPO PG B OFX QSPEVDU 'JHVSF HJWFT BO FYBNQMF PG SFMBUJPOTIJQ NJOJOH JO B NPCJMF DBMMJOH OFUXPSL ɩF MFGU mHVSF JT UIF JOQVU PG UIF QSPCMFN JO B NPCJMF DBMMJOH OFUXPSL DPOTJTUJOH PG VTFST DBMMT BOE NFTTBHFT CFUXFFO VTFST BOE VTFST MPDBUJPO MPHT FUD ɩF PCKFDUJWF JT UP JOGFS UIF UZQF PG UIF SFMBUJPOTIJQT JO UIF OFUXPSL *O UIF SJHIU mHVSF UIF VTFST XIP BSF GBNJMZ NFNCFST BSF DPOOFDUFE XJUI SFEDPMPSFE MJOFT GSJFOET BSF #"$,(306/% DPOOFDUFE XJUI CMVFDPMPSFE EBTI MJOFT BOE DPMMFBHVFT BSF DPOOFDUFE XJUI HSFFODPMPSFE EPUUFE MJOFT ɩF QSPCBCJMJUZ BTTPDJBUFE XJUI FBDI SFMBUJPOTIJQ SFQSFTFOUT PVS DPOmEFODF PO UIF EFUFDUFE SFMBUJPOTIJQ UZQFT ɩFSF BSF TFWFSBM XPSLT PO NJOJOH UIF SFMBUJPOTIJQ TFNBOUJDT %JFIM FU BM <> USJFE UP JEFOUJGZ UIF NBOBHFSTVCPSEJOBUF SFMBUJPOTIJQT CZ MFBSOJOH B SBOLJOH GVODUJPO ɩFZ EFmOFE B SBOLJOH PCKFDUJWF GVODUJPO BOE DBTU UIF SFMBUJPOTIJQ JEFOUJmDBUJPO BT B SFMBUJPOTIJQ SBOLJOH QSPC MFN .FOPO FU BM <> QSPQPTFE B MPHMJOFBS NBUSJY NPEFM GPS EZBEJD QSFEJDUJPO ɩFZ VTFE NBUSJY GBDUPSJ[BUJPO UP EFSJWF MBUFOU GFBUVSFT BOE JODPSQPSBUF UIF MBUFOU GFBUVSFT GPS QSFEJDUJOH UIF MBCFM PG VTFS SFMBUJPOTIJQT 8BOH FU BM <> QSPQPTFE B QSPCBCJMJTUJD NPEFM GPS NJOJOH UIF BEWJTPSBEWJTFF SFMBUJPOTIJQT GSPN UIF QVCMJDBUJPO OFUXPSL ɩF QSPQPTFE NPEFM JT SFGFSSFE UP BT UJNFDPOTUSBJOFE QSPCBCJMJTUJD GBDUPS HSBQI NPEFM 5'(. XIJDI TVQQPSUT CPUI TVQFSWJTFE BOE VOTVQFSWJTFE MFBSOJOH &BHMF FU BM <> QSFTFOUFE TFWFSBM QBUUFSOT EJTDPWFSFE JO NPCJMF QIPOF EBUB BOE USZ UP VTF UIFTF QBUUFSO UP JOGFS UIF GSJFOETIJQ OFUXPSL 5BOH FU BM <> EFWFMPQFE B DMBTTJmDBUJPO GSBNFXPSL PG TPDJBM NFEJB CBTFE PO EJĊFSFOUJBUJOH EJĊFSFOU UZQFT PG TPDJBM DPOOFD UJPOT )PXFWFS UIFTF BMHPSJUINT NBJOMZ GPDVT PO B TQFDJmD EPNBJO XIJMF PVS NPEFM JT HFOFSBM BOE DBO CF BQQMJFE UP EJĊFSFOU EPNBJOT .PSFPWFS UIFTF NFUIPET BMTP EP OPU FYQMJDJUMZ DPOTJEFS UIF DPSSFMBUJPO JOGPSNBUJPO CFUXFFO EJĊFSFOU SFMBUJPOTIJQT "OPUIFS SFTFBSDI CSBODI JT UP QSFEJDU BOE SFDPNNFOE VOLOPXO MJOLT JO TPDJBM OFUXPSLT -JCFO/PXFMM FU BM <> TUVEJFE UIF QSPCMFN PG JOGFSSJOH OFX JOUFSBDUJPOT BNPOH VTFST HJWFO B TOBQTIPU PG B TPDJBM OFUXPSL ɩFZ EFWFMPQFE TFWFSBM VOTVQFSWJTFE BQQSPBDIFT UP EFBM XJUI UIJT QSPCMFN CBTFE PO NFBTVSFT GPS BOBMZ[JOH UIF iQSPYJNJUZw PG OPEFT JO B OFUXPSL ɩF QSJODJQMF JT NBJOMZ CBTFE PO TJNJMBSJUZ PG FJUIFS DPOUFOU PS TUSVDUVSF CFUXFFO VTFST #BDLTUSPN FU BM <> QSPQPTFE B TVQFSWJTFE SBOEPN XBML BMHPSJUIN UP FTUJNBUF UIF TUSFOHUI PG TPDJBM MJOLT -FTLPWFD FU BM <> FNQMPZFE B MPHJTUJD SFHSFTTJPO NPEFM UP QSFEJDU QPTJUJWF BOE OFHBUJWF MJOLT JO POMJOF TPDJBM OFUXPSLT XIFSF UIF QPTJUJWF MJOLT JOEJDBUF UIF SFMBUJPOTIJQT TVDI BT GSJFOETIJQ XIJMF OFHBUJWF JOEJDBUFT PQQPTJUJPO )PXFWFS UIFTF XPSLT DPOTJEFS POMZ UIF CMBDLXIJUF TPDJBM OFUXPSLT BOE EP OPU DPOTJEFS UIF UZQFT PG UIF SFMBUJPOTIJQT 3FDFOUMZ )PQDSPGU FU BM <> FYQMPSFE UIF QSPCMFN PG SFDJQSPDBM SFMBUJPOTIJQ QSFEJDUJPO BOE -PV FU BM <> FYUFOEFE UP TUVEZ IPX TPDJBM SFMBUJPOTIJQT EFWFMPQ JOUP USJBEJD DMPTVSF ɩFZ QSPQPTFE B MFBSOJOH GSBNFXPSL UP GPSNVMBUF UIF QSPCMFN PG SFDJQSPDBM SFMBUJPOTIJQ QSFEJDUJPO JOUP B HSBQIJDBM NPEFM BOE FWBMVBUF UIF QSPQPTFE NFUIPE PO B 5XJUUFS EBUB TFU ɩF GSBNFXPSL JT EFNPOTUSBUFE UP CF WFSZ FĊFDUJWF JF JU JT QPTTJCMF UP BDDVSBUFMZ JOGFS PG SFDJQSPDBM SF MBUJPOTIJQT JO B EZOBNJD OFUXPSL 5BOH FU BM <> GVSUIFS QSPQPTFE B HFOFSBM GSBNFXPSL GPS DMBTTJGZJOH UIF UZQF PG TPDJBM SFMBUJPOTIJQT CZ MFBSOJOH BDSPTT IFUFSPHFOFPVT OFUXPSLT ɩF JEFB JT UP VTF TPDJBM UIFPSJFT FH TPDJBM CBMBODF UIFPSZ TPDJBM TUBUVT UIFPSZ TUSVDUVSBM IPMF UIFPSZ UXPTUFQ nPX UIFPSZ BOE TUSPOHXFBL UJF BT CSJEHF UP DPOOFDU EJĊFSFOU TPDJBM OFUXPSLT 4PDJBM UIFPSZCBTFE GFBUVSFT BSF EFmOFE BOE JODPSQPSBUFE JOUP B USJBECBTFE GBDUPS HSBQI NPEFM UP JOGFS UIF UZQF PG TPDJBM SFMBUJPOTIJQT JO EJĊFSFOU OFUXPSLT */530%6$5*0/ “Love Obama”
I hate Obama, the worst I love Obama president ever B Obama is 1st try, 0.7>0.5 fantastic θ = 0.2 θ = 0.5 0.3 0.7 A C 0.74 st 0.2 1 try Obama is great! 0.40 0.10.1 0.74<0.8 No Obama in 0.05 2012! 0.50 2nd try, 0.1 0.74+0.1>0.80
He cannot be the θ = 0.5 θ = 0.8 next president! θ = 0.4 Positive Negative
'JHVSF "O FYBNQMF PG TPDJBM JOnVFODF GPS QPMJUJDBM NPCJMJ[BUJPO ɩF MFGU mHVSF JT UIF JOQVU PG UIF UBTL BOE UIF SJHIU mHVSF JT UIF PVUQVU JOnVFODF QSPCBCJMJUZ CFUXFFO VTFST JOEJWJEVBM DPOGPSNJUZ PG FBDI VTFS BOE LFZ JOnVFODFST " # $
"OPUIFS SFMBUFE SFTFBSDI UPQJD JT SFMBUJPOBM MFBSOJOH < > )PXFWFS UIF QSPCMFN QSF TFOUFE JO UIJT CPPL JT WFSZ EJĊFSFOU 3FMBUJPOBM MFBSOJOH GPDVTFT PO UIF DMBTTJmDBUJPO QSPCMFNT XIFO PCKFDUT PS FOUJUJFT BSF QSFTFOUFE JO SFMBUJPOT XIJMF TPDJBM UJF BOBMZTJT GPDVTFT PO FYQMPSJOH UIF SFMBUJPOTIJQ UZQFT JO TPDJBM OFUXPSL " OVNCFS PG TVQFSWJTFE NFUIPET GPS MJOL QSFEJDUJPO JO SFMBUJPOBM EBUB IBWF CFFO EFWFMPQFE < >
40$*"- */'-6&/$& "/"-:4*4 4PDJBM JOnVFODF PDDVST XIFO POFT PQJOJPOT FNPUJPOT PS CFIBWJPST BSF BĊFDUFE CZ PUIFST JOUFO UJPOBMMZ PS VOJOUFOUJPOBMMZ <> 3FDFOUMZ TPDJBM JOnVFODF BOBMZTJT IBT BUUSBDUFE B MPU PG JOUFSFTU GSPN CPUI SFTFBSDI BOE JOEVTUSZ DPNNVOJUJFT *O HFOFSBM FYJTUJOH SFTFBSDI PO TPDJBM JOnVFODF BOBMZTJT DBO CF DMBTTJmFE JOUP UISFF DBUFHPSJFT JOnVFODF UFTU JOnVFODF NFBTVSF BOE JOnVFODF EJĊVTJPO NPEFMT 'JHVSF TIPXT BO FYBNQMF PG TPDJBM JOnVFODF GPS QPMJUJDBM NPCJMJ[BUJPO ɩF MFGU mHVSF JT UIF JOQVU PG UIF UBTL PQJOJPO PG FBDI VTFS GPS i0CBNBw JO UIF TPDJBM OFUXPSL BOE UIF SJHIU mHVSF JT UIF PVUQVU JOnVFODF QSPCBCJMJUZ CFUXFFO VTFST PO UIJT UPQJD i0CBNB w JOEJWJEVBM DPOGPSNJUZ PG FBDI VTFS BOE LFZ JOnVFODFST " # $ *OnVFODF 5FTU 4FWFSBM FĊPSUT IBWF CFFO NBEF GPS JEFOUJGZJOH UIF FYJTUFODF PG UIF TPDJBM JOnV FODF JO UIF POMJOF TPDJBM OFUXPSLT 'PS FYBNQMF "OBHOPTUPQPVMPT FU BM <> HBWF B UIFPSFUJDBM KVTUJmDBUJPO UP JEFOUJGZ JOnVFODF BT B TPVSDF PG TPDJBM DPSSFMBUJPO XIFO UIF UJNF TFSJFT PG VTFS BD UJPOT JT BWBJMBCMF ɩFZ QSPQPTF B TIVČF UFTU UP QSPWF UIF FYJTUFODF PG UIF TPDJBM JOnVFODF 4JOHMB BOE 3JDIBSETPO <> TUVEJFE UIF DPSSFMBUJPO CFUXFFO QFSTPOBM CFIBWJPST BOE UIFJS JOUFSFTUT ɩFZ GPVOE UIBU JO UIF POMJOF TZTUFN QFPQMF XIP DIBU XJUI FBDI PUIFS VTJOH JOTUBOU NFTTBHJOH BSF NPSF MJLFMZ UP TIBSF JOUFSFTUT UIFJS 8FC TFBSDIFT BSF UIF TBNF PS UPQJDBMMZ TJNJMBS BOE UIF NPSF UJNF UIFZ TQFOE UBMLJOH UIF TUSPOHFS UIJT SFMBUJPOTIJQ JT #POE FU BM <> SFQPSUFE SFTVMUT GSPN B SBOEPNJ[FE DPOUSPMMFE USJBM PG QPMJUJDBM NPCJMJ[BUJPO NFTTBHFT EFMJWFSFE UP NJMMJPO 'BDFCPPL VTFST ɩFZ GPVOE UIBU XIFO POF JT BXBSF UIBU UIFJS GSJFOET IBWF NBEF UIF QPMJUJDBM WPUFT UIFJS #"$,(306/% MJLFMJIPPE UP WPUF XJMM TJHOJmDBOUMZ JODSFBTF $SBOEBMM FU BM <> GVSUIFS JOWFTUJHBUFE UIF DPSSF MBUJPO CFUXFFO TPDJBM TJNJMBSJUZ BOE JOnVFODF .PSF SFDFOUMZ TPNF FĊPSUT IBWF CFFO NBEF GPS BOBMZ[JOH UIF EZOBNJDT JO UIF TPDJBM OFUXPSL 'PS FYBNQMF 4DSJQQT FU BM <> JOWFTUJHBUFE IPX EJĊFSFOU QSFQSPDFTTJOH EFDJTJPOT BOE EJĊFSFOU OFUXPSL GPSDFT TVDI BT TFMFDUJPO BOE JOnVFODF BĊFDU UIF NPEFMJOH PG EZOBNJD OFUXPSLT 0UIFS TJNJMBS XPSL DBO CF SFGFSSFE UP %PVSJTCPVSF FU BM <> *OnVFODF .FBTVSF ɩF HPBM PG JOnVFODF NFBTVSF JT UP RVBOUJGZ UIF TUSFOHUI PG JOnVFODF CFUXFFO VTFST 5BOH FU BM <> JOUSPEVDFE UIF QSPCMFN PG UPQJDCBTFE TPDJBM JOnVFODF BOBMZTJT ɩFZ QSPQPTFE B 5PQJDBM "ċOJUZ 1SPQBHBUJPO 5"1 BQQSPBDI UP EFTDSJCF UIF QSPCMFN WJB VTJOH B HSBQIJDBM QSPCBCJMJTUJD NPEFM )PXFWFS UIFTF XPSLT OFJUIFS DPOTJEFS IFUFSPHFOFPVT JOGPSNBUJPO OPS MFBSO UPQJDT BOE JOnVFODF TUSFOHUI KPJOUMZ (PZBM FU BM <> BOE 4BJUP FU BM <> NFBTVSFE UIF QBJSXJTF JOnVFODF CFUXFFO UXP JOEJWJEVBMT CBTFE PO UIF JEFB PG JOEFQFOEFOU DBTDBEF NPEFM <> -JV FU BM <> BMTP TUVEJFE UIF QSPCMFN PG NFBTVSJOH UIF JOnVFODF PO EJĊFSFOU UPQJDT ɩFZ QSPQPTFE B HFOFSBUJWF HSBQIJDBM NPEFM XIJDI MFWFSBHFT CPUI IFUFSPHFOFPVT MJOL JOGPSNBUJPO BOE UFYUVBM DPOUFOU BTTPDJBUFE XJUI FBDI VTFS JO UIF OFUXPSL UP NJOF UPQJDMFWFM JOnVFODF TUSFOHUI #BTFE PO UIF MFBSOFE EJSFDU JOnVFODF XF GVSUIFS TUVEZ UIF JOnVFODF QSPQBHBUJPO BOE BHHSFHBUJPO NFDIBOJTNT DPOTFSWBUJWF BOE OPODPOTFSWBUJWF QSPQBHBUJPOT UP EFSJWF UIF JOEJSFDU JOnVFODF 9JO FU BM <> TUVEJFE UIF JOEJSFDU JOnVFODF VTJOH UIF UIFPSZ PG RVBOUVN DPHOJUJPO .ZFST FU BM <> QSPQPTFE B QSPCBCJMJTUJD NPEFM UP RVBOUJGZ UIF FYUFSOBM JOnVFODF PVUPGOFUXPSL TPVSDFT #FMBL FU BM <> JOWFTUJHBUFE BOE NFBTVSFE UIF JOnVFODF PO UIF DSPTTDPNNVOJUZ MFWFM TP BT UP QSPWJEF B DPBSTFHSBJOFE QJDUVSF PG B QPUFOUJBMMZ WFSZ MBSHF OFUXPSL ɩFZ QSFTFOUFE B GSBNFXPSL GPS DSPTTDPNNVOJUZ JOnVFODF BOBMZTJT BOE FWBMVBUFE UIF QSPQPTFE NFUIPE PO B UFOZFBS EBUB TFU GSPN UIF MBSHFTU *SJTI POMJOF EJTDVTTJPO TZTUFN #PBSETJF #PBSETJF JT UIF OBNF PG UIF TZTUFN ;IBOH FU BM <> QSPQPTFE UIF OPUJPO PG TPDJBM JOnVFODF MPDBMJUZ BOE BQQMJFE JU GPS NPEFMJOH VTFST SFUXFFUJOH CFIBWJPST JO UIF TPDJBM OFUXPSLT ɩFZ EFWFMPQFE UXP JOTUBOUJBUJPO GVODUJPOT CBTFE PO QBJSXJTF JOnVFODF BOE TUSVDUVSBM EJWFSTJUZ *OnVFODF %JąVTJPO .PEFMT 4PDJBM JOnVFODF IBT CFFO BQQMJFE JO UIF BQQMJDBUJPO PG JOnVFODF NBYJNJ[BUJPO JO WJSBM NBSLFUJOH %PNJOHPT BOE 3JDIBSETPO < > XFSF UIF mSTU UP TUVEZ JOnVFODF NBYJNJ[BUJPO BT BO BMHPSJUINJD QSPCMFN ,FNQF FU BM <> UPPL UIF mSTU TUFQ UP GPS NVMBUJOH JOnVFODF NBYJNJ[BUJPO BT B EJTDSFUF PQUJNJ[BUJPO QSPCMFN -FTLPWFD FU BM <> BOE $IFO FU BM < > NBEF FĊPSUT UP JNQSPWF UIF FċDJFODZ PG JOnVFODF NBYJNJ[BUJPO (SVIM FU BM <> QSPQPTFE B UJNFEFDBZFE EJĊVTJPO NPEFM GPS CMPHHJOH XSJUJOH BOE VTF BO &.MJLF BM HPSJUIN UP FTUJNBUF UIF JOnVFODF QSPCBCJMJUJFT :BOH FU BM <> TUVEJFE UIF JOUFSQMBZ CFUXFFO VTFST TPDJBM SPMFT BOE UIFJS JOnVFODF PO JOGPSNBUJPO EJĊVTJPO ɩFZ QSPQPTFE B 3PMF"XBSF */ GPSNBUJPO EJĊVTJPO NPEFM 3"*/ UIBU JOUFHSBUFT TPDJBM SPMF SFDPHOJUJPO BOE EJĊVTJPO NPEFMJOH JOUP B VOJmFE GSBNFXPSL */530%6$5*0/ 64&3 .0%&-*/( "/% "$5*0/4 6TFS NPEFMJOH EFTDSJCFT UIF QSPDFTT PG CVJMEJOH VQ B VTFS NPEFM UP DIBSBDUFSJ[F VTFST TLJMMT EFDMBSBUJWF LOPXMFEHF BOE TQFDJmD OFFET UP B TZTUFN <> " OVNCFS PG NPEFMT IBWF CFFO QSPQPTFE UP NPEFM VTFST CFIBWJPST JO EZOBNJD TPDJBM OFU XPSLT 4BSLBS FU BM <> EFWFMPQFE B HFOFSBMJ[FE NPEFM BTTPDJBUJOH FBDI FOUJUZ JO &VDMJEFBO MBUFOU TQBDF BOE VTFE LFSOFM GVODUJPOT GPS TJNJMBSJUZ JO MBUFOU TQBDF UP NPEFM GSJFOETIJQ ESJGUJOH PWFS UJNF 5BO FU BM <> TUVEJFE IPX VTFST CFIBWJPST BDUJPOT JO B TPDJBM OFUXPSL BSF JOnVFODFE CZ WBSJPVT GBDUPST TVDI BT QFSTPOBM JOUFSFTUT TPDJBM JOnVFODF BOE HMPCBM USFOET ɩFZ QSPQPTFE B /PJTF 5PMFSBOU 5JNFWBSZJOH 'BDUPS (SBQI .PEFM /55'(. GPS NPEFMJOH BOE QSFEJDUJOH TPDJBM BDUJPOT XIJDI TJNVMUBOFPVTMZ NPEFMT TPDJBM OFUXPSL TUSVDUVSF VTFS BUUSJCVUFT BOE VTFS BDUJPO IJTUPSZ GPS CFUUFS QSFEJDUJPO PG UIF VTFST GVUVSF BDUJPOT 5BO FU BM <> JOWFTUJHBUFE IPX VTFST TFOUJNFOU DBO CF JOGFSSFE JO UIF TPDJBM OFUXPSL CZ JODPSQPSBUJOH UIF TPDJBM OFUXPSL JOGPSNB UJPO 4DSJQQT FU BM <> QSFTFOUFE B NPEFM UP JOWFTUJHBUF IPX EJĊFSFOU QSFQSPDFTTJOH EFDJTJPOT BOE EJĊFSFOU OFUXPSL GPSDFT TVDI BT TFMFDUJPO BOE JOnVFODF BĊFDU UIF NPEFMJOH PG EZOBNJD OFU XPSLT ɩFZ BMTP EFNPOTUSBUFE UIF FĊFDUT PG BUUSJCVUF ESJGUJOH BOE UIF JNQPSUBODF PG JOEJWJEVBM BUUSJCVUFT JO GPSNJOH MJOLT PWFS UJNF (SPVQ BOBMZTJT JT CBTFE PO UIF WJFX UIBU EFFQ MBTUJOH DIBOHF DBO PDDVS XJUIJO B DBSFGVMMZ GPSNFE HSPVQ XIPTF DPNCJOFE NFNCFSTIJQ SFnFDUT UIF XJEFS OPSNT PG TPDJFUZ ɩFSF JT BO JO UFSFTU JO HSPVQ BOBMZTJT PO UIF SFMBUJPOTIJQ CFUXFFO UIF JOEJWJEVBM HSPVQ NFNCFS BOE UIF SFTU PG UIF HSPVQ SFTVMUJOH JO B TUSFOHUIFOJOH PG CPUI BOE B CFUUFS JOUFHSBUJPO PG UIF JOEJWJEVBM XJUI IJT PS IFS DPNNVOJUZ GBNJMZ BOE TPDJBM OFUXPSL 4IJ FU BM <> TUVEJFE UIF QBUUFSO PG VTFS QBS UJDJQBUJPO CFIBWJPS BOE UIF GFBUVSF GBDUPST UIBU JOnVFODF TVDI CFIBWJPS PO EJĊFSFOU GPSVN EBUB TFUT #BDLTUSPN FU BM <> QSPQPTFE B QBSUJUJPOJOH PO UIF EBUB UIBU TFMFDUT GPS BDUJWF DPNNVOJUJFT PG FOHBHFE JOEJWJEVBMT
(3"1)*$"- .0%&-4 'SPN UIF QFSTQFDUJWF PG NBDIJOF MFBSOJOH BOE EBUB NJOJOH GPS BOBMZ[JOH OFUXPSLJOH EBUB HSBQI JDBM QSPCBCJMJTUJD NPEFMT BSF PGUFO FNQMPZFE UP EFTDSJCF UIF EFQFOEFODJFT CFUXFFO PCTFSWBUJPO EBUB #BZFTJBO OFUXPSLT <> .BSLPW SBOEPN mFME <> GBDUPS HSBQI < > 3FTUSJDUFE #PMU[ NBOO .BDIJOF 3#. <> EFFQ OFVSBM OFUXPSLT <> BOE NBOZ PUIFST BSF XJEFMZ VTFE HSBQI JDBM NPEFMT
#00, 065-*/& %FTQJUF NVDI XPSL IBWJOH CFFO DPOEVDUFE GPS NJOJOH TPDJBM OFUXPSLT XF BSF TUJMM GBDJOH B OVN CFS PG DIBMMFOHFT *O UIJT CPPL GSPN UIF NJDSPTDPQJD WJFXQPJOU XF JOUSPEVDF LFZ UFDIOPMPHJFT GPS TPDJBM UJF BOBMZTJT TPDJBM JOnVFODF BOBMZTJT BOE VTFS CFIBWJPS NPEFMJOH 'JHVSF HJWFT BO PWFSWJFX PG UIF UPQJDT DPWFSFE JO UIJT CPPL BOE UIFJS SFMBUJPOTIJQT 4QFDJmDBMMZ UIF CPPL JT PSHB OJ[FE BT GPMMPXT #00, 065-*/&
'JHVSF 0VUMJOF PG UIJT CPPL
t *O $IBQUFS XF CFHJO XJUI UIF BOBMZUJDT PG TPDJBM JOUFSBDUJPOT CFUXFFO VTFST ɩF mSTU RVFTUJPO XF USZ UP BOTXFS JT i8IBU BSF UIF GVOEBNFOUBM GBDUPST UIBU GPSN UIF EJĊFSFOU DBU FHPSJFT PG TPDJBM UJFT w 8F JODPSQPSBUF TPDJBM OFUXPSL UIFPSJFT JOUP B QSPCBCJMJTUJD HSBQIJDBM NPEFM GPS MFBSOJOH UP BVUPNBUJDBMMZ JOGFS UIF UZQFT PG TPDJBM SFMBUJPOTIJQT t *O $IBQUFS XF JOWFTUJHBUF UIF QSPCMFN PG TPDJBM JOnVFODF 8F JOUSPEVDF UIFPSFUJDBM NFUIPEPMPHJFT GPS WFSJGZJOH UIF FYJTUFODF PG TPDJBM JOnVFODF BOE GPS RVBOUJGZJOH UIF JO nVFODF TUSFOHUI CFUXFFO VTFST PO EJĊFSFOU UPQJDT t *O $IBQUFS XF TUVEZ IPX UP NPEFM BOE QSFEJDU VTFS CFIBWJPST 0OF GVOEBNFOUBM QSPCMFN JT UP EJTUJOHVJTI UIF FĊFDUT PG EJĊFSFOU TPDJBM GBDUPST TVDI BT TPDJBM JOnVFODF IPNPQIJMZ BOE JOEJWJEVBMT DIBSBDUFSJTUJDT 8F JOUSPEVDF B QSPCBCJMJTUJD NPEFM UP BEESFTT UIJT QSPCMFN t *O $IBQUFS XF VTF "SOFU.JOFS BO BDBEFNJD TPDJBM OFUXPSL EFWFMPQFE CZ UIF BVUIPST BT BO FYBNQMF UP EFNPOTUSBUF IPX XF BQQMZ UIF JOUSPEVDFE UFDIOPMPHJFT GPS NJOJOH SFBM TPDJBM OFUXPSLT BU UIF NJDSPMFWFM t 'JOBMMZ JO $IBQUFS XF QSFTFOU QPUFOUJBM GVUVSF EJSFDUJPOT JO UIJT mFME
$ )"15&3 4PDJBM 5JF "OBMZTJT
4PDJBM UJFT BMTP SFGFSSFE UP BT JOUFSQFSTPOBM UJFT BSF EFmOFE BT JOGPSNBUJPODBSSZJOH DPOOFDUJPOT CFUXFFO QFPQMF *O HFOFSBM GSPN B TPDJPMPHJDBM QFSTQFDUJWF TPDJBM UJFT DBO CF DBUFHPSJ[FE JOUP UISFF WBSJFUJFT TUSPOH XFBL PS BCTFOU 'SPN UIF DPNQVUBUJPOBM QFSTQFDUJWF SFMBUFE SFTFBSDI PO TPDJBM UJF BOBMZTJT JODMVEFT QSFEJDUJOH NJTTJOH MJOLT JOGFSSJOH TPDJBM UJFT BOE QSFEJDUJOH SFDJ QSPDJUZ
07&37*&8 *O TPDJBM OFUXPSLT UIF CBTJT GPS TPDJBM UJF BOBMZTJT JT QSFEJDUJOH NJTTJOH MJOLT -JCFO/PXFMM BOE ,MFJOCFSH <> TZTUFNBUJDBMMZ JOWFTUJHBUFE UIF QSPCMFN PG JOGFSSJOH OFX MJOLT BNPOH VTFST HJWFO B TOBQTIPU PG B TPDJBM OFUXPSL ɩFZ JOUSPEVDFE TFWFSBM VOTVQFSWJTFE BQQSPBDIFT UP EFBM XJUI UIJT QSPCMFN CBTFE PO iQSPYJNJUZw PG OPEFT JO B OFUXPSLPS UIF QSJODJQMF PG IPNPQIJMZ <> iCJSET PG B GFBUIFS nPDL UPHFUIFSw <> #FTJEFT QSFEJDUJOH OFX MJOLT BOPUIFS JNQPSUBOU UPQJD JO TPDJBM UJF BOBMZTJT JT UP BVUPNBUJDBMMZ SFDPHOJ[F UIF TFNBOUJDT BTTPDJBUFE XJUI FBDI TPDJBM SFMBUJPOTIJQ SFGFSSFE UP BT JOGFSSJOH TPDJBM UJFT *O POMJOF TPDJBM OFUXPSLT NPTU SFMBUJPOTIJQT BSF OPU NFBOJOHGVMMZ MBCFMFE FH iDPMMFBHVFw BOE iJOUJNBUF GSJFOETw TJNQMZ CFDBVTF VTFST EP OPU XBOU UP MBCFM UIFN JO PSEFS UP QSPUFDU QSJWBDZ 4UBUJTUJDT TIPX UIBU POMZ PG NPCJMF QIPOF VTFST JO &VSPQF IBWF DSFBUFE DVTUPN DPOUBDU HSPVQT < > BOE MFTT UIBO DPOOFDUJPOT PO -JOLFE*O IBWF CFFO MBCFMFE "XBSFOFTT PG UIF UZQFT PG TPDJBM SFMBUJPOTIJQT DBO CFOFmU NBOZ BQQMJDBUJPOT 'PS FYBNQMF JG XF DPVME IBWF FYUSBDUFE GSJFOETIJQT CFUXFFO VTFST GSPN UIF NPCJMF DPNNVOJDBUJPO OFUXPSL XF DBO MFWFSBHF UIF GSJFOETIJQT GPS B iXPSEPGNPVUIw QSPNPUJPO PG B OFX QSPEVDU <> 'JHVSF TIPXT UIF NBKPS SFTFBSDI UPQJDT PO TPDJBM UJF BOBMZTJT *O BEEJUJPO UP QSFEJDUJOH NJTTJOH MJOLT BOE JOGFSSJOH TPDJBM UJFT BOPUIFS JNQPSUBOU UPQJD UP VOEFSTUBOE JT IPX B TPDJBM SFDJQSPDBM UXPXBZ SFMBUJPOTIJQ IBT CFFO EFWFMPQFE GSPN B QBSBTPDJBM POFXBZ SFMBUJPOTIJQ BOE XIZ ɩF QSPCMFN JT DBMMFE SFDJQSPDJUZ *O UIJT DIBQUFS XF XJMM GPDVT PO JOUSPEVDJOH UIF mSTU UXP QSPCMFNT QSFEJDUJOH NJTTJOH MJOLT BOE JOGFSSJOH TPDJBM UJFT 'PS QSFEJDUJOH SFDJQSPDJUZ UIF JOUFSFTUFE SFBEFS TIPVME SFGFS UP )PQDSPGU FU BM <> BOE -PV FU BM <> 5P CFHJO XJUI MFU VT EFmOF UIF HFOFSBM JOQVU PG UIF QSPCMFNT XF XJMM BEESFTT JO UIJT DIBQUFS G .V; E/ V V N E #BTJDBMMZ XF BSF HJWFO B TPDJBM OFUXPSL D XIFSF JT B TFU PG j jD VTFST BOE ! V V E M eij E " JT B TFU PG j jD SFMBUJPOTIJQT CFUXFFO VTFST -FU 2 EFOPUF B EJSFDUFE SFMBUJPOTIJQ vi vj eij eji eij GSPN VTFS UP VTFS *O B VOEJSFDUFE OFUXPSL XF IBWF D *O UIJT DBTF XF VTF FJUIFS PS eji UP SFQSFTFOU UIF SFMBUJPOTIJQ CFUXFFO vi BOE VTFS vj IUUQFOXJLJQFEJBPSHXJLJ*OUFSQFSTPOBM@UJFT 40$*"- 5*& "/"-:4*4
Predicting missing links You You
?
Lady Gaga Shiteng Lady Gaga Shiteng
Family
Inferring social ties ? Friend
? Predicting reciprocity
You Lady Gaga You Lady Gaga
'JHVSF 3FTFBSDI PO TPDJBM UJF BOBMZTJT
13&%*$5*/( .*44*/( -*/,4
*O UIJT TFDUJPO XF DPOEVDUFE B TVSWFZ PG FYJTUJOH BQQSPBDIFT GPS MJOL QSFEJDUJPO JO TPDJBM OFUXPSLT "T TIPXO JO 5BCMF XF DMBTTJGZ UIPTF BQQSPBDIFT JOUP TFWFSBM HSPVQT 4JNJMBSJUZ .FUSJD#BTFE .FUIPET 4JNJMBSJUZ NFUSJDCBTFE NFUIPET DPNQVUF B TJNJMBSJUZ TDPSF CFUXFFO B QBJS PG OPEFT VTFST BOE QSFEJDU UIF NJTTJOH MJOLT CBTFE PO UIF PCUBJOFE TJNJMBSJUZ TDPSFTB IJHIFS TJNJMBSJUZ TDPSF SFTVMUT JO B IJHIFS QSPCBCJMJUZ UP DSFBUF B MJOL -JCFO/PXFMM BOE ,MFJOCFSH <> QSPQPTFE B TJNJMBSJUZ NFUSJDCBTFE NFUIPE UP TPMWF UIF MJOL QSFEJDUJPO QSPCMFN (JWFO B TPDJBM OFUXPSL UIFZ mSTU DPNQVUFE UIF TJNJMBSJUZ CFUXFFO B QBJS PG WFSUJDFT CZ WBSJPVT HSBQICBTFE TJNJMBSJUZ NFUSJDT BOE UIFO VTFE UIF TJNJMBSJUZ TDPSFT UP QSFEJDU UIF NJTTJOH MJOL CFUXFFO UXP WFSUJDFT ,BTIJNB FU BM QSFTFOUFE B QBSBNFUFSJ[FE QSPCB CJMJTUJD NPEFM PG OFUXPSL FWPMVUJPO CBTFE PO UIF UPQPMPHJDBM GFBUVSFT PG OFUXPSL TUSVDUVSFT GPS MJOL QSFEJDUJPO <> 4DIJGBOFMMB FU BM <> TIPXFE TFNBOUJD TJNJMBSJUZ NFBTVSFT BNPOH VTFST CBTFE TPMFMZ PO UIFJS TPDJBM NFEJB BOOPUBUJPO NFUBEBUB BSF QSFEJDUJWF PG TPDJBM MJOLT 3JDIBSE FU BM QSPQPTFE mOEJOH UIF NJTTJOH MJOLT VTJOH UIF EZOBNJDT PG UIF HSBQI UISPVHI B TFU PG UPQPMPHJDBM GFBUVSFT TVDI BT UIF EFHSFFT PG UIF WFSUJDFT GPS BEEJUJPOBM JOGPSNBUJPO TFF <> $MBVTFU FU BM <> TIPXFE UIBU LOPXMFEHF PG IJFSBSDIJDBM TUSVDUVSF DBO CF VTFE UP QSFEJDU NJTTJOH DPOOFDUJPOT JO QBSUMZ LOPXO OFUXPSLT XJUI IJHI BDDVSBDZ *O <> UIFZ QSFTFOUFE UIF DPNQVUBUJPOBMMZ MFTT FYQFOTJWF GFBUVSFT CBTFE PO TPDJBM WFDUPS DMPDLT UP TPMWF UIF MJOL QSFEJDUJPO QSPCMFN 13&%*$5*/( .*44*/( -*/,4 5BCMF 4VSWFZ PG NBKPS NFUIPEPMPHJFT GPS NJTTJOH MJOL QSFEJDUJPO $BUFHPSZ .FUIPE %FTDSJQUJPO -11 <> 4JNJMBSJUZ 4VSWFZ 11. <> 5PQPMPHJDBM 'FBUVSFT '*'<> 'FBUVSFT GPS 'PMLT JO 'PMLTPOPNJFT ('5<> (SBQI 'FBUVSF 5SBDLJOH )4-1<> )JFSBSDIJDBM 4USVDUVSFCBTFE 4JNJMBSJUZ 47$<> 4PDJBM 7FDUPS $MPDLT 7$1 <> 7FSUFY $PMMPDBUJPO 1SPm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
-JDIUFOXBMUFS FU BM<> JOUSPEVDFE UIF DPODFQU PG B WFSUFY DPMMPDBUJPO QSPmMF 7$1 GPS UIF QVSQPTF PG UPQPMPHJDBM MJOL BOBMZTJT BOE QSFEJDUJPO 7$1T QSPWJEF OFBSMZ DPNQMFUF JOGPSNBUJPO BCPVU UIF TVSSPVOEJOH MPDBM TUSVDUVSF PG FNCFEEFE WFSUFY QBJST %F FU BM DPNCJOFE UIF HMPCBM QSPQFSUJFT HSBQI DPOEVDUBODF IJUUJOH PS DPNNVUF UJNFT ,BU[ TDPSF MPDBM QSPQFSUJFT "EBNJD "EBS PS OPEF GFBUVSF WFDUPST BOE UIF MJOL EFOTJUJFT BU UIF JOUFSNFEJBUF MFWFM PG DPNNVOJUJFT JOUP B EJTDSJNJOBUJWF MJOL QSFEJDUPS <> 8BOH FU BM <> BOE 4DFMMBUP FU BM <> QSFTFOUFE 40$*"- 5*& "/"-:4*4 EJĊFSFOU GFBUVSFT GPS MJOL QSFEJDUJPO JO NPCJMF QIPOF TPDJBM OFUXPSLT BOE MPDBUJPOCBTFE TPDJBM OFUXPSLT SFTQFDUJWFMZ 0ZBNB FU BM QSPQPTFE B EJNFOTJPO SFEVDUJPO BQQSPBDI UP DSPTTUFNQPSBM MJOL QSFEJDUJPO CZ KPJOUMZ MFBSOJOH B TFU PG GFBUVSF QSPKFDUJPO NBUSJDFT GSPN UIF USBJOJOH EBUB <> ;IV <> QSFTFOUFE B NBYNBSHJO OPOQBSBNFUSJD MBUFOU GFBUVSF NPEFM UP EJTDPWFS EJTDSJNJOBUJWF MBUFOU GFBUVSFT GPS MJOL QSFEJDUJPO BOE UP BVUPNBUJDBMMZ JOGFS UIF VOLOPXO MBUFOU TPDJBM EJNFOTJPO 1BQBEPQPVMPT FU BM TIPXFE UIBU QPQVMBSJUZ JT KVTU POF EJNFOTJPO PG BUUSBDUJWFOFTT BOPUIFS EJNFOTJPO JT TJNJMBSJUZ ɩFZ EFWFMPQFE B GSBNFXPSL JO XIJDI OFX DPOOFDUJPOT PQUJNJ[F DFSUBJO USBEFPĊT CFUXFFO QPQVMBSJUZ BOE TJNJMBSJUZ XIJDI QSFEJDUT UIF QSPCBCJMJUZ PG OFX MJOLT XJUI IJHI QSFDJTJPO JO UIF UFDIOPMPHJDBM CJPMPHJDBM BOE TPDJBM OFUXPSLT <> -JDIUFOXBMUFS FU BM <> FY QMPSFE NBOZ GBDUPST TJHOJmDBOU JO JOnVFODJOH BOE HVJEJOH DMBTTJmDBUJPO BOE QSFTFOUFE BO FĊFDUJWF nPXCBTFE QSFEJDUJOH BMHPSJUIN XIJDI PĊFST GPSNBM CPVOET PO JNCBMBODF JO TQBSTF OFUXPSL MJOL QSFEJDUJPO .BUSJY 'BDUPSJ[BUJPO#BTFE .FUIPET .BUSJY GBDUPSJ[BUJPOCBTFE NFUIPET NPEFM UIF TPDJBM OFUXPSL BT B NBUSJY BOE TPMWF UIF QSPCMFN PG MJOL QSFEJDUJPO VTJOH UIF NBUSJY EFDPNQPTJUJPOT GSPN MJOFBS BMHFCSB PS HSBQI UIFPSJFT ,VOFHJT BOE -PNNBU[TDI <> QSFTFOUFE B VOJmFE GSBNFXPSL GPS MFBSOJOH MJOL QSFEJD UJPO BOE FEHF XFJHIU QSFEJDUJPO GVODUJPOT JO MBSHF OFUXPSLT CBTFE PO UIF USBOTGPSNBUJPO PG B HSBQIT BMHFCSBJD TQFDUSVN ɩFJS BQQSPBDI HFOFSBMJ[FT TFWFSBM HSBQI LFSOFMT BOE EJNFOTJPOBMJUZ SFEVDUJPO NFUIPET BOE QSPWJEFT B NFUIPE UP FTUJNBUF UIF QBSBNFUFST FċDJFOUMZ ,VOFHJT BOE 'MJFHF <> BMTP QSFTFOUFE B NFUIPE GPS USVTU QSFEJDUJPO CBTFE PO OPOEJBHPOBM EFDPNQPTJUJPOT PG UIF BTZNNFUSJD BEKBDFODZ NBUSJY PG B EJSFDUFE OFUXPSL ɩFZ VTFE B OPOEJBHPOBM EFDPNQPTJUJPO JOUP EJSFDUFE DPNQPOFOUT %&%*$0. UP MFBSO UIF DPFċDJFOUT PG B NBUSJY QPMZOPNJBM PG UIF OFUXPSLT BEKBDFODZ NBUSJY ɩFJS NFUIPE DBO CF VTFE UP DPNQVUF CFUUFS MPXSBOL BQQSPYJNBUJPOT UP B QPMZOPNJBM PG B OFUXPSLT BEKBDFODZ NBUSJY UIBO VTJOH UIF TJOHVMBS WBMVF EFDPNQPTJUJPO 1SPCBCJMJTUJD (SBQI .PEFM#BTFE .FUIPET ɩ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mFE JO OPJTZ OFUXPSL PCTFSWBUJPOT 8BOH FU BM QSPQPTFE B UJNFDPOTUSBJOFE QSPCBCJMJTUJD GBDUPS HSBQI NPEFM 51'( XIJDI UBLFT B SFTFBSDI QVCMJDBUJPO OFUXPSL BT JOQVU BOE NPEFMT UIF BEWJTPSBEWJTFF SFMBUJPOTIJQ NJOJOH QSPCMFN VTJOH B KPJOUMZ MJLFMJIPPE PCKFDUJWF GVODUJPO <> -FSPZ FU BM <> QSPQPTFE B UXP QIBTF NFUIPE CBTFE PO UIF CPPUTUSBQ QSPCBCJMJTUJD HSBQI ɩF mSTU QIBTF HFOFSBUFT BO JNQMJDJU TPDJBM OFUXPSL VOEFS UIF GPSN PG B QSPCBCJMJTUJD HSBQI ɩF TFDPOE QIBTF BQQMJFT QSPCBCJMJTUJD HSBQICBTFE NFBTVSFT UP QSPEVDF UIF mOBM QSFEJDUJPO :JO FU BM <> QSFTFOUFE FTUJNBUJOH UIF 13&%*$5*/( .*44*/( -*/,4 MJOL SFMFWBODF VTJOH B SBOEPN XBML BMHPSJUIN PO BO BVHNFOUFE TPDJBM HSBQI XJUI CPUI BUUSJCVUF BOE TUSVDUVSF JOGPSNBUJPO #BDLTUSPN FU BM EFWFMPQFE BO BMHPSJUIN CBTFE PO TVQFSWJTFE SBOEPN XBMLT UIBU OBUVSBMMZ DPNCJOFT UIF JOGPSNBUJPO GSPN UIF OFUXPSL TUSVDUVSF XJUI OPEF BOE FEHF MFWFM BUUSJCVUFT <> .BUIVS FU BM <> VUJMJ[FE B EZOBNJD #BZFTJBO OFUXPSL UP EFUFDU JOUFSBDUJPO MJOLT JO B DPMMBCPSBUJOH HSPVQ VTJOH NBOVBMMZ BOOPUBUFE EBUB ;IV FU BM DPNCJOFE DMBTTJD JEFBT JO UPQJD NPEFMJOH XJUI B WBSJBOU PG UIF NJYFENFNCFSTIJQ CMPDL NPEFM BOE QSPQPTFE UIF NJYFEUPQJD MJOL NPEFMT GPS VOTVQFSWJTFE UPQJD DMBTTJmDBUJPO BOE MJOL QSFEJDUJPO <> ;IBOH FU BM NPEFMFE MJOL GPSNBUJPO BT SFTVMUT PG JOEJWJEVBMT GSJFOENBLJOH CFIBWJPST DPNCJOFE XJUI QFSTPOBM JOUFS FTUT <> ɩFZ QSPQPTFE UIF -BUFOU 'SJFOETIJQ 1SPQBHBUJPO /FUXPSL -'1/ UP EFQJDU UIF FWPMVUJPO QSPHSFTT PG POFT FHPDFOUSJD OFUXPSL BOE NPEFMFE JOEJWJEVBMT TPDJBM CFIBWJPST VTJOH UIF -BUFOU 'SJFOETIJQ 1SPQBHBUJPO .PEFM -'1. *O <> 8V FU BM QSPQPTFE BO JOUFSBD UJWF MFBSOJOH GSBNFXPSL UP GPSNVMBUF UIF QSPCMFN PG SFDPNNFOEJOH QBUFOU QBSUOFST JOUP B GBDUPS HSBQI NPEFM ɩF GSBNFXPSL JOWPMWFT UISFF QIBTFT DBOEJEBUF HFOFSBUJPO DBOEJEBUF SFmOFNFOU BOE JOUFSBDUJWF MFBSOJOH NFUIPE UP FċDJFOUMZ VQEBUF UIF FYJTUJOH SFDPNNFOEBUJPO NPEFM CBTFE PO JOWFOUPST GFFECBDL )FBVLVMBOJ FU BM QSPQPTFE B MBUFOU GFBUVSF QSPQBHBUJPO NPEFM GPS MJOL QSFEJDUJPO CZ DBQUVSJOH IPX PCTFSWFE TPDJBM SFMBUJPOTIJQT GSPN UIF QBTU BĊFDU GVUVSF VOPCTFSWFE TUSVDUVSF JO UIF OFUXPSL <> *O UIF GPMMPXJOH TFDUJPO XF mSTU JOUSPEVDF TPNF EJĊFSFOU LJOET PG BQQSPBDIFT GPS NJTTJOH MJOL QSFEJDUJPO
4*.*-"3*5: .&53*$4 8F mSTU JOUSPEVDF EJĊFSFOU TJNJMBSJUZ NFUSJDT GPS MJOL QSFEJDUJPO JODMVEJOH UIF OPEF OFJHICPS IPPE CBTFE NFUSJDT QBUICBTFE NFUSJDT OPEF BOE FEHF BUUSJCVUFTCBTFE NFUSJDT BOE MBUFOU NFU SJDT ɩFO XF JOUSPEVDF UIF QSJNBSZ DIBMMFOHF GPS MJOL QSFEJDUJPO BT DMBTTJmDBUJPO .PTU PG UIF TJNJMBSJUZ GFBUVSFT IBWF CFFO TVSWFZFE JO "M )BTBO BOE ;BLJ <>
/PEF /FJHICPSIPPECBTFE .FUSJDT
$PNNPO /FJHICPST 'PS UXP VTFST OPEFT u BOE v UIF OVNCFS PG UIFJS DPNNPO OFJHICPST JT .u/ .v/ . / EFOPUFE BT j \ j XIFSF # SFQSFTFOUT UIF TFU PG OFJHICPST PG B OPEF ɩF JEFB PG VTJOH UIF TJ[F PG DPNNPO OFJHICPST JT KVTU BO BUUFTUBUJPO UP UIF OFUXPSL USBOTJUJWJUZ QSPQFSUZ *O PUIFS XPSET JG VTFS u BOE VTFS v BSF DPOOFDUFE CZ NBOZ DPNNPO OPEFT UIFO JU JT WFSZ MJLFMZ UIBU VTFS u BOE v BSF PS XJMM CF DPOOFDUFE +BDDBSE $PFĆDJFOU ɩF DPNNPO OFJHICPST NFUSJD XJMM CJBT UPXBSE IJHIEFHSFF VTFST +BDDBSE $PFċDJFOU JT B NFUSJD UP BEESFTT UIJT QSPCMFN CZ OPSNBMJ[JOH UIF OVNCFS PG DPNNPO OFJHICPST .u/ .v/ Jaccard coefficient.u; v/ j \ j: $ D .u/ .v/ j [ j 40$*"- 5*& "/"-:4*4 $PODFQUVBMMZ JU EFmOFT UIF QSPCBCJMJUZ UIBU B DPNNPO OFJHICPS PG B QBJS PG OPEFT u BOE v XPVME CF TFMFDUFE JG UIF TFMFDUJPO JT NBEF SBOEPNMZ GSPN UIF VOJPO PG UIF OFJHICPSTFUT PG u BOE v ɩVT GPS B IJHI OVNCFS PG DPNNPO OFJHICPST UIF TDPSF XPVME CF IJHIFS "EBNJD"EBS "EBNJD BOE "EBS <> QSPQPTFE B OFX TDPSF BT B NFUSJD PG TJNJMBSJUZ CFUXFFO UXP OPEFT *U JT EFmOFE BT CFMPX 1 Adamic Adar.u; v/ $ D .z/ z MPH GSFR X XIFSF z EFOPUFT BOZ GFBUVSF TIBSFE CZ u BOE v BOE GSFR.z/ EFOPUFT UIF GSFRVFODZ PG GFBUVSF PDDVSSJOH CFUXFFO u BOE v 8IFO DPOTJEFSJOH DPNNPO OFJHICPST BT GFBUVSFT UIFO UIF NFUSJD DBO CF SFXSJUUFO BT 1 Adamic Adar.u; v/ : $ D .z/ z .u/ .v/ MPH 2 X\ j j #BTFE PO UIF QBTU SFTVMUT PG FYJTUJOH MJUFSBUVSF PO MJOL QSFEJDUJPO "EBNJD"EBS VTVBMMZ XPSLT CFUUFS UIBO UIF QSFWJPVT UXP NFUSJDT
1BUI#BTFE .FUSJDT
4IPSUFTU 1BUI %JTUBODF ɩF CBTJD JEFB PG UIJT NFUIPE JT UIBU JG UXP OPEFT EJTUBODF CZ TIPSUFTU QBUI JO B TPDJBM OFUXPSL JT TIPSU UIFO JU JT MJLFMZ UIBU B MJOL XPVME CF DSFBUFE CFUXFFO UIF UXP OPEFT )PXFWFS BDDPSEJOH UP UIF UIFPSZ PG TJY EFHSFFT PG TFQBSBUJPO FWFSZPOF BOE FWFSZUIJOH JT TJY PS GFXFS TUFQT BXBZ <> ɩVT UIJT GFBUVSF TPNFUJNFT EPFT OPU XPSL UIBU XFMM ,BU[ -FP ,BU[ QSPQPTFE UIJT NFUSJD BT BO FYUFOTJPO PG UIF TIPSUFTU QBUI EJTUBODF *U XPSLT NVDI CFUUFS GPS MJOL QSFEJDUJPO *U EJSFDUMZ TVNT PWFS BMM UIF QBUIT UIBU FYJTU CFUXFFO B QBJS PG OPEFT u BOE v 5P QFOBMJ[F UIF DPOUSJCVUJPO PG MPOHFS QBUIT JO UIF TJNJMBSJUZ DPNQVUBUJPO JU FYQPOFOUJBMMZ EBNQT UIF DPOUSJCVUJPO PG B QBUI CZ B GBDUPS PG ˇl XIFSF l JT UIF QBUI MFOHUI ɩF FYBDU FRVBUJPO UP DPNQVUF UIF ,BU[ TDPSF JT BT CFMPX
1 l Katz.u; v/ ˇl pathsh i ; D #j u;vj l 1 XD paths l l u v ˇ. 1/ XIFSF h i JT B TFU PG QBUIT PG MFOHUI GSPN UP ɩF QBSBNFUFS Ä DBO CF VTFE UP SFHVMBSJ[F UIJT GFBUVSF " TNBMM ˇ JOEJDBUFT UIBU XF POMZ DPOTJEFS TIPSUFS QBUIT *O BO FYUSFNF DBTF UIJT NFUSJD XPVME CFIBWF MJLF OPEF OFJHICPSIPPECBTFE NFUSJDT 0OF QSPCMFN XJUI UIJT GFBUVSF JT UIBU JU JT DPNQVUBUJPOBMMZ FYQFOTJWF *U DBO CF TIPXO UIBU UIF ,BU[ TDPSF CFUXFFO BMM .I ˇA/ 1 I A UIF QBJST PG OPEFT DBO CF DPNQVUFE CZ mOEJOH $ ! $ XIFSF JT UIF BEKBDFODZ NBUSJY BOE I JT BO JEFOUJUZ NBUSJY PG QSPQFS TJ[F ɩJT UBTL IBT SPVHIMZ DVCJD DPNQMFYJUZ XIJDI DPVME CF JOGFBTJCMF GPS MBSHF TPDJBM OFUXPSLT 13&%*$5*/( .*44*/( -*/,4 )JUUJOH 5JNF ɩF DPODFQU PG IJUUJOH UJNF DPNFT GSPN SBOEPN XBMLT PO B HSBQI 'PS UXP OPEFT u BOE v JO B HSBQI UIF IJUUJOH UJNF Hu;v EFOPUFT UIF FYQFDUFE OVNCFS PG TUFQT SFRVJSFE GPS B SBOEPN XBML TUBSUJOH BU u UP SFBDI v 4IPSUFS IJUUJOH UJNF EFOPUFT UIBU UIF OPEFT BSF TJNJMBS UP FBDI PUIFS TP UIFZ IBWF B IJHIFS DIBODF PG MJOLJOH JO UIF GVUVSF 4JODF UIJT NFUSJD JT OPU TZNNFUSJD Cu;v Hu;v Hv;u GPS VOEJSFDUFE HSBQIT UIF DPNNVUF UJNF D C DBO CF VTFE ɩF CFOFmU PG UIJT NFUSJD JT UIBU JU JT FBTZ UP DPNQVUF CZ QFSGPSNJOH TPNF USJBM SBOEPN XBMLT 0O UIF EPXOTJEF JUT WBMVF DBO IBWF IJHI WBSJBODF IFODF QFSGPSNBODF PG MJOL QSFEJDUJPO CZ UIJT NFUSJD DPVME CF OPU JEFBM 'PS JOTUBODF UIF IJUUJOH UJNF CFUXFFO u BOE v DBO CF BĊFDUFE CZ B OPEF w XIJDI JT GBS BXBZ GSPN u BOE v GPS JOTUBODF JG w IBT IJHI TUBUJPOBSZ QSPCBCJMJUZ UIFO JU DPVME CF IBSE GPS B SBOEPN XBML UP FTDBQF GSPN UIF OFJHICPSIPPE PG w 5P QSPUFDU BHBJOTU UIJT QSPCMFN XF DBO VTF SBOEPN XBMLT XJUI SFTUBSU XIFSF XF QFSJPEJDBMMZ SFTFU UIF SBOEPN XBML CZ SFUVSOJOH UP u XJUI B mYFE QSPCBCJMJUZ ˛ JO FBDI TUFQ %VF UP UIF TDBMFGSFF OBUVSF PG B TPDJBM OFUXPSL TPNF PG UIF OPEFT NBZ IBWF WFSZ IJHI TUBUJPOBSZ QSPCBCJMJUZ " JO B SBOEPN XBML UP TBGFHVBSE BHBJOTU JU UIF IJUUJOH UJNF DBO CF OPSNBMJ[FE CZ NVMUJQMZJOH JU XJUI UIF TUBUJPOBSZ QSPCBCJMJUZ PG UIF SFTQFDUJWF OPEF BT TIPXO CFMPX
Normalized Hitting Time.u; v/ Hu;v "v Hv;u "u: $ $ D # C #
3PPUFE 1BHFSBOL 1BHFSBOL WBMVF DBO BMTP CF VTFE BT B NFUSJD GPS MJOL QSFEJDUJPO )PXFWFS TJODF 1BHFSBOL JUTFMG RVBOUJmFT UIF JNQPSUBODF PG B TJOHMF WFSUFY JU SFRVJSFT UP CF NPEJmFE TP UIBU JU DBO FTUJNBUF B TJNJMBSJUZ CFUXFFO B QBJS PG WFSUJDFT u BOE v ɩF PSJHJOBM EFmOJUJPO PG 1BHFSBOL EFOPUFT UIF JNQPSUBODF PG B WFSUFY VOEFS UXP BTTVNQUJPOT GPS TPNF mYFE QSPCBCJMJUZ ˛ B TVSGFS BU B XFCQBHF KVNQT UP B SBOEPN XFCQBHF XJUI QSPCBCJMJUZ ˛ BOE GPMMPXT B MJOLFE IZQFSMJOL 1 ˛ v XJUI QSPCBCJMJUZ $ 6OEFS UIJT SBOEPN XBML UIF JNQPSUBODF PG B XFCQBHF JT UIF FYQFDUFE TVN PG UIF JNQPSUBODF PG BMM UIF XFCQBHFT u UIBU MJOL UP v *O SBOEPN XBML UFSNJOPMPHZ POF DBO SFQMBDF UIF UFSN JNQPSUBODF CZ UIF UFSN TUBUJPOBSZ EJTUSJCVUJPO 'PS MJOL QSFEJDUJPO UIF SBOEPN XBML BTTVNQUJPO PG UIF PSJHJOBM 1BHFSBOL DBO CF BMUFSFE BT CFMPX TJNJMBSJUZ TDPSF CFUXFFO UXP OPEFT u BOE v DBO CF NFBTVSFE BT UIF TUBUJPOBSZ QSPCBCJMJUZ PG v JO B SBOEPN XBML UIBU SFUVSOT u 1 ˛ ˛ UP XJUI QSPCBCJMJUZ $ JO FBDI TUFQ NPWJOH UP B SBOEPN OFJHICPS XJUI QSPCBCJMJUZ ɩJT NFUSJD JT BTZNNFUSJD BOE DBO CF NBEF TZNNFUSJD CZ TVNNJOH XJUI UIF DPVOUFSQBSU XIFSF UIF SPMF PG u BOE v BSF SFWFSTFE XIJDI JT BMTP OBNFE BT SPPUFE 1BHFSBOL ɩF SPPUFE 1BHFSBOL CFUXFFO BMM OPEF QBJST SFQSFTFOUFE BT RPR DBO CF EFSJWFE BT GPMMPXT -FU D CF B EJBHPOBM EFHSFF NBUSJY DŒi; i AŒi; j N D 1A XJUI D j -FU D ! CF UIF BEKBDFODZ NBUSJY XJUI SPX TVNT OPSNBMJ[FE UP ɩFO P
1 RPR .1 ˛/ .I ˛N /! : D $ # $ 40$*"- 5*& "/"-:4*4 .FUSJDT #BTFE PO /PEF BOE &EHF "UUSJCVUFT 7FSUFY BOE FEHF BUUSJCVUFT QMBZ BO JNQPSUBOU SPMF GPS MJOL QSFEJDUJPO /PUF UIBU JO B TPDJBM OFU XPSL UIF MJOLT BSF EJSFDUMZ NPUJWBUFE CZ UIF VUJMJUZ PG UIF JOEJWJEVBM SFQSFTFOUJOH UIF OPEFT BOE UIF VUJMJUZ JT B GVODUJPO PG OPEF BOE FEHF BUUSJCVUFT .BOZ TUVEJFT TIPXFE UIBU OPEF PS FEHF BU USJCVUFT BT QSPYJNJUZ GFBUVSFT DBO TJHOJmDBOUMZ JODSFBTF UIF QFSGPSNBODF PG MJOL QSFEJDUJPO UBTLT 'PS FYBNQMF )BTBO FU BM <> TIPXFE UIBU GPS MJOL QSFEJDUJPO JO B DPBVUIPSTIJQ TPDJBM OFUXPSL BUUSJCVUFT TVDI BT UIF EFHSFF PG PWFSMBQ BNPOH UIF SFTFBSDI LFZXPSET VTFE CZ B QBJS PG BVUIPST JT UIF UPQ SBOLFE BUUSJCVUF GPS TPNF EBUBTFUT )FSF UIF OPEF BUUSJCVUF JT UIF SFTFBSDI LFZXPSE TFU BOE UIF BTTVNQUJPO JT UIBU B QBJS PG BVUIPST BSF DMPTF JO UIF TFOTF PG B TPDJBM OFUXPSL UP FBDI PUIFS JG UIFJS SFTFBSDI XPSL FWPMWFT BSPVOE B MBSHFS TFU PG DPNNPO LFZXPSET 4JNJMBSMZ UIF ,BU[ NFUSJD DPNQVUFE UIF TJNJMBSJUZ CFUXFFO UXP XFCQBHFT CZ UIF EFHSFF UP XIJDI UIFZ IBWF B MBSHFS TFU PG DPNNPO XPSET XIFSF UIF XPSET JO UIF XFCQBHF BSF UIF WFSUFY BUUSJCVUFT ɩF BEWBOUBHF PG TVDI B NFUSJD TFU JT UIBU JU JT HFOFSBMMZ DIFBQ UP DPNQVUF 0O UIF EPXOTJEF UIF NFUSJDT BSF WFSZ UJHIUMZ UJFE XJUI UIF EPNBJO TP JU SFRVJSFT HPPE EPNBJO LOPXMFEHF UP JEFOUJGZ UIFN #FMPX XF XJMM QSPWJEF B HFOFSJD BQQSPBDI UP TIPX IPX UIFTF GFBUVSFT DBO CF JODPSQPSBUFE JOUP B MJOL QSFEJDUJPO UBTL /PEF 'FBUVSF "HHSFHBUJPO 0ODF XF JEFOUJGZ BO BUUSJCVUF a PG B OPEF JO B TPDJBM OFUXPSL XF OFFE UP EFWJTF TPNF NFBOJOHGVM BHHSFHBUJPO GVODUJPO f 5P DPNQVUF UIF TJNJMBSJUZ WBMVF CFUXFFO OPEFT u BOE v f BDDFQUT UIF DPSSFTQPOEJOH BUUSJCVUF WBMVFT PG UIFTF OPEFT UP QSPEVDF B TJNJMBSJUZ TDPSF ɩF DIPJDF PG GVODUJPO FOUJSFMZ EFQFOET PO UIF UZQF PG UIF BUUSJCVUF *O UIF GPMMPXJOH XF TIPX UXP FYBNQMFT XIFSF XF BHHSFHBUFE TPNF MPDBM NFUSJD PG B OPEF
t 1SFGFSFOUJBM "UUBDINFOU 4DPSF *O HFOFSBM B OPEF DPOOFDUT UP PUIFS OPEFT JO UIF OFUXPSL CBTFE PO UIF QSPCBCJMJUZ PG UIFJS EFHSFF 4P JG XF DPOTJEFS UIF OFJHICPSIPPE TJ[F BT GFBUVSF WBMVF UIFO NVMUJQMJDBUJPO DBO CF BO BHHSFHBUJPO GVODUJPO XIJDI JT OBNFE BT QSFGFSFOUJBM BUUBDINFOU TDPSF
Preferential Attachment Score.u; v/ .u/ .v/: $ $ D #
t $MVTUFSJOH $PFĆDJFOU 4DPSF $MVTUFSJOH DPFċDJFOU PG B WFSUFY u JT EFOPUFE BT CFMPX
3 triangles adjacent to v Clustering Coefficient.u/ " : $ D possible triples adjacent to v
5P DPNQVUF B TDPSF GPS MJOL QSFEJDUJPO CFUXFFO UIF WFSUFY u BOE v POF DBO TVN PS NVMUJQMZ UIF DMVTUFSJOH DPFċDJFOU TDPSF PG u BOE v 13&%*$5*/( .*44*/( -*/,4 (FOFSJD 4JN3BOL +FI BOE 8JEPN TVHHFTUFE B HFOFSJD NFUSJD DBMMFE 4JN3BOL XIJDI SFDVSTJWFMZ DBQUVSFT UIBU iUXP PCKFDUT BSF TJNJMBS JG UIFZ BSF TJNJMBS UP UXP TJNJMBS PCKFDUTw ɩF 4JN3BOL TDPSF JT UIF mYFE QPJOU PG UIF GPMMPXJOH SFDVSTJWF FRVBUJPO 1 if u v SimRank.u; v/ .a;b/ D : a .u/ b .v/ SimRank D ( $ 2 .u/2 .v/ otherwise # P Pj j"j j
-BUFOU 'FBUVSFCBTFE .FUSJDT *O NBOZ MJOL QSFEJDUJPO QSPCMFNT XIJMF UIF GFBUVSF WFDUPST SFQSFTFOUJOH EBUB PCKFDUT BSF IJHI EJNFOTJPOBM UIF OVNCFS PG MBUFOU GFBUVSFT BDUVBMMZ FĊFDUJWF GPS QSFEJDUJOH MJOLT JT BTTVNFE UP CF SFMBUJWFMZ TNBMM ɩFSFGPSF UIF BDDVSBDZ PG MJOL QSFEJDUJPO DBO CF JNQSPWFE CZ JEFOUJGZJOH BOE XPSLJOH JO B MPXEJNFOTJPOBM MBUFOU GFBUVSF TQBDF *O TVQFSWJTFE MJOFBS EJNFOTJPOSFEVDUJPO NFUIPET B MJOFBS QSPKFDUJPO W GSPN UIF PSJHJOBM DEJNFOTJPOBM GFBUVSF TQBDF UP B d Wx Wy ; k $ k BT TNBMM BT QPTTJCMF XIFSF x BOE y BSF UXP OPEFT LOPXO UP IBWF B MJOL CFUXFFO UIFN "GUFS UIF MFBSOJOH QSPDFTT JT DPNQMFUFE UXP EBUB PCKFDUT XJUI BO VOLOPXO MJOL TUBUVT BSF NBQQFE UP UIF MBUFOU TQBDF CZ VTJOH W *G UIF NBQQFE JNBHFT PG UIF UXP EBUB PCKFDUT BSF TVċDJFOUMZ DMPTF UP FBDI PUIFS UIFZ BSF DPOTJEFSFE UP IBWF B MJOL CFUXFFO UIFN "TTVNF UIBU XF IBWF N USBJOJOH EBUB PCKFDUT x1;:::;xN BOE UIBU FBDI EBUB PCKFDU xi JT SFQSFTFOUFE JO B D EJNFOTJPOBM GFBUVSF WFDUPS <> 0OF DBO VTF MPDBMJUZ QSFTFSWJOH QSPKFDUJPOT UP mOE UIF PQUJNBM MJOFBS QSPKFDUJPO NBUSJY W # CZ TPMWJOH UIF GPMMPXJOH PQUJNJ[BUJPO QSPCMFN 2 W # Aij Wxi Wxj 2; D BSH NJOW k $ k Xi;j 2 A Aij XIFSF k#k JT UIF &VDMJEFBO OPSN OPSN BOE Df g JT UIF BEKBDFODZ NBUSJY EFmOFE CZ 1 if xi and xj have a link Aij D 0 otherwise: ! $IBMMFOHF GPS -JOL 1SFEJDUJPO BT $MBTTJmDBUJPO ɩF NBJO DIBMMFOHF JO TJNJMBSJUZ NFUSJDCBTFE TVQFSWJTFE MJOL QSFEJDUJPO JT FYUSFNF DMBTT TLFX OFTT ɩF OVNCFS PG QPTTJCMF MJOLT JT RVBESBUJD JO UIF OVNCFS PG WFSUJDFT JO B TPDJBM OFUXPSL IPXFWFS UIF OVNCFS PG BDUVBM MJOLT UIF FEHFT JO UIF HSBQI BEEFE UP UIF HSBQI JT POMZ B UJOZ 40$*"- 5*& "/"-:4*4 GSBDUJPO PG UIJT OVNCFS ɩJT SFTVMUT JO MBSHF DMBTT TLFXOFTT DBVTJOH USBJOJOH BOE JOGFSFODF UP CFDPNF EJċDVMU UBTLT <> ɩF QSPCMFN PG DMBTT TLFXOFTT JO TVQFSWJTFE MFBSOJOH JT XFMM LOPXO JO NBDIJOF MFBSOJOH ɩF QPPS QFSGPSNBODF PG B MFBSOJOH BMHPSJUIN JO UIJT DBTF SFTVMUT GSPN CPUI UIF WBSJBODF JO UIF NPEFMT FTUJNBUFT BOE UIF JNCBMBODF JO UIF DMBTT EJTUSJCVUJPO &WFO JG B MPX QSPQPSUJPO PG OFHBUJWF JOTUBODFT IBWF UIF QSFEJDUPS WBMVF TJNJMBS UP UIF QPTJUJWF JOTUBODFT UIF NPEFM XJMM FOE VQ XJUI B MBSHF SBX OVNCFS PG GBMTF QPTJUJWFT 5P DPQF XJUI DMBTT TLFX FYJTUJOH SFTFBSDI TVHHFTUT TFWFSBM EJĊFSFOU BQQSPBDIFT ɩFTF NFUIPET JODMVEF UIF BMUFSJOH PG UIF USBJOJOH TBNQMF CZ VQTBNQMJOH PS EPXOTBNQMJOH BMUFS JOH UIF MFBSOJOH NFUIPE CZ NBLJOH UIF QSPDFTT BDUJWF PS DPTUTFOTJUJWF BOE BMTP NPSF HFOFSBMMZ CZ USFBUJOH UIF DMBTTJmFS TDPSF XJUI EJĊFSFOU UISFTIPMET *O HFOFSBM MFBSOJOH GSPN JNCBMBODFE EBUBTFUT JT B WFSZ JNQPSUBOU SFTFBSDI DPOTJEFSBUJPO BOE 8FJTT <> IBT B HPPE EJTDVTTJPO PG WBS JPVT UFDIOJRVFT UP TPMWF UIJT ."53*9 '"$503*;"5*0/ 8F CSJFnZ JOUSPEVDF UXP TFSJFT PG NBUSJY GBDUPSJ[BUJPO CBTFE NFUIPET XIJDI BSF UP QSFEJDU VOEJ SFDUFE BOE EJSFDUFE MJOLT SFTQFDUJWFMZ 1SFEJDUJOH 6OEJSFDUFE -JOLT VTJOH 4QFDUSBM (SBQI 5SBOTGPSNBUJPOT "QQSPBDIJOH UIF QSPCMFN PG MJOL QSFEJDUJPO BMHFCSBJDBMMZ XF DBO DPOTJEFS B HSBQI BEKBDFODZ NBUSJY A BOE MPPL GPS B GVODUJPO F.A/ SFUVSOJOH B NBUSJY PG UIF TBNF TJ[F XIPTF FOUSJFT DBO CF VTFE GPS QSFEJDUJPO ,VOFHJT FU BMT BQQSPBDI DPOTJTUT PG DPNQVUJOH B NBUSJY EFDPNQPTJUJPO A UDVT F.A/ UF.D/V T F.D/ D BOE DPOTJEFSJOH GVODUJPOT PG UIF GPSN D XIFSF BQQMJFT B GVODUJPO PO SFBMT UP FBDI FMFNFOU PG UIF HSBQI TQFDUSVN D TFQBSBUFMZ <> ɩF BVUIPST TIPX UIBU B DFSUBJO OVNCFS PG DPNNPO MJOLT BOE FEHF XFJHIU QSFEJDUJPO BMHPSJUINT DBO CF NBQQFE UP UIJT GPSN "T B SFTVMU UIF NFUIPE QSPWJEFT B NFDIBOJTN GPS FTUJNBUJOH BOZ QBSBNFUFST PG TVDI MJOL QSFEJDUJPO BMHPSJUINT "OBMPHPVTMZ UIFZ BMTP DPOTJEFS B OFUXPSLT -BQMBDJBO NBUSJY BT UIF CBTJT GPS MJOL QSFEJDUJPO A 0; 1 n n -FU 2f g $ CF UIF BEKBDFODZ NBUSJY PG B TJNQMF VOEJSFDUFE VOXFJHIUFE BOE DPO OFDUFE HSBQI PO n OPEFT BOE F.A/ B GVODUJPO UIBU NBQT A UP B NBUSJY PG UIF TBNF EJNFOTJPO ɩF GPMMPXJOH TVCTFDUJPOT EFTDSJCF MJOL QSFEJDUJPO GVODUJPOT F.A/ UIBU SFTVMU JO NBUSJDFT PG UIF TBNF EJNFOTJPO BT A BOE XIPTF FOUSJFT DBO CF VTFE GPS MJOL QSFEJDUJPO .PTU PG UIFTF NFUIPET SFTVMU JO B QPTJUJWFTFNJEFmOJUF NBUSJY BOE DBO CF RVBMJmFE BT HSBQI LFSOFMT ɩF MFUUFS ˛ XJMM CF VTFE UP EFOPUF QBSBNFUFST PG UIFTF GVODUJPOT n n D R $ 'VODUJPOT PG UIF "EKBDFODZ1=2 .BUSJY1=2 -FU 2 CF UIF EJBHPOBM EFHSFF NBUSJY XJUI Dii Aij D¦ AD¦ D j ɩFO D JT UIF OPSNBMJ[FE BEKBDFODZ NBUSJY 5SBOTGPSNBUJPOT PG AA UIF BEKBDFODZP NBUSJDFT BOE A HJWF SJTF UP UIF FYQPOFOUJBM BOE WPO /FVNBOO HSBQI LFSOFMT F .A/ .˛A/ EXP D FYQ 13&%*$5*/( .*44*/( -*/,4 F . / .˛ / EXP A D FYQ A 1 F .A/ .I ˛A/! NEU D $ 1 F . / .I ˛ /! ; NEU A D $ A XIFSF ˛<1JT B QPTJUJWF QBSBNFUFS ɩF DPOTUSBJOU ˛<1JT SFRVJSFE CZ UIF WPO /FVNBOO LFSOFMT L D A -BQMBDJBO1=2 ,FSOFMT1=2 D ¦ JT UIF DPNCJOBUPSJBM -BQMBDJBO PG UIF HSBQI BOE L D I D¦ LD¦ ¦A D JT UIF OPSNBMJ[FE -BQMBDJBO ɩF -BQMBDJBO NBUSJDFT BSF TJOHVMBS BOE QPTJUJWFTFNJEFmOJUF ɩFJS .PPSF1FOSPTF QTFVEPJOWFSTF JT DBMMFE UIF DPNNVUF UJNF PS SFTJT UBODF EJTUBODF LFSOFM ɩF DPNCJOBUPSJBM -BQMBDJBO NBUSJY JT BMTP LOPXO BT UIF ,JSDIIPĊ NBUSJY EVF UP JUT DPOOFDUJPO UP FMFDUSJDBM SFTJTUBODF OFUXPSLT F .L/ LC COM D F . / C: COM L D L #Z SFHVMBSJ[BUJPO UIF SFHVMBSJ[FE -BQMBDJBO LFSOFMT BSF 1 F .L/ .I ˛L/! COMR D C 1 F . / .I ˛ /! : COMR L D C L "T B TQFDJBM DBTF UIF OPOOPSNBMJ[FE SFHVMBSJ[FE -BQMBDJBO LFSOFM JT DBMMFE UIF SBOEPN ˛ 1 GPSFTU LFSOFM GPS D ɩF OPSNBMJ[FE SFHVMBSJ[FE -BQMBDJBO JT FRVJWBMFOU UP UIF OPSNBMJ[FE .1 ˛ / 1 .1 ˛/.I ˛ / 1 WPO /FVNBOO LFSOFM CZ OPUJOH UIBU C L ¦ D C ¦ A ¦ ɩF IFBU EJĊVTJPO LFSOFM JT EFmOFE BT F .L/ . ˛L/ HEAT D FYQ $ F . / . ˛ /: HEAT L D FYQ $ L ɩF OPSNBMJ[FE˛ IFBU EJĊVTJPO LFSOFM JT FRVJWBMFOU UP UIF OPSNBMJ[FE FYQPOFOUJBM LFSOFM . ˛ / e¦ .˛ / FYQ ¦ D FYQ L A A UƒU T k 3BOL 3FEVDUJPO 6TJOH UIF FJHFOWBMVF EFDPNQPTJUJPO D B SBOL BQQSPYJNB ƒ UJPO PG A L BOE JT HJWFO CZ B USVODBUJPO MFBWJOH POMZ k FJHFOWBMVFT BOE FJHFOWFDUPST JO ƒ U A L BOE T F.k/.A/ U.k/ƒ.k/U : D .k/ A 'PS BOE A UIF CJHHFTU FJHFOWBMVFT BSF VTFE XIJMF UIF TNBMMFTU FJHFOWBMVFT BSF VTFE GPS UIF -BQMBDJBO NBUSJDFT F.k/.A/ DBO CF VTFE GPS QSFEJDUJPO JUTFMG PS TFSWF BT UIF CBTJT GPS BOZ PG UIF HSBQI LFSOFMT *O QSBDUJDF POMZ SBOLSFEVDFE WFSTJPOT PG HSBQI LFSOFMT DBO CF DPNQVUFE GPS MBSHF OFUXPSLT n 1BUI $PVOUJOH 0OF DBO FYQMPJU UIF GBDU UIBU QPXFST A PG UIF BEKBDFODZ NBUSJY PG BO VOXFJHIUFE HSBQI DPOUBJO UIF OVNCFS PG QBUIT PG MFOHUI n DPOOFDUJOH BMM OPEF QBJST 0O UIF 40$*"- 5*& "/"-:4*4 CBTJT UIBU OPEFT DPOOFDUFE CZ NBOZ QBUIT TIPVME CF DPOTJEFSFE OFBSFS UP FBDI PUIFS UIBO OPEFT DPOOFDUFE CZ GFX QBUIT B XFJHIUFE NFBO PG QPXFST PG A DBO CF DPNQVUFE BT B MJOL QSFEJDUJPO GVODUJPO d i FP .A/ ˛i A : D i 0 XD ɩF SFTVMU JT B NBUSJY QPMZOPNJBM PG EFHSFF d ɩF DPFċDJFOUT ˛i TIPVME CF EFDSFBTJOH UP SFnFDU UIF BTTVNQUJPO UIBU MJOLT BSF NPSF MJLFMZ UP BSJTF CFUXFFO OPEFT UIBU BSF DPOOFDUFE CZ TIPSU QBUIT UIBO OPEFT DPOOFDUFE CZ MPOH QBUIT ɩVT TVDI B GVODUJPO UBLFT CPUI QBUI MFOHUIT BOE QBUI DPVOUT JOUP BDDPVOU ɩF FYQPOFOUJBM BOE WPO /FVNBOO LFSOFMT DBO CF FYQSFTTFE BT JOmOJUF TFSJFT PG NBUSJY QPXFST i 1 ˛ . ˛A/ Ai FYQ $ D iŠ i 0 XD 1 1 i i .I ˛A/! ˛ A : $ D i 0 XD F F.X/ X (FOFSBMJ[BUJPO "MM UIFTF MJOL QSFEJDUJPO NFUIPET DBO CF XSJUUFO BT D XIFSF A; ; L; F JT POF PG f A Lg BOE JT FJUIFS B NBUSJY QPMZOPNJBM NBUSJY QTFVEP JOWFSTJPO UIF NBUSJY FYQPOFOUJBM PS B GVODUJPO EFSJWFE QJFDFXJTF MJOFBSMZ GSPN POF PG UIFTF 4VDI GVODUJPOT F IBWF UIF A UƒU T F.A/ UF.ƒƒƒ/U T QSPQFSUZ UIBU GPS B TZNNFUSJD NBUSJY D UIFZ DBO CF XSJUUFO BT D ƒ XIFSF F.ƒƒ/ BQQMJFT UIF DPSSFTQPOEJOH GVODUJPO PO SFBMT UP FBDI FJHFOWBMVF TFQBSBUFMZ *O PUIFS XPSET UIFTF MJOL QSFEJDUJPO NFUIPET SFTVMU JO QSFEJDUJPO NBUSJDFT UIBU BSF TJNVMUBOFPVTMZ EJBH POBMJ[BCMF XJUI UIF LOPXO BEKBDFODZ NBUSJY 4VDI GVODUJPOT BSF DBMMFE TQFDUSBM USBOTGPSNBUJPOT F BOE DBO CF XSJUUFO BT 2 S (JWFO B HSBQI G UIF UBSHFU JT UP mOE B TQFDUSBM USBOTGPSNBUJPO F UIBU QFSGPSNT XFMM BU MJOL QSFEJDUJPO GPS UIJT QBSUJDVMBS HSBQI 5P UIBU FOE UIF FEHF TFU PG G JT EFWJEFE JOUP B USBJOJOH TFU BOE B UFTU TFU BOE UIFO UIF QVSQPTF JT UP MPPL GPS BO F UIBU NBQT UIF USBJOJOH TFU UP UIF UFTU TFU XJUI NJOJNBM FSSPS 'PSNBMMZ MFU A BOE B CF UIF BEKBDFODZ NBUSJDFT PG UIF USBJOJOH BOE UFTU TFU SFTQFDUJWFMZ A JT UIF TPVSDF NBUSJY BOE B JT UIF UBSHFU NBUSJY ɩF TPMVUJPO UP UIF GPMMPXJOH PQUJNJ[BUJPO QSPCMFN HJWFT UIF PQUJNBM TQFDUSBM USBOTGPSNBUJPO GPS UIF UBTL PG QSFEJDUJOH UIF FEHFT JO UIF UFTU TFU 1SPCMFN -FU A BOE B CF UXP BEKBDFODZ NBUSJDFT PWFS UIF TBNF WFSUFY TFU " TQFDUSBM USBOT GPSNBUJPO UIBU NBQT A BOE B XJUI NJOJNBM FSSPS JT HJWFO CZ UIF TPMVUJPO UP F.A/ B F s:t: F NJOF k $ k 2 S F XIFSF k#k EFOPUFT UIF 'SPCFOJVT OPSN 13&%*$5*/( .*44*/( -*/,4 5BCMF 4VNNBSZ PG OFUXPSL EBUBTFUT VTFE JO UIF FYQFSJNFOUT <> Name #Vertices #Edges Weights k Description DBLP 12,563 49,779 {1} 126 Citation graph Hep-th 27,766 352,807 {1} 54 Citation graph Advogato 7,385 57,627 { 0.6, 0.8, 1.0} 192 Trust network Slashdot 71,523 488,440 { 1, +1 } 24 Friend/foe network Epinions 131,828 841,372 { 1, +1 } 14 Trust/distrust network WWW 325,729 1,497,135 {1} 49 Hyperlink graph WT10G 1,601,787 8,063,026 {1} 49 Hyperlink graph A UƒU T 1SPCMFN DBO CF TPMWFE CZ DPNQVUJOH UIF FJHFOWBMVF EFDPNQPTJUJPO D BOE VTJOH UIF GBDU UIBU UIF 'SPCFOJVT OPSN JT JOWBSJBOU VOEFS NVMUJQMJDBUJPO CZ BO PSUIPHPOBM NBUSJY T T F.A/ B F UF.ƒƒƒ/U B F F.ƒƒƒ/ U BU F : k $ k Dk $ k Dk $ k ɩF 'SPCFOJVT OPSN JO DBO CF EFDPNQPTFE JOUP UIF TVN PG TRVBSFT PG PĊEJBHPOBM F.ƒƒƒ/ U T BU F FOUSJFT PG $ XIJDI JT JOEFQFOEFOU PG BOE JOUP UIF TVN PG TRVBSFT PG JUT EJBHPOBM FOUSJFT ɩJT MFBET UP UIF GPMMPXJOH MFBTUTRVBSFT QSPCMFN FRVJWBMFOU UP 1SPCMFN ƒ T 1SPCMFN *G UƒU JT UIF FJHFOWBMVF EFDPNQPTJUJPO PG A UIFO UIF TPMVUJPO UP 1SPCMFN F.ƒƒƒ/ii f.ƒƒii/ f .x/ JT HJWFO CZ D XIFSF JT UIF TPMVUJPO UP UIF GPMMPXJOH NJOJNJ[BUJPO QSPCMFN T 2 .f .ƒƒii/ U i BU i / : NJOf $ " " i X ɩJT QSPCMFN JT B POFEJNFOTJPOBM MFBTUTRVBSFT DVSWF mUUJOH QSPCMFN PG TJ[F n 4JODF FBDI GVODUJPO F.A/ DPSSFTQPOET UP B GVODUJPO f .x/ POF DBO DIPPTF B MJOL QSFEJDUJPO GVODUJPO F BOE MFBSO JUT QBSBNFUFST CZ JOTQFDUJOH UIF DPSSFTQPOEJOH DVSWF mUUJOH QSPCMFN 3FTVMUT ɩF JOTQFDUFE OFUXPSL EBUBTFUT BSF TVNNBSJ[FE JO 5BCMF %#-1¤ JT B DJUBUJPO HSBQI )FQUI JT UIF DJUBUJPO HSBQI PG "SYJWT IJHI FOFSHZ QIZTJDTUIFPSZ TFDUJPO "EWPHBUP JT B USVTU OFUXPSL XJUI UISFF MFWFMT PG USVTU 4MBTIEPU JT B TPDJBM OFUXPSL XIFSF VTFST UBH FBDI PUIFS BT GSJFOET BOE GPFT &QJOJPOT JT BO PQJOJPO TJUF XIFSF VTFST DBO BHSFF PS EJTBHSFF XJUI FBDI PUIFS 888 BOE 85( BSF IZQFSMJOL OFUXPSL EBUBTFUT FYUSBDUFE GSPN B TVCTFU PG UIF 8PSME 8JEF 8FC "T B NFBTVSF PG QFSGPSNBODF GPS UIF MJOL QSFEJDUJPO NFUIPET UIF 1FBSTPO DPSSFMBUJPO DPFG mDJFOU CFUXFFO UIF QSFEJDUFE BOE LOPXO SBUJOHT JO UIF UFTU TFU JT DPNQVUFE ɩF DPSSFMBUJPO SFQ SFTFOUT B USBEFPĊ CFUXFFO UIF SPPU NFBO TRVBSFE FSSPS UP NJOJNJ[F BOE NPSF EBUBTFUEFQFOEFOU NFBTVSFT TVDI BT QSFDJTJPO BOE SFDBMM XIJDI DBOOPU CF BQQMJFE UP BMM EBUBTFUT ɩF SFTVMUT PG UIF FWBMVBUJPO BSF TIPXO JO 5BCMF ¤IUUQECMQVOJUSJFSEF 40$*"- 5*& "/"-:4*4 Rational Commute time 0.554 Polynomial Sum of powers 0.563 Polynomial Sum of powers 0.739 Exponential Heatusion di f 0.453 Linear function Rank reduction 0.293 > Nonnegative odd polynomial Sum of powers 0.354 B B + B Nonnegative odd polynomial Sum of powers 0.263 + B B LB L A A AB LA AA ɩF SFTVMUT PG UIF FYQFSJNFOUBM FWBMVBUJPO 'PS FBDI EBUBTFU UIF TPVSDFUBSHFU NBUSJDFT UIF DVSWF mUUJOH NPEFM BOE UIF DBLP Hep-th WWW Dataset Best transformation Best fitting curve Best graph kernel Correlation WT10G Slashdot Epinions Advogato BCMF 5 MJOL QSFEJDUJPO NFUIPE UIBU QFSGPSN CFTU BSF HJWFO < */'&33*/( 40$*"- 5*&4 */'&33*/( 40$*"- 5*&4 ɩF PCKFDUJWF PG JOGFSSJOH TPDJBM UJFT JT UP FĊFDUJWFMZ JOGFS UIF UZQF PG TPDJBM SFMBUJPOTIJQT CFUXFFO UXP VTFST .PSF QSFDJTFMZ XF mSTU EFmOF UIF PVUQVU PG PVS QSPCMFN OBNFMZ SFMBUJPOTIJQ TFNBOUJDT 4QFDJmDBMMZ HJWFO VTFST CFIBWJPS IJTUPSZ BOE JOUFSBDUJPOT CFUXFFO VTFST DBO XF FTUJNBUF IPX MJLFMZ UIFZ BSF UP CF GBNJMZ NFNCFST PS DPMMFBHVFT 0OF DIBMMFOHF JT IPX UP EFTJHO B VOJmFE NPEFM TP UIBU JU DBO CF FBTJMZ BQQMJFE UP EJĊFSFOU EPNBJOT PS EJĊFSFOU OFUXPSLT ɩFSF FYJTU B GFX SFMBUFE TUVEJFT 'PS FYBNQMF %JFIM FU BM <> USJFE UP JEFOUJGZ UIF SFMBUJPOTIJQT CZ MFBSOJOH B SBOLJOH GVODUJPO 8BOH FU BM <> QSPQPTFE BO VOTVQFSWJTFE BMHPSJUIN GPS NJOJOH UIF BEWJTPS BEWJTFF SFMBUJPOTIJQT GSPN UIF QVCMJDBUJPO OFUXPSL )PXFWFS %JFI FU BM <> POMZ DPOTJEFST UIF DPNNVOJDBUJPO BSDIJWF XIJMF 8BOH FU BM <> JT B EPNBJOTQFDJmD VOTVQFSWJTFE BMHPSJUIN #PUI BMHPSJUINT BSF OPU FBTZ UP FYUFOE UP PUIFS EPNBJOT "OPUIFS DIBMMFOHF JT UIBU POMJOF TPDJBM OFUXPSLT BSF CFDPNJOH NPSF BOE NPSF DPNQMFY BOE EZOBNJD &WFO UIF CFTU QFSGPSNBODF BDIJFWFE CZ UIF TUBUFPGUIFBSU BMHPSJUINT JT TUJMM VOEFS ɩF SFTVMU JT VOTBUJTGBDUPSZ BOE JOWBSJBCMZ DPOUBJOT B OVNCFS PG FSSPST " QSPNJTJOH TPMVUJPO JT UP EFTJHO BO JOUFSBDUJWF JOUFSGBDF UP BMMPX VTFST UP QSPWJEF GFFECBDLT PO UIF JOGFSSJOH SFTVMUT )PXFWFS XF TIPVME CF BXBSF UIBU UIF JOUFSBDUJWF QSPDFTT NJHIU CF UFEJPVT FSSPSQSPOF BOE UJNF DPOTVNJOH 'PS FYBNQMF GPS JOGFSSJOH BEWJTPSBEWJTFF SFMBUJPOTIJQT GSPN UIF DPBVUIPS OFUXPSL BO BVUIPS NBZ IBWF IVOESFET PG DPBVUIPST© ɩF VTFS NBZ TPPO CFDPNF UJSFE JG TIFIF JT BTLFE UP DBSFGVMMZ HP UISPVHI BMM IFSIJT SFMBUJPOTIJQT UP WBMJEBUF UIF JOGFSSFE SFTVMUT *EFBMMZ BO BMHPSJUIN TIPVME CF BCMF UP BDUJWFMZ TFMFDU POMZ B GFX QPUFOUJBMMZ XSPOH SFMBUJPOTIJQT UP RVFSZ UIF VTFS JOTUFBE PG QBTTJWFMZ XBJUJOH GPS VTFS GFFECBDLT ɩF QSPCMFN JT SFGFSSFE UP BT BDUJWFMZ MFBSOJOH UP JOGFS TPDJBM UJFT 5P JMMVTUSBUF UIF QSPCMFN 'JHVSF HJWFT BO FYBNQMF PG BDUJWFMZ JOGFSSFE UJFT JO B NPCJMF DPNNVOJDBUJPO OFUXPSL ɩF MFGU mHVSF HJWFT UIF JOQVU PG PVS QSPCMFN B NPCJMF TPDJBM OFUXPSL XIJDI DPOTJTUT PG VTFST DBMMT NBEF BOE NFTTBHFT TFOU CFUXFFO VTFST BOE VTFST BUUSJCVUF JOGPS NBUJPO TVDI BT MPDBUJPO ɩF PCKFDUJWF JT UP DMBTTJGZ UIF UZQF PG TPDJBM SFMBUJPOTIJQT JO UIF OFUXPSL ɩF NJEEMF mHVSF TIPXT UIF SFTVMU PG UIF QSPQPTFE 1-1'(. NPEFM B TFNJTVQFSWJTFE MFBSOJOH NPEFM ɩF CMVF TPMJE MJOFT TUBOE GPS GSJFOE SFMBUJPOTIJQ CFUXFFO VTFST BOE UIF HSFFO EBTI MJOFT JOEJDBUF DPMMFBHVFT ɩF QSPCBCJMJUZ BTTPDJBUFE XJUI FBDI SFMBUJPOTIJQ SFQSFTFOUT IPX DPOmEFOU UIF MFBSOJOH NPEFM JT JO UIF JOGFSSFE UZQF PG UIF SFMBUJPOTIJQ 'VSUIFS BO BDUJWF MFBSOJOH BMHP SJUIN TFMFDUT B VODFSUBJO SFMBUJPOTIJQ BTTPDJBUFE XJUI B RVFTUJPO NBSL UP RVFSZ UIF VTFS 0ODF UIF VTFS HJWFT UIF BOTXFS UIF MFBSOJOH NPEFM QSPQBHBUFT UIF DPSSFDUJPO JO UIF TPDJBM OFUXPSL BOE GVSUIFS DPSSFDUT PUIFS SFMBUJPOTIJQT ɩFSFGPSF UIF GVOEBNFOUBM QSPCMFN JT IPX UP EFTJHO B nFYJCMF NPEFM GPS FĊFDUJWFMZ BOE FċDJFOUMZ MFBSOJOH UP JOGFS TPDJBM UJFT JO EJĊFSFOU OFUXPSLT ɩJT QSPCMFN JT OPOUSJWJBM BOE QPTFT B TFU PG VOJRVF DIBMMFOHFT 'JSTU XIBU BSF UIF VOEFSMZJOH GBDUPST UIBU GPSN B TQFDJmD UZQF PG TPDJBM SFMBUJPOTIJQ 4FDPOE UIF JOQVU TPDJBM OFUXPSL JT QBSUJBMMZ MBCFMFE 8F NBZ IBWF TPNF MBCFMFE SFMBUJPOTIJQT CVU NPTU PG UIF SFMBUJPOTIJQT BSF VOLOPXO 5P MFBSO B IJHIRVBMJUZ QSFEJDUJWF NPEFM ©"O FYBNQMF DBO CF GPVOE PO IUUQBSOFUNJOFSPSHQFSTPOKJBXFJIBOIUNM 40$*"- 5*& "/"-:4*4 'JHVSF "O FYBNQMF PG MFBSOJOH UP JOGFS TPDJBM UJFT JO B NPCJMF DPNNVOJDBUJPO OFUXPSL ɩF MFGU mHVSF JT UIF JOQVU PG PVS QSPCMFN BOE UIF NJEEMF mHVSF TIPXT UIF PVUQVU UIF JOGFSSFE SFMBUJPOTIJQT PG UIF QSPCMFN ɩF SFMBUJPOTIJQ BTTPDJBUFE XJUI UIF RVFTUJPO NBSL JOEJDBUFT B SFMBUJPOTIJQ TFMFDUFE CZ BO BDUJWF MFBSOJOH BMHPSJUIN UP RVFSZ UIF VTFS ɩF SJHIU mHVSF JT UIF JNQSPWFE SFTVMU XJUI UIF VTFST GFFECBDL WJB BDUJWF MFBSOJOH XF TIPVME OPU POMZ DPOTJEFS UIF LOPXMFEHF QSPWJEFE CZ UIF MBCFMFE SFMBUJPOTIJQT CVU BMTP MFWFSBHF UIF VOMBCFMFE OFUXPSL JOGPSNBUJPO ɩJSE IPX EPFT POF NBLF PQUJNBM VTF PG VTFS JOUFSBDUJPO ɩF TFMFDUJPO TIPVME DPOTJEFS CPUI UIF VODFSUBJOUZ BOE UIF OFUXPSL TUSVDUVSF JOGPSNBUJPO 'JOBMMZ SFBM TPDJBM OFUXPSLT BSF HFUUJOH CJHHFS XJUI UIPVTBOET FWFO NJMMJPOT PG OPEFT *U JT JNQPSUBOU UP EFWFMPQ B NFUIPE UIBU DBO TDBMF XFMM UP SFBM MBSHF OFUXPSLT *O UIF GPMMPXJOH XF GPSNBMMZ GPSNVMBUF UIF QSPCMFN PG JOGFSSJOH B TPDJBM SFMBUJPOTIJQ JO MBSHF OFUXPSLT BOE QSPQPTF B QBSUJBMMZ MBCFMFE QBJSXJTF GBDUPS HSBQI NPEFM 1-1'(. 5P NBLF PQUJNBM VTF PG VTFS JOUFSBDUJPOT UXP TUSBUFHJFTBO JOnVFODF NBYJNJ[BUJPOCBTFE TUSBU FHZ BOE B CFMJFG NBYJNJ[BUJPOCBTFE TUSBUFHZXFSF EFWJTFE UP BDUJWFMZ TFMFDU QPUFOUJBMMZ XSPOH CVU NPTU VTFGVM SFMBUJPOTIJQT UP RVFSZ UIF VTFS 8F GVSUIFS FYUFOE UIF NPEFM CZ JODPSQPSBUJOH TPDJBM UIFPSJFT JOUP UIF TFNJTVQFSWJTFE MFBSOJOH GSBNFXPSL *O UIJT XBZ UIF NPEFM JT BCMF UP TVQQPSU USBOTGFSSJOH TVQFSWJTFE JOGPSNBUJPO GSPN B TPVSDF OFUXPSL UP IFMQ JOGFS TPDJBM UJFT JO B IFUFSPHFOFPVT UBSHFU OFUXPSL */'&33*/( 40$*"- 5*&4 130#-&. '03.6-"5*0/ G .V; E/ ɩF JOQVU JT TUJMM B TPDJBM OFUXPSL D ɩF PVUQVU PG UIF QSPCMFN IFSF BSF SFMBUJPOTIJQ TFNBOUJDT %FmOJUJPO 3FMBUJPOTIJQ TFNBOUJDT 3FMBUJPOTIJQ TFNBOUJDT JT B USJQMF .eij ;rij ;pij / XIFSF eij E rij 2 JT B TPDJBM SFMBUJPOTIJQ 2 Y JT B MBCFM BTTPDJBUFE XJUI UIF SFMBUJPOTIJQ Y JT UIF TFU PG BMM UIF MBCFMT pij JT UIF QSPCBCJMJUZ DPOmEFODF PCUBJOFE CZ BO BMHPSJUIN GPS JOGFSSJOH SFMBUJPOTIJQ UZQF 4PDJBM SFMBUJPOTIJQT NJHIU CF VOEJSFDUFE JO TPNF OFUXPSLT FH UIF GSJFOETIJQ EJTDPWFSFE GSPN UIF NPCJMF DPNNVOJDBUJPO OFUXPSL PS EJSFDUFE JO PUIFS OFUXPSLT FH UIF BEWJTPSBEWJTFF SFMBUJPOTIJQ JO UIF QVCMJDBUJPO OFUXPSL 5P CF DPOTJTUFOU XF EFmOF BMM TPDJBM SFMBUJPOTIJQT BT EJSFDUFE SFMBUJPOTIJQT *O BEEJUJPO SFMBUJPOTIJQT NBZ CF TUBUJD FH UIF GBNJMZNFNCFS SFMBUJPO TIJQ PS EZOBNJD PWFS UJNF FH DPMMFBHVF SFMBUJPOTIJQ *O UIJT CPPL XF GPDVT PO TUBUJD SFMBUJPO TIJQT BOE MFBWF UIF EZOBNJD DBTF UP PVS GVUVSF XPSL 5P JOGFS SFMBUJPOTIJQ TFNBOUJDT XF DPVME DPOTJEFS EJĊFSFOU GBDUPST TVDI BT VTFSTQFDJmD JOGPSNBUJPO MJOLTQFDJmD JOGPSNBUJPO BOE HMPCBM DPOTUSBJOUT DG 5BCMF GPS FYBNQMFT 'PS FYBNQMF UP EJTDPWFS BEWJTPSBEWJTFF SFMBUJPOTIJQT GSPN B QVCMJDBUJPO OFUXPSL XF DBO DPOTJEFS IPX NBOZ QBQFST XFSF DPBVUIPSFE CZ UXP BVUIPST IPX NBOZ QBQFST JO UPUBM BO BVUIPS IBT QVC MJTIFE BOE XIFO UIF mSTU QBQFS XBT QVCMJTIFE CZ FBDI BVUIPS #FTJEFT UIFSF NBZ FYJTU TPNF MBCFMFE SFMBUJPOTIJQT 'PSNBMMZ XF DBO EFmOF UIF JOQVU PG PVS QSPCMFN B QBSUJBMMZ MBCFMFE OFU XPSL %FmOJUJPO 1BSUJBMMZ MBCFMFE OFUXPSL " QBSUJBMMZ MBCFMFE OFUXPSL JT BO BVHNFOUFE TPDJBM G .V; EL;EU ;RL; W / EL OFUXPSL EFOPUFE BT D XIFSF JT B TFU PG MBCFMFE SFMBUJPOTIJQT BOE EU EL EU E RL JT B TFU PG VOMBCFMFE SFMBUJPOTIJQT XJUI [ D JT B TFU PG MBCFMT DPSSFTQPOEJOH EL W V UP UIF SFMBUJPOTIJQT JO JT BO BUUSJCVUF NBUSJY BTTPDJBUFE XJUI VTFST JO XIFSFth FBDI SPX DPSSFTQPOET UP B VTFS FBDI DPMVNO BO BUUSJCVUF BOE BO FMFNFOU wij UIF WBMVF PG UIF j BUUSJCVUF PG VTFS vi #BTFE PO UIF BCPWF DPODFQUT XF DBO EFmOF UIF QSPCMFN PG JOGFSSJOH TPDJBM SFMBUJPOTIJQT (JWFO B QBSUJBMMZ MBCFMFE OFUXPSL UIF HPBM JT UP EFUFDU UIF UZQFT MBCFMT PG BMM VOLOPXO SFMBUJPO TIJQT JO UIF OFUXPSL .PSF QSFDJTFMZ XF IBWF UIF GPMMPXJOH 1SPCMFN G L U L 4PDJBM SFMBUJPOTIJQ NJOJOH (JWFO B QBSUJBMMZ MBCFMFE OFUXPSL D .V; E ;E ;R ; 8/ UIF PCKFDUJWF JT UP MFBSO B QSFEJDUJWF GVODUJPO f G .V; EL;EU ;RL; W / R: W D ! 40$*"- 5*& "/"-:4*4 "OPUIFS JNQPSUBOU RVFTUJPO JT IPX XF DBO MFBSO UIF NBQQJOH GVODUJPO f FĊFDUJWFMZ *O NBOZ TJUVBUJPOT MBCFMFE EBUB JT MJNJUFE BOE FYQFOTJWF ɩF QSPCMFN JT DBO XF EFTJHO B TUSBUFHZ UP BDUJWFMZ MFBSO UIF NPEFM XJUI NJOJNBM MBCFMJOH DPTU 'PSNBMMZ XF IBWF UIF GPMMPXJOH 1SPCMFN G L U L "DUJWF SFMBUJPOTIJQ NJOJOH (JWFO B QBSUJBMMZ MBCFMFE OFUXPSL D .V; E ;E ;R ; W / BOE B MBCFMJOH CVEHFU b OVNCFS PG VTFS JOUFSBDUJPOT 0VS PCKFD A EU b UJWF JT UP TFMFDU B TVCTFU PG VOLOPXO SFMBUJPOTIJQT ! XJUIJO UIF DPOTUSBJOU PG UP MBCFM TP UIBU UIF QFSGPSNBODF PG QSFEJDUJWF GVODUJPO f DBO CF NBYJNBMMZ JNQSPWFE ɩFSFGPSF UIF QSPCMFN JT IPX UP mOE B GVODUJPO f UIBU DBO MFWFSBHF CPUI UIF MBCFMFE SFMBUJPOTIJQT BOE UIF VOMBCFMFE SFMBUJPOTIJQT UP JOGFS UIF VOLOPXO SFMBUJPOTIJQT 6/461&37*4&% -&"3/*/( 50 */'&3 40$*"- 5*&4 "DRVJSJOH TVċDJFOU MBCFMFE SFMBUJPOTIJQT JT BMXBZT FYQFOTJWF -FU VT CFHJO XJUI UIF VOTVQFSWJTFE MFBSOJOH NFUIPE GPS JOGFSSJOH UIF UZQF PG TPDJBM SFMBUJPOTIJQT XJUIPVU MBCFMFE EBUB 4VDI B NFUIPE JT VTVBMMZ UBTLPSJFOUFE 'PS FYBNQMF 8BOH FU BM <> QSPQPTFE B UXPTUBHF GSBNFXPSL SFGFSSFE UP BT 51'( GPS JOGFSSJOH BEWJTPSBEWJTFF SFMBUJPOTIJQT JO UIF DPBVUIPS OFUXPSL ɩF NBJO JEFB JT UP MFWFSBHF B UJNFDPOTUSBJOFE QSPCBCJMJTUJD GBDUPS HSBQI NPEFM UP EFDPNQPTF UIF KPJOU QSPCBCJMJUZ PG UIF VOLOPXO BEWJTPS PG FWFSZ BVUIPS ɩF UJNFSFMBUFE JOGPSNBUJPO BTTPDJBUFE UP UIF IJEEFO TPDJBM SPMF JT DBQUVSFE WJB GBDUPS GVODUJPOT XIJDI GPSN UIF CBTJD DPNQPOFOUT PG UIF GBDUPS HSBQI NPEFM #Z NBYJNJ[JOH UIF KPJOU QSPCBCJMJUZ PG UIF GBDUPS HSBQI POF DBO JOGFS UIF SFMBUJPOTIJQ BOE DPNQVUF B SBOLJOH TDPSF GPS FBDI SFMBUJPOTIJQ PO UIF DBOEJEBUF HSBQI .PSF TQFDJmDBMMZ BU UIF mSTU TUBHF PG UIF GSBNFXPSL DPNNPO TFOTF JT EFmOFE BT SFDPHOJ[ JOH JOUFSFTUJOH TFNBOUJD SFMBUJPOTIJQT )FSF UIF BVUIPST USZ UP NBLF B GFX HFOFSBM BTTVNQUJPOT CBTFE PO DPNNPO LOPXMFEHF BCPVU BEWJTPSBEWJTFF SFMBUJPOTIJQT t "U FBDI UJNF t EVSJOH UIF QVCMJDBUJPO IJTUPSZ PG BO BVUIPS x x JT FJUIFS CFJOH BEWJTFE PS OPU CFJOH BEWJTFE 0ODF x TUBSUT UP BEWJTF BOPUIFS BVUIPS JU XJMM OPU CF BEWJTFE BHBJO t "OPUIFS BTTVNQUJPO JOEJDBUFT UIBU GPS B HJWFO QBJS PG BEWJTPS BOE BEWJTFF UIF BEWJTPS BMXBZT IBT B MPOHFS QVCMJDBUJPO IJTUPSZ UIBO UIF BEWJTFF #BTFE PO UIF UXP BTTVNQUJPOT UIF GSBNFXPSL QSPDFTTFT UIF UBTL JO UIF GPMMPXJOH UXP TUBHFT 4UBHF 1SFQSPDFTTJOH ɩF QVSQPTF PG QSFQSPDFTTJOH JT UP HFOFSBUF UIF DBOEJEBUF HSBQI H 0 BOE SFEVDF UIF TFBSDI TQBDF XIJMF LFFQJOH UIF SFBM BEWJTPS OPU FYDMVEFE GSPN UIF DBOEJEBUF QPPM JO NPTU DBTFT 'JSTU POF OFFET UP HFOFSBUF BDDPSEJOH UP UIF DPBVUIPS JOGPSNBUJPO B IPNPHFOFPVT BVUIPS OFUXPSL G0 CZ QSPDFTTJOH UIF QBQFST JO UIF OFUXPSL POF CZ POF 'PS FBDI QBQFS pi XF DBO DPOTUSVDU BO FEHF CFUXFFO FWFSZ QBJS PG JUT BVUIPST ɩFO B mMUFSJOH QSPDFTT JT QFSGPSNFE UP SFNPWF VOMJLFMZ SFMBUJPOT PG BEWJTPSBEWJTFF 'PS FBDI FEHF eij PO G0 ai BOE aj IBT DPMMBCPSBUJPO 5P EFDJEF XIFUIFS aj JT ai T QPUFOUJBM BEWJ TPS UIF GPMMPXJOH DPOEJUJPOT BSF DIFDLFE 'JSTU UIF TFDPOE BTTVNQUJPO JT DIFDLFE 0OMZ JG aj */'&33*/( 40$*"- 5*&4 TUBSUFE UP QVCMJTI FBSMJFS UIBO ai JT UIF QPTTJCJMJUZ DPOTJEFSFE 4FDPOE TPNF IFVSJTUJD SVMFT BSF BQQMJFE XIJDI BSF CBTFE PO UIF QSJPS JOUVJUJWF LOPXMFEHF BCPVU BEWJTPSBEWJTFF SFMBUJPOT 'PS NPSF EFUBJMFE EFmOJUJPOT PG UIPTF SVMFT QMFBTF SFGFS UP 8BOH FU BM <> 4UBHF DzF GBDUPS HSBQI NPEFM 'SPN UIF DBOEJEBUF HSBQI H 0 XF LOPX UIF QPUFOUJBM BEWJTPST PG FBDI BVUIPS BOE UIF MJLFMJIPPE CBTFE PO MPDBM JOGPSNBUJPO #Z NPEFMJOH UIF OFUXPSL BT B XIPMF XF DBO JODPSQPSBUF CPUI TUSVDUVSBM JOGPSNBUJPO BOE UFNQPSBM DPOTUSBJOU BOE CFUUFS BOBMZ[F UIF SFMBUJPOTIJQ BNPOH JOEJWJEVBM MJOLT #Z MFBSOJOH UIF GBDUPS HSBQI NPEFM XF DBO mOE B DPOmHVSBUJPO PG UIF MBUFOU WBSJBCMFT GPS FBDI OPEF JO UIF DBOEJEBUF HSBQI H 0 UIBU NBYJNJ[F UIF PCKFDUJWF GVODUJPO 'PS MFBSOJOH UIF NPEFM POF DBO DPOTJEFS UIF TVNQSPEVDU BOE UIF KVODUJPO USFF BMHPSJUINT <> 3FTVMUT 5P FWBMVBUF UIF VOTVQFSWJTFE NFUIPE XF USJFE UP DPMMFDU BO BDBEFNJD DJUBUJPO EBUBCBTF "SOFU.JOFS <>ņ BOE UIF MBCFMFE BEWJTPSBEWJTFF SFMBUJPOTIJQT GSPN TFWFSBM POMJOF SFTPVSDFT TVDI BT UIF .BUIFNBUJDT (FOFBMPHZ QSPKFDU BOE "* (FOFBMPHZ QSPKFDU ɩF EBUBCBTF DPOTJTUT PG BVUIPST BOE QVCMJDBUJPOT GSPN o #Z BQQMZJOH UIF QSPQPTFE 51'( NPEFM UP UIF QVCMJDBUJPO EBUBTFU XF DPVME BDIJFWF B QFSGPSNBODF PG o JO UFSNT PG ' .FBTVSF 461&37*4&% -&"3/*/( 50 */'&3 40$*"- 5*&4 8F OPX JOUSPEVDF IPX UP MFWFSBHF TVQFSWJTFE MFBSOJOH GPS JOGFSSJOH TPDJBM UJFT #BTJDBMMZ XF IBWF UISFF CBTJD JOUVJUJPOT 'JSTU UIF VTFSTQFDJmD PS MJOLTQFDJmD BUUSJCVUFT XJMM DPOUBJO JNQMJDJU JOGPS NBUJPO BCPVU UIF SFMBUJPOTIJQT 'PS FYBNQMF UXP VTFST XIP NBLF B OVNCFS PG DBMMT JO XPSLJOH IPVST NJHIU CF DPMMFBHVFT XIJMF UXP VTFST XIP GSFRVFOUMZ DPOUBDU XJUI FBDI PUIFS JO UIF FWFOJOH BSF NPSF MJLFMZ UP CF GBNJMZ NFNCFST PS JOUJNBUF GSJFOET 4FDPOE SFMBUJPOTIJQT BNPOH EJĊFSFOU VTFST NBZ IBWF B DPSSFMBUJPO 'PS FYBNQMF JO UIF NPCJMF OFUXPSL JG VTFS vi NBLFT B DBMM UP VTFS vj JNNFEJBUFMZ BGUFS DBMMJOH VTFS vk UIFO VTFS vi NBZ IBWF B TJNJMBS SFMBUJPOTIJQ GBNJMZ NFNCFS PS DPMMFBHVF XJUI VTFS vj BOE VTFS vk ɩJSE XF BMTP OFFE UP DPOTJEFS TPNF HMPCBM DPOTUSBJOUT TVDI BT DPNNPO LOPXMFEHF PS VTFSTQFDJmD DPOTUSBJOUT #BTFE PO UIF JOUVJUJPOT BCPWF XF QSPQPTF B 1BSUJBMMZ-BCFMFE 1BJSXJTF 'BDUPS (SBQI .PEFM 1-1'(. ɩJT BMMPXT VT UP UBLF BMM PG UIF GBDUPST NFOUJPOFE BCPWF JOUP BDDPVOU UP CFUUFS JOGFS UIF TPDJBM SFMBUJPOTIJQT 5ZQJDBMMZ UIFSF BSF UXP XBZT UP NPEFM UIF TPDJBM UJF JOGFSSJOH QSPCMFN ɩF mSTU XBZ JT UP NPEFM FBDI VTFS BT B OPEF BOE GPS FBDI OPEF UP FTUJNBUF UIF QSPCBCJMJUZ EJTUSJCVUJPO PG EJĊFSFOU SFMBUJPOTIJQT ɩF SFTVMUBOU HSBQIJDBM NPEFM UIVT DPOTJTUT PG N WBSJBCMF d OPEFT &BDI OPEF DPOUBJOT B "jYj NBUSJY UP SFQSFTFOU UIF QSPCBCJMJUZ EJTUSJCVUJPOT PG EJĊFSFOU SFMBUJPOTIJQT CFUXFFO UIF VTFS BOE IFSIJT OFJHICPST XIFSF d JT UIF OVNCFS PG OFJHICPST PG UIF OPEF ɩJT NPEFM JT JOUVJUJWF CVU JU TVĊFST GSPN TPNF MJNJUBUJPOT 'PS FYBNQMF JU JT EJċDVMU UP NPEFM UIF DPSSFMBUJPOT CFUXFFO UXP SFMBUJPOTIJQT BOE JUT DPNQVUBUJPOBM DPNQMFYJUZ JT IJHI "O BMUFSOBUJWF XBZ JT UP NPEFM FBDI SFMBUJPOTIJQ BT B OPEF JO UIF HSBQIJDBM NPEFM BOE UIF SFMBUJPOTIJQ ņIUUQBNJOFSPSH 40$*"- 5*& "/"-:4*4 y21=coauthor g (y12, y24) y24 PLP-FGM y34=? g (y , y ) g (y , y ) 34 35 y35=? 24 34 y34 y12=advisor y12 y35 g (y45, y35) g (y34,y45) Input: Social Network y45 g (y24, y45) y45=coauthor f(y24,x24) v3 f(y35,x35) v4 f(y12,x12) f(y34,x34) f(y45,x45) v5 r12 r34 r35 v2 r24 r45 v1 relationships 'JHVSF (SBQIJDBM SFQSFTFOUBUJPO PG UIF 1-1'(. NPEFM NJOJOH UBTL CFDPNFT IPX UP QSFEJDU UIF TFNBOUJD MBCFM GPS FBDI SFMBUJPOTIJQ OPEF JO UIF NPEFM ɩJT NPEFM DPOUBJOT M OPEFT 2M XIFO UIF JOQVU TPDJBM OFUXPSL JT VOEJSFDUFE ɩJT NPEFM JT BCMF UP JODPSQPSBUF EJĊFSFOU DPSSFMBUJPOT CFUXFFO SFMBUJPOTIJQT TVDI BT UIF BCPWF JOUVJUJPOT 8F QSPQPTF B 1BSUJBMMZ-BCFMFE 1BJSXJTF 'BDUPS (SBQI .PEFM 1-1'(. 'JHVSF .v ;v / e TIPXT UIF HSBQIJDBM SFQSFTFOUBUJPO PG UIF 1-1'(. &BDI SFMBUJPOTIJQ i1 i2 PS i1i2 JO UIF QBSUJBMMZ MBCFMFE OFUXPSL G JT NBQQFE UP B SFMBUJPOTIJQ OPEF ri JO 1-1'(. 8F EFOPUF UIF Y y1;y2;:::;yM G TFU PG SFMBUJPOTIJQ OPEFT BT Df g ɩF SFMBUJPOTIJQTL JOU BSF QBSUJBMMZ MBCFMFE UIVT BMM OPEFT JO 1-1'(. DBO CF EJWJEFE JOUP UXP TVCTFUT Y BOE Y DPSSFTQPOEJOH UP UIF yi .vi ;vi ;ri i / MBCFMFE BOE VOMBCFMFE SFMBUJPOTIJQT SFTQFDUJWFMZ 'PS FBDI SFMBUJPOTIJQ OPEF D 1 2 1 2 wi ; wi xi XF DPNCJOF UIF BUUSJCVUFT f 1 2 g JOUP B SFMBUJPOTIJQ BUUSJCVUF WFDUPS /PX XF FYQMBJO UIF 1-1'(. JO EFUBJM ɩF SFMBUJPOTIJQT JO UIF JOQVU BSF NPEFMFE CZ SFMBUJPOTIJQ OPEFT JO 1-1'(. $PSSFTQPOEJOH UP UIF UISFF JOUVJUJPOT XF EFmOF UIF GPMMPXJOH UISFF GBDUPST t "UUSJCVUF GBDUPS f .yi ; xi / SFQSFTFOUT UIF QPTUFSJPS QSPCBCJMJUZ PG UIF SFMBUJPOTIJQ yi HJWFO UIF BUUSJCVUF WFDUPS xi t $PSSFMBUJPO GBDUPS g.yi ; G.yi // EFOPUFT UIF DPSSFMBUJPO CFUXFFO UIF SFMBUJPOTIJQT XIFSF G.yi / JT UIF TFU PG DPSSFMBUFE SFMBUJPOTIJQT UP yi t $POTUSBJOU GBDUPS h.yi ; H.yi // SFnFDUT UIF DPOTUSBJOUT CFUXFFO SFMBUJPOTIJQT XIFSF H.yi / JT UIF TFU PG SFMBUJPOTIJQT DPOTUSBJOFE PO yi G .V; EL;EU ;RL; W / (JWFO B QBSUJBMMZ MBCFMFE OFUXPSL D XF DBO EFmOF UIF KPJOU EJT USJCVUJPO PWFS Y BT */'&33*/( 40$*"- 5*&4 p.Y G/ f .yi ; xi /g.yi ; G.yi //h.yi ; H.yi //: j D Yi ɩF UISFF GBDUPST DBO CF JOTUBOUJBUFE JO EJĊFSFOU XBZT *O UIJT CPPL XF VTF FYQPOFOUJBM MJOFBS GVODUJPOT *O QBSUJDVMBS XF EFmOF UIF BUUSJCVUF GBDUPS BT 1 T f .yi ; xi / & ˆˆ.yi ; xi / ; D Z" FYQf g & ˆ XIFSF & JT B XFJHIUJOH WFDUPS BOE ˆ JT B WFDUPS PG GFBUVSF GVODUJPOT 4JNJMBSMZ XF EFmOF UIF DPSSFMBUJPO GBDUPS BOE DPOTUSBJOU GBDUPS BT 1 T g.yi ; G.yi // ˛ g.yi ;yj / D Z˛ FYQf g yj G.yi / 2X 1 T h.yi ; H.yi // ˇ h.yi ;yj / ; D Zˇ FYQf g yj H.yi / 2X XIFSF g BOE h DBO CF EFmOFE BT B WFDUPS PG JOEJDBUPS GVODUJPOT ɩJT GFBUVSF EFmOJUJPO XBT PG UFO VTFE JO B HSBQIJDBM NPEFMT TVDI BT .BSLPW 3BOEPN 'JFMET <> PS $POEJUJPOBM 3BOEPN 'JFMET <> ' .&;˛˛˛;ˇˇˇ/ .PEFM -FBSOJOH -FBSOJOH 1-1'(. JT UP FTUJNBUF B QBSBNFUFS DPOmHVSBUJPO D TP UIBU UIF MPHMJLFMJIPPE PG PCTFSWBUJPO JOGPSNBUJPO MBCFMFE SFMBUJPOTIJQT BSF NBYJNJ[FE 'PS yi s.yi / QSFTFOUBUJPOT TJNQMJDJUZ XFT DPODBUFOBUF BMM GBDUPST T GVODUJPOT GPS B SFMBUJPOTIJQ OPEF BT D .ˆˆˆ.yi ; xi / ; g.yi ;yj / ; h.yi ;yj / / yj yj ɩF KPJOU QSPCBCJMJUZ EFmOFE JO &R DBO CF SFXSJUUFO BTP P 1 T 1 T 1 T p.Y G/ ' s.yi / ' s.yi / ' S ; j D Z FYQf g D Z FYQf g D Z FYQf g i i Y X Z Z"Z˛Zˇ S XIFSF D JT B OPSNBMJ[BUJPO GBDUPS BMTPDBMMFE QBSUJUJPO GVODUJPO JT UIF BHHSFHB S s.yi / UJPO PG GBDUPS GVODUJPOT PWFS BMM SFMBUJPOTIJQ OPEFT JF D i 0OF DIBMMFOHF GPS MFBSOJOH UIF 1-1'(. NPEFM JT UIBUP UIF JOQVU EBUB JT QBSUJBMMZ MBCFMFE 5P DBMDVMBUF UIF QBSUJUJPO GVODUJPO Z POF OFFET UP TVN VQ UIF MJLFMJIPPE PG QPTTJCMF TUBUFT GPS BMM OPEFT JODMVEJOH VOMBCFMFE OPEFT 5P EFBM XJUI UIJT XF VTF UIF MBCFMFE EBUB UP JOGFS VOLOPXO Y Y L Y MBCFMT )FSF j EFOPUFT B MBCFMJOH DPOmHVSBUJPO JOGFSSFE GSPN UIF LOPXO MBCFMT ɩVT XF .' / DBO EFmOF UIF GPMMPXJOH MPHMJLFMJIPPE PCKFDUJWF GVODUJPO O 40$*"- 5*& "/"-:4*4 *OQVU MFBSOJOH SBUF ( ' 0VUQVU MFBSOFE QBSBNFUFST ' ' *OJUJBMJ[F ' SFQFBU L Ep" .Y Y ;G/S $BMDVMBUF j VTJOH -#1 Ep" .Y G/S $BMDVMBUF j VTJOH -#1 $BMDVMBUF UIF HSBEJFOU PG ' BDDPSEJOH UP &R L # Ep" .Y Y ;G/S Ep" .Y G/S r D j $ j 6QEBUF QBSBNFUFS ' XJUI UIF MFBSOJOH SBUF ( ' ' ( # OFX D PME $ #r# VOUJM $POWFSHFODF "MHPSJUIN -FBSOJOH 1-1'(. 1 .' / p.Y L G/ ' T S O D MPH j D MPH Z FYQf g Y Y L Xj ' T S Z D MPH FYQf g $ MPH Y Y L Xj ' T S ' T S : D MPH FYQf g$MPH FYQf g Y Y L Y Xj X 5P TPMWF UIF PCKFDUJWF GVODUJPO XF DPOTJEFS B HSBEJFOU EFDFOU NFUIPE PS B /FXUPO 3BQITPO NFUIPE 4QFDJmDBMMZ XF mSTU DBMDVMBUF UIF HSBEJFOU GPS FBDI QBSBNFUFS ' T T @ L ' S ' S @ .' / MPH Y Y FYQ MPH Y FYQ O j $ @' D " P @' P Á T T L ' Y Y ' S S Y ' S S j FYQ # FYQ T T # D Y Y L ' S $ Y ' S P j FYQ P FYQ L Ep" .Y Y ;G/S Ep" .Y G/S: D P j $ j P "OPUIFS DIBMMFOHF IFSF JT UIBU UIF HSBQIJDBM TUSVDUVSF JO 1-1'(. DBO CF BSCJUSBSZ BOE Ep" .Y G/S NBZ DPOUBJO DZDMFT XIJDI NBLFT JU JOUSBDUBCMF UP EJSFDUMZ DBMDVMBUF UIF FYQFDUBUJPO j " OVNCFS PG BQQSPYJNBUF BMHPSJUINT IBWF CFFO QSPQPTFE TVDI BT -PPQZ #FMJFG 1SPQBHBUJPO -#1 */'&33*/( 40$*"- 5*&4 <> *O UIJT CPPL XF VUJMJ[F -PPQZ #FMJFG 1SPQBHBUJPO 4QFDJmDBMMZ XF BQQSPYJNBUF NBSHJOBM p.yi ' / p.yi ;yj ' / QSPCBCJMJUJFT j BOE j VTJOH -#1 8JUI UIF NBSHJOBM QSPCBCJMJUJFT UIF HSBEJFOU DBO CF PCUBJOFE CZ TVNNJOH PWFS BMM SFMBUJPOTIJQ OPEFT *U JT XPSUI OPUJOH UIBU XF OFFE UP QFSGPSN p.y G/ UIF -#1 QSPDFTT UXJDF JO FBDI JUFSBUJPO POF UJNF GPS FTUJNBUJOH UIF NBSHJOBM QSPCBCJMJUZ j p.y Y L;G/ BOE UIF PUIFS GPS j 'JOBMMZ XJUI UIF HSBEJFOU XF VQEBUF FBDI QBSBNFUFS XJUI B MFBSOJOH SBUF ( ɩF MFBSOJOH BMHPSJUIN JT TVNNBSJ[FE JO "MHPSJUIN *OGFSSJOH 6OLOPXO 4PDJBM 5JFT 8F OPX UVSO UP EFTDSJCJOH IPX UP JOGFS UIF UZQF PG VOLOPXO ' TPDJBM SFMBUJPOTIJQT #BTFE PO MFBSOFE QBSBNFUFST ' XF DBO QSFEJDU UIF MBCFM PG FBDI SFMBUJPOTIJQ CZ mOEJOH B MBCFM DPOmHVSBUJPO XIJDI NBYJNJ[FT UIF KPJOU QSPCBCJMJUZ &R JF Y # Y Y L p.Y G/: D BSHNBY j j "HBJO XF VUJMJ[F UIF -PPQZL #FMJFG 1SPQBHBUJPO -#1 UP DPNQVUF UIF NBSHJOBM QSPCBCJMJUZ p.yi Y ;G/ PG FBDI SFMBUJPOTIJQ OPEF j BOE UIFO QSFEJDU UIF UZQF PG B SFMBUJPOTIJQ BT UIF MBCFM XJUI UIF MBSHFTU NBSHJOBM QSPCBCJMJUZ ɩF NBSHJOBM QSPCBCJMJUZ JT UBLFO BT UIF QSFEJDUJPO DPOmEFODF 5JNF $PNQMFYJUZ "OBMZTJT 8F VTF )1;)2;)3 UP EFOPUF UIF OVNCFS PG BUUSJCVUF GBDUPST DPSSF MBUJPO GBDUPST BOE DPOTUSBJOU GBDUPST JO PVS 1-1'(. SFTQFDUJWFMZ *O FBDI SPVOE PG -#1 UIF .)1 .ˆˆˆ/ )2 .g/ )3 .h// . / UJNF DPTU PG QSPQBHBUJPO JT O # EJN C # EJN C # EJN XIFSF EJN # JT UIF EJ NFOTJPO PG B WFDUPS 8F FYFDVUF UIF MFBSOJOH BMHPSJUIN GPS n JUFSBUJPOT BOE JO FBDI SPVOE XF n ..)1 .ˆˆˆ/ FYFDVUF -#1 GPS LBP JUFSBUJPOT ɩVT XF DBO FTUJNBUF UIF UJNF DPNQMFYJUZ BT O # EJN C )2 .g/ )3 .h// n n / # EJN C # EJN " " LBP %JTUSJCVUFE -FBSOJOH "T SFBM TPDJBM OFUXPSLT NBZ DPOUBJO NJMMJPOT PG VTFST BOE SFMBUJPOTIJQT JU JT JNQPSUBOU GPS UIF MFBSOJOH BMHPSJUIN UP TDBMF XFMM XJUI MBSHF OFUXPSLT 5P BEESFTT UIJT JTTVF XF EFWFMPQ B EJT USJCVUFE MFBSOJOH NFUIPE CBTFE PO .1* .FTTBHF 1BTTJOH *OUFSGBDF ɩF MFBSOJOH BMHPSJUIN DBO CF WJFXFE BT UXP TUFQT DPNQVUF UIF HSBEJFOU GPS FBDI QBSBNFUFS WJB MPPQZ CFMJFG QSPQBHBUJPO BOE PQUJNJ[F BMM QBSBNFUFST XJUI UIF HSBEJFOU EFTDFOUT ɩF NPTU FYQFOTJWF QBSU JT UIF TUFQ PG DBMDVMBUJOH UIF HSBEJFOU ɩFSFGPSF XF EFWFMPQ B EJTUSJCVUFE BMHPSJUIN UP TQFFE VQ UIF QSPDFTT 8F BEPQU B NBTUFSTMBWF BSDIJUFDUVSF JF POF NBTUFS OPEF JT SFTQPOTJCMF GPS PQUJNJ[JOH QBSBNFUFST BOE UIF PUIFS TMBWF OPEFT BSF SFTQPOTJCMF GPS DBMDVMBUJOH HSBEJFOUT "U UIF CFHJOOJOH PG UIF BMHPSJUIN UIF HSBQIJDBM NPEFM PG 1-1'(. JT QBSUJUJPOFE JOUP P SPVHIMZ FRVBM QBSUT XIFSF P JT UIF OVNCFS PG TMBWF QSPDFTTPST ɩJT QSPDFTT JT BDDPNQMJTIFE CZ HSBQI TFHNFOUBUJPO TPGUXBSF .&5*4 <> ɩF TVCHSBQIT BSF UIFO EJTUSJCVUFE PWFS TMBWF OPEFT /PUF UIBU JO PVS JNQMFNFOUBUJPO UIF FEHFT GBDUPST CFUXFFO EJĊFSFOU TVCHSBQIT BSF FMJNJOBUFE XIJDI SFTVMUT JO ' BO BQQSPYJNBUF TPMVUJPO *O FBDI JUFSBUJPO UIF NBTUFS OPEF TFOET UIF OFXFTU QBSBNFUFST ' UP BMM TMBWFT 4MBWF OPEFT UIFO TUBSU UP QFSGPSN -PPQZ #FMJFG 1SPQBHBUJPO PO UIF DPSSFTQPOEJOH TVCHSBQI UP DBMDVMBUF UIF NBSHJOBM QSPCBCJMJUJFT UIFO GVSUIFS DPNQVUF UIF QBSBNFUFS HSBEJFOU BOE TFOE 40$*"- 5*& "/"-:4*4 5BCMF %BUB USBOTGFSSFE JO EJTUSJCVUFE MFBSOJOH BMHPSJUIN Phase From To Data Description Initialization Master Slave -th subgraph Iteration Beginning Master Slave Current parametersθ Iteration Ending Slave Master Gradient in -th subgraph 5BCMF 4UBUJTUJDT PG UISFF EBUB TFUT Data set Users Unlabeled Relationships Labeled Relationships Publication 1,036,990 1,984,164 6,096 Email 151 3,424 148 Mobile 107 5,122 314 JU CBDL UP UIF NBTUFS 'JOBMMZ UIF NBTUFS OPEF DPMMFDUT BOE TVNT VQ BMM HSBEJFOUT PCUBJOFE GSPN EJĊFSFOU TVCHSBQIT BOE VQEBUFT QBSBNFUFST CZ UIF HSBEJFOU EFTDFOU NFUIPE ɩF EBUB USBOTGFSSFE CFUXFFO UIF NBTUFS BOE TMBWF OPEFT BSF TVNNBSJ[FE JO 5BCMF &WBMVBUJPO ɩF QSPQPTFE SFMBUJPOTIJQ NJOJOH BQQSPBDI JT HFOFSBM BOE DBO CF BQQMJFE UP NBOZ EJĊFSFOU TDF OBSJPT *O UIJT TFDUJPO XF QSFTFOU FYQFSJNFOUT PO UISFF EJĊFSFOU HFOSFT PG EBUB TFUT UP FWBMVBUF UIF FĊFDUJWFOFTT BOE FċDJFODZ PG PVS QSPQPTFE BQQSPBDI "MM EBUB TFUT BOE DPEFT BSF QVCMJDMZ BWBJMBCMFŇ %BUB 4FUT BOE 'BDUPS %FmOJUJPOT 8F FWBMVBUF UIF QSPQPTFE NFUIPET PO UISFF EJĊFSFOU EBUB TFUT 1VCMJDBUJPO &NBJM BOE .PCJMF 4UBUJTUJDT PG UIF EBUB TFUT BSF MJTUFE JO 5BCMF t 1VCMJDBUJPO *O UIF QVCMJDBUJPO EBUB TFU XF USZ UP JOGFS UIF BEWJTPSBEWJTFF SFMBUJPOTIJQ GSPN UIF DPBVUIPS OFUXPSL ɩF EBUB TFU JT QSPWJEFE CZ <> 4QFDJmDBMMZ XF IBWF DPMMFDUFE QVCMJDBUJPOT GSPN "SOFU.JOFS <> GSPN o XJUI BVUIPST JOWPMWFE ɩF HSPVOE USVUI JT PCUBJOFE JO UISFF XBZT NBOVBMMZ DSBXMFE GSPN SFTFBSDIFST IPNFQBHF FYUSBDUFE GSPN .BUIFNBUJDT (FOFBMPHZ QSPKFDU ň BOE FYUSBDUFE GSPN "* (FOFBMPHZ QSPKFDUʼn *O UPUBM XF IBWF DPMMFDUFE BEWJTPSBEWJTFF QBJST BT QPTJUJWF DBTFT BOE BOPUIFS QBJST PG DPMMFBHVFT BT OFHBUJWF DBTFT ɩF NJOJOH SFTVMUT GPS BEWJTPS BEWJTFF SFMBUJPOTIJQT BSF BMTP BWBJMBCMF JO UIF POMJOF TZTUFN "SOFUNJOFSPSH ŇIUUQBSOFUNJOFSPSHTPDJBMUJF ň?iiT,ffrrrX;2M2 HQ;vXK i?XM/bmXMQ/ FX2/m ʼn?iiT,ff B;TX22+bXmKB+?X2/m */'&33*/( 40$*"- 5*&4 t &NBJM *O UIF FNBJM EBUB TFU XF BJN UP JOGFS UIF NBOBHFSTVCPSEJOBUF SFMBUJPOTIJQ GSPN UIF FNBJM DPNNVOJDBUJPO OFUXPSL ɩF EBUB TFU DPOTJTUT PG FNBJMT CFUXFFO &OSPO FNQMPZFFT ɩF HSPVOE USVUI PG NBOBHFSTVCPSEJOBUF SFMBUJPOTIJQT JT QSPWJEFE CZ <> t .PCJMF *O UIF NPCJMF EBUB TFU XF USZ UP JOGFS UIF GSJFOETIJQ JO NPCJMF DBMMJOH OFUXPSL ɩF EBUB TFU JT GSPN &BHMF FU BM JO <> *U DPOTJTUT PG DBMM MPHT CMVFUPPUI TDBOOJOH MPHT BOE MPDBUJPO MPHT DPMMFDUFE CZ B TPGUXBSF JOTUBMMFE JO NPCJMF QIPOFT PG VTFST EVSJOH B NPOUI QFSJPE *O UIF EBUB TFU VTFST QSPWJEF MBCFMT GPS UIFJS GSJFOETIJQT *O UPUBM QBJST PG VTFST BSF MBCFMFE BT GSJFOET *O UIF 1VCMJDBUJPO EBUB TFU SFMBUJPOTIJQT BSF FTUBCMJTIFE CFUXFFO BVUIPST vi BOE vj JG UIFZ DPBVUIPSFE BU MFBTU POF QBQFS 'PS FBDI QBJS PG DPBVUIPST .vi ;vj / PVS HPBM JT UP JEFOUJGZ XIFUIFS vi JT UIF BEWJTPS PG BVUIPS vj *O UIJT EBUB TFU XF DPOTJEFS UXP UZQFT PG DPSSFMBUJPOT $PBEWJTFF ɩF BTTVNQUJPO JT CBTFE PO UIF GBDU UIBU POF DPVME IBWF POMZ B MJNJUFE OVNCFS PG BEWJTPST JO IFSIJT SFTFBSDI DBSFFS #BTFE PO UIJT XF EFmOF B DPSSFMBUJPO GBDUPS h1 CFUXFFO OPEFT rij BOE rkj vi vj rij 1 vi $PBEWJTPS "OPUIFS PCTFSWBUJPO JT UIBU JG JT UIF BEWJTPS PG JF D UIFO JT WFSZ MJLFMZ UP CF UIF BEWJTPS PG TPNF PUIFS TUVEFOU vk XIP JT TJNJMBS UP vj 8F EFmOF BOPUIFS GBDUPS GVODUJPO h2 CFUXFFO OPEFT rij BOE rik *O UIF &NBJM EBUB TFU XF USZ UP EJTDPWFS UIF iNBOBHFSTVCPSEJOBUFw SFMBUJPOTIJQ " SFMB UJPOTIJQ .vi ;vj / JT FTUBCMJTIFE XIFO UXP FNQMPZFFT IBWF BU MFBTU POF FNBJM DPNNVOJDBUJPO *O UPUBM UIFSF BSF SFMBUJPOTIJQT BNPOH XIJDI BSF MBCFMFE BT NBOBHFSTVCPSEJOBUF SFMB UJPOTIJQT 8F USZ UP JEFOUJGZ UIF SFMBUJPOTIJQ UZQFT GSPN UIF FNBJM USBċD OFUXPSL 'PS FYBNQMF JG NPTU PG BO FNQMPZFFT FNBJMT XFSF TFOU UP UIF TBNF QFSTPO UIFO UIF SFDJQJFOU JT WFSZ MJLFMZ UP CF IFS NBOBHFS " DPSSFMBUJPO OBNFE DPSFDJQJFOU JT EFmOFE UIBU JT JG B VTFS vi TFOU NPSF UIBO # FNBJMT PG XIJDI SFDJQJFOUT JODMVEJOH CPUI vj BOE vk # JT B UISFTIPME BOE JT TFU BT JO PVS FYQFSJNFOU UIFO UIF SFMBUJPOTIJQ rij BOE rik BSF WFSZ MJLFMZ UP CF UIF TBNF ɩFSFGPSF B DPS SFMBUJPO GBDUPS JT BEEFE CFUXFFO UIF UXP SFMBUJPOTIJQT 5XP DPOTUSBJOUT OBNFE DPNBOBHFS BOE DPTVCPSEJOBUF BSF BMTP JOUSPEVDFE JO BO BOBMPHPVT XBZ BT UIBU GPS UIF QVCMJDBUJPO EBUB *O UIF .PCJMF EBUB TFU XF USZ UP JEFOUJGZ XIFUIFS UXP VTFST IBWF B GSJFOETIJQ JG UIFSF XFSF BU MFBTU POF WPJDF DBMM PS POF UFYU NFTTBHF TFOU GSPN POF UP UIF PUIFS 5XP LJOET PG DPSSFMBUJPOT BSF DPOTJEFSFE $PMPDBUJPO *G NPSF UIBO UISFF VTFST BSSJWFE BU UIF TBNF MPDBUJPO SPVHIMZ UIF TBNF UJNF XF FTUBCMJTI DPSSFMBUJPOT CFUXFFO BMM UIF SFMBUJPOTIJQT JO UIJT HSPVQT 3FMBUFEDBMM 8IFO vi NBLFT B DBMM UP CPUI vk BOE vj GSPN UIF TBNF MPDBUJPO PS NBLFT B DBMM UP vk JNNFEJBUFMZ BGUFS UIF DBMM XJUI vj XF BEE B SFMBUFEDBMM DPSSFMBUJPO GBDUPS CFUXFFO rij BOE rik *O BEEJUJPO XF BMTP DPOTJEFS TPNF PUIFS GBDUPST JO UIF UISFF EBUB TFUT " EFUBJMFE EFTDSJQUJPO PG UIF GBDUPS EFmOJUJPO GPS FBDI EBUB TFU JT HJWFO JO 5BCMF 4QFDJmDBMMZ JO UIF 1VCMJDBUJPO EBUB TFU XF EFmOF mWF DBUFHPSJFT PG BUUSJCVUF GBDUPST 1BQFS DPVOU 1BQFS SBUJP $PBVUIPS SBUJP $POGFSFODF DPWFSBHF BOE 'JSTUQBQFSZFBSEJĊ ɩF EFmOJUJPOT PG UIF BUUSJCVUFT BSF TVNNBSJ[FE JO 5BCMF *O UIF &NBJM EBUB TFU USBċDCBTFE GFBUVSFT BSF FYUSBDUFE 'PS B SFMBUJPOTIJQ XF DPNQVUF UIF OVNCFS PG FNBJMT GPS EJĊFSFOU DPNNVOJDBUJPO UZQFT *O UIF .PCJMF EBUB TFU UIF 40$*"- 5*& "/"-:4*4 5BCMF "UUSJCVUFT VTFE JO UIF FYQFSJNFOUT *O UIF 1VCMJDBUJPO EBUB TFU XF VTF Pi BOE Pj UP EFOPUF UIF TFU PG QBQFST QVCMJTIFE CZ BVUIPS vi BOE vj SFTQFDUJWFMZ 'PS B HJWFO SFMBUJPOTIJQ .vi ;vj / mWF DBUFHPSJFT PG BUUSJCVUFT BSF FYUSBDUFE *O UIF &NBJM EBUB TFU GPS SFMBUJPOTIJQ .vi ;vj / OVNCFS PG FNBJMT GPS EJĊFSFOU DPNNVOJDBUJPO UZQFT BSF DPNQVUFE *O UIF .PCJMF EBUB TFU UIF BUUSJCVUFT BSF GSPN UIF WPJDF DBMMNFTTBHFQSPYJNJUZ MPHT Data set Factor Description Paper count |Pi|, |Pj | Paper ratio |Pi|/|Pj | Publication Coauthorratio |Pi ∩ Pj |/|Pi|, |Pi ∩ Pj |/|Pj | Conference coverage Te proportion of the conferences which both vi and vj attended among conferences vj attended. First-paper-year-diff Te difference in year of the earliest publication of vi and vj . Sender Recipients Include vi vj Email Traffics vj vi vi vk and not vj vj vk and not vi vk vi and not vj vk vj and not vi vk vi and vj #voice calls Te total number of voice call logs be- tween two users. #messages Number of messages between two users. Mobile Night-call ratio Te proportionof calls at night(8pm to 8am). Call duration Te total durationtime of calls between two users. #proximity Te total number of proximity logs be- tween two users. In-role proximity ratio Te proportion of proximity logs in “working place” and in working hours (8am to 8pm). */'&33*/( 40$*"- 5*&4 BUUSJCVUFT XF FYUSBDUFE BSF WPJDF DBMMT NFTTBHFT /JHIUDBMM SBUJP $BMM EVSBUJPO QSPYJNJUZ BOE *OSPMF QSPYJNJUZ SBUJP &WBMVBUJPO .FBTVSFT 5P RVBOUJUBUJWFMZ FWBMVBUF UIF QSPQPTFE NFUIPE XF DPOTJEFS UXP BT QFDUT QFSGPSNBODF BOE TDBMBCJMJUZ 'PS UIF SFMBUJPOTIJQ NJOJOH QFSGPSNBODF XF DPOTJEFS UXP GPME DSPTTWBMJEBUJPO JF IBMG USBJOJOH BOE IBMG UFTUJOH BOE FWBMVBUF UIF BQQSPBDIFT JO UFSNT PG BDDVSBDZ QSFDJTJPO SFDBMM BOE 'TDPSF 'PS TDBMBCJMJUZ XF FYBNJOF UIF FYFDVUJPO UJNF PG UIF NPEFM MFBSOJOH 8F DPNQBSF PVS BQQSPBDI XJUI UIF GPMMPXJOH NFUIPET GPS JOGFSSJOH SFMBUJPOTIJQ UZQFT 47. *U VTFT UIF SFMBUJPOTIJQ BUUSJCVUF WFDUPS Yi UP USBJO B DMBTTJmDBUJPO NPEFM BOE QSF EJDU UIF SFMBUJPOTIJQT CZ FNQMPZJOH UIF DMBTTJmDBUJPO NPEFM 8F VTF UIF 47.MJHIU QBDLBHF UP JNQMFNFOU 47. 51'( *U JT BO VOTVQFSWJTFE NFUIPE QSPQPTFE JO 8BOH FU BM <> GPS NJOJOH BEWJTPS BEWJTFF SFMBUJPOTIJQT JO QVCMJDBUJPO OFUXPSL ɩJT NFUIPE JT EPNBJOTQFDJmD BOE UIVT XF POMZ DPNQBSF JU XJUI UIF 1VCMJDBUJPO EBUB TFU 1-1'(.4 ɩF QSPQPTFE 1-1'(. JT CBTFE PO UIF QBSUJBMMZ MBCFMFE OFUXPSL "O BM UFSOBUJWF TUSBUFHZ JT UP USBJO UIF NPEFM QBSBNFUFST XJUI UIF MBCFMFE OPEFT POMZ 8F VTF UIJT NFUIPE UP FWBMVBUF UIF OFDFTTJUZ PG UIF QBSUJBM MFBSOJOH "MM UIF DPEFT BSF JNQMFNFOUFE JO $ BOE BMM FYQFSJNFOUT BSF DPOEVDUFE PO B TFSWFS SVO OJOH 8JOEPXT 4FSWFS XJUI *OUFM 9FPO $16 & ()[ DPSFT BOE (# NFNPSZ ɩF EJTUSJCVUFE MFBSOJOH BMHPSJUIN JT JNQMFNFOUFE PO .1* .FTTBHF 1BTTJOH *OUFS GBDF 5BCMF 1FSGPSNBODF PG SFMBUJPOTIJQ NJOJOH XJUI EJĊFSFOU NFUIPET PO UISFF EBUB TFUT 1VCMJDBUJPO &NBJM BOE .PCJMF Data set Method Accuracy Precision Recall F1-score SVM 76.6 72.5 54.9 62.1 Publication TPFG 81.2 82.8 89.4 86.0 PLP-FGM-S 84.1 77.1 78.4 77.7 PLP-FGM 92.7 91.4 87.7 89.5 SVM 82.6 79.1 88.6 83.6 Email PLP-FGM-S 85.6 85.8 85.6 85.7 PLP-FGM 88.0 88.6 87.2 87.9 SVM 80.0 92.7 64.9 76.4 Mobile PLP-FGM-S 80.9 88.1 71.3 78.8 PLP-FGM 83.1 89.4 75.2 81.6 "DDVSBDZ 1FSGPSNBODF 5BCMF MJTUT UIF BDDVSBDZ QFSGPSNBODF PG JOGFSSJOH UIF UZQF PG TPDJBM SFMBUJPOTIJQT CZ UIF EJĊFSFOU NFUIPET 40$*"- 5*& "/"-:4*4 1FSGPSNBODF $PNQBSJTPO 0VS NFUIPE DPOTJTUFOUMZ PVUQFSGPSNT PUIFS DPNQBSBUJWF NFUIPET PO BMM UIF UISFF EBUB TFUT *O UIF 1VCMJDBUJPO EBUB TFU 1-1'(. BDIJFWFT B JO UFSNT PG 'TDPSF JNQSPWFNFOU DPNQBSFE XJUI 47. BOE PVUQFSGPSNT 51'( CZ ' TDPSF BOE JO UFSNT PG BDDVSBDZ 8F PCTFSWF UIBU 51'( BDIJFWFT UIF CFTU SFDBMM BNPOH BMM UIF GPVS NFUIPET ɩJT JT CFDBVTF 51'( UFOET UP QSFEJDU NPSF QPTJUJWF DBTFT JF JOGFSSJOH NPSF BEWJTPSBEWJTFF SFMBUJPOTIJQT JO UIF DPBVUIPS OFUXPSL UIVT IVSUJOH UIF QSFDJTJPO "T B SFTVMU 51'( VOEFSQFSGPSNT PVS NFUIPE CZ JO UFSNT PG QSFDJTJPO *O &NBJM BOE .PCJMF EBUB TFU 1-1'(. PVUQFSGPSNT 47. CZ BOE SFTQFDUJWFMZ 6OMBCFMFE %BUB 0ąFST *NQSPWFNFOU 'SPN UIF SFTVMU JU JT DMFBSMZ TIPXO UIBU CZ VUJMJ[ JOH UIF VOMBCFMFE EBUB PVS NPEFM JOEFFE PCUBJOT B TJHOJmDBOU JNQSPWFNFOU 8JUIPVU VTJOH UIF VOMBCFMFE EBUB PVS NPEFM 1-1'(.4 SFTVMUT JO B MBSHF QFSGPSNBODF SFEVDUJPO $ JO UFSNT PG 'TDPSF PO UIF QVCMJDBUJPO EBUB TFU 0O UIF PUIFS UXP EBUB TFUT XF BMTP PCTFSWF B DMFBS QFSGPSNBODF SFEVDUJPO 5BCMF 'BDUPS DPOUSJCVUJPO BOBMZTJT PO UISFF EBUB TFUT Data set Factors used Accuracy Precision Recall F1-score Attributes 77.1 71.1 59.8 64.9 + Co-advisor 83.5 80.9 69.8 75.0 (+10.1%) Publication + Co-advisee 83.1 79.7 70.2 74.7 (+9.8%) All 92.7 91.4 87.7 89.5(+24.6%) Attributes 80.1 79.5 81.2 80.3 + Co-recipient 80.8 81.5 79.7 80.6 (+0.3%) Email + Co-manager 83.1 82.8 83.5 83.2 (+2.9%) + Co-subordinate 85.0 84.4 85.7 85.0 (+4.7%) All 88.0 88.6 87.2 87.9 (+7.6%) Attributes 81.8 88.6 73.3 80.2 + Co-location 82.2 89.2 73.3 80.4 (+0.2%) Mobile + Related-call 81.8 88.6 73.3 80.2 (+0.0%) All 83.1 89.4 75.2 81.6 (+1.4%) 'BDUPS $POUSJCVUJPO "OBMZTJT 8F QFSGPSN BO BOBMZTJT UP FWBMVBUF UIF DPOUSJCVUJPO PG EJG GFSFOU GBDUPST EFmOFE JO PVS NPEFM 8F mSTU SFNPWF BMM UIF DPSSFMBUJPODPOTUSBJOU GBDUPST BOE POMZ LFFQ UIF BUUSJCVUF GBDUPS BOE UIFO BEE FBDI PG UIF GBDUPST JOUP UIF NPEFM BOE FWBMVBUF UIF QFS GPSNBODF JNQSPWFNFOU CZ FBDI GBDUPS 5BCMF TIPXT UIF SFTVMU PG GBDUPS BOBMZTJT 8F TFF UIBU BMNPTU BMM UIF GBDUPST BSF VTFGVM GPS JOGFSSJOH UIF TPDJBM SFMBUJPOTIJQT CVU UIF DPOUSJCVUJPO JT WFSZ EJĊFSFOU 'PS FYBNQMF GPS JOGFSSJOH UIF NBOBHFSTVCPSEJOBUF SFMBUJPOTIJQ UIF DPTVCPSEJOBUF GBDUPS JT UIF NPTU VTFGVM GBDUPS XIJDI BDIJFWFT B JNQSPWFNFOU CZ 'TDPSF BOE UIF DP NBOBHFS GBDUPS BDIJFWFT B JNQSPWFNFOU XIJMF UIF DPSFDJQJFOU GBDUPS POMZ SFTVMUT JO B JNQSPWFNFOU #Z DPNCJOJOH BMM UIF GBDUPST UPHFUIFS XF DBO GVSUIFS PCUBJO B JNQSPWFNFOU */'&33*/( 40$*"- 5*&4 3000 12 Our method 2500 10 Perfect 2000 8 1500 6 1000 Speedup(x) 4 500 2 Runningonetimeof iteration (s) 0 0 1 2 3 4 8 12 0 2 4 6 8 10 12 #Cores (Graph Partitions) #Cores (Graph Partitions) B 3VOOJOH UJNF WT DPSFT C 4QFFEVQ WT DPSFT 'JHVSF 4DBMBCJMJUZ QFSGPSNBODF 95 95 90 90 85 85 80 80 75 75 Accuracy(%) F1 − Score(%) 70 70 65 Accuracy−METIS 65 F1−METIS Accuracy−Random F1−Random 60 60 0 5 10 15 0 5 10 15 #Cores (Graph Partitions) #Cores (Graph Partitions) 'JHVSF "QQSPYJNBUJPO PG HSBQI QBSUJUJPO "O FYUSFNF QIFOPNFOPO BQQFBST PO UIF .PCJMF EBUB TFU 8JUI FBDI PG UIF UXP GBDUPST DP MPDBUJPO BOE SFMBUFEDBMM XF DBOOPU PCUBJO B DMFBS JNQSPWFNFOU BOE CZ ' )PX FWFS XIFO DPNCJOJOH UIF UXP GBDUPST BOE UIF BUUSJCVUF GBDUPS UPHFUIFS XF DBO BDIJFWF B JNQSPWFNFOU UJNFT IJHIFS UIBO UIBU PCUBJOFE CZ UIF TFQBSBUFE DBTF ɩJT JT CFDBVTF PVS NPEFM OPU POMZ DPOTJEFST EJĊFSFOU GBDUPST CVU BMTP DPOTJEFST UIF DPSSFMBUJPO CFUXFFO UIFN 4DBMBCJMJUZ 1FSGPSNBODF 8F DPOEVDU B TFSJFT PG FYQFSJNFOUT UP FWBMVBUF UIF TDBMBCJMJUZ QFSGPS NBODF PG PVS EJTUSJCVUFE MFBSOJOH BMHPSJUIN PO UIF 1VCMJDBUJPO EBUB TFU 'JHVSF TIPXT UIF SVOOJOH UJNF BOE TQFFEVQ PG UIF EJTUSJCVUFE BMHPSJUIN XJUI EJĊFSFOU OVNCFS PG DPNQVUFS OPEFT 40$*"- 5*& "/"-:4*4 DPSFT VTFE ɩF TQFFEVQ DVSWF JT DMPTF UP UIF QFSGFDU MJOF BU UIF CFHJOOJOH "MUIPVHI 8 UIF TQFFEVQ JOFWJUBCMZ EFDSFBTFT XIFO UIF OVNCFS PG DPSFT JODSFBTFT JU DBO BDIJFWF & " TQFFEVQ XJUI DPSFT *U JT OPUJDFBCMF UIBU UIF TQFFEVQ DVSWF JT CFZPOE UIF QFSGFDU MJOF XIFO VTJOH DPSFT JU JT OPU TUSBOHF TJODF PVS EJTUSJCVUFE TUSBUFHZ JT BQQSPYJNBUFE *O PVS EJTUSJCVUFE JNQMFNFOUB UJPO HSBQIT BSF QBSUJUJPOFE JOUP TVCHSBQIT BOE UIF GBDUPST BDSPTT EJĊFSFOU QBSUT BSF EJTDBSEFE ɩVT UIF HSBQI QSPDFTTFE JO EJTUSJCVUFE WFSTJPO DPOUBJOT MFTT FEHFT NBLJOH UIF DPNQVUBUJPOBM DPTU MFTT UIBO UIF BNPVOU JO UIF PSJHJOBM BMHPSJUIN ɩF FĊ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ċDJFOU BMHPSJUIN JT QSPQPTFE UP MFBSO NPEFM QBSBNFUFST BOE QSFEJDU VOLOPXO SFMBUJPOTIJQT &YQFSJNFOUBM SFTVMUT PO UISFF EJĊFS FOU UZQFT PG EBUB TFUT WBMJEBUF UIF FĊFDUJWFOFTT PG UIF QSPQPTFE NPEFM 5P GVSUIFS TDBMF VQ UP MBSHF OFUXPSLT B EJTUSJCVUFE MFBSOJOH BMHPSJUIN JT EFWFMPQFE &YQFSJNFOUT EFNPOTUSBUF HPPE QBSBMMFM FċDJFODZ PG UIF EJTUSJCVUFE MFBSOJOH BMHPSJUIN "$5*7&-: -&"3/*/( 50 */'&3 40$*"- 5*&4 "OPUIFS JNQPSUBOU RVFTUJPO JT IPX XF DBO MFBSO UIF NBQQJOH GVODUJPO f FĊFDUJWFMZ *O NBOZ TJUVBUJPOT MBCFMFE EBUB JT MJNJUFE BOE FYQFOTJWF ɩF QSPCMFN JT DBO XF EFTJHO B TUSBUFHZ UP BDUJWFMZ MFBSO UIF NPEFM XJUI NJOJNBM MBCFMJOH DPTU 'PSNBMMZ XF IBWF UIF GPMMPXJOH 1SPCMFN G L U L "DUJWF TPDJBM UJF JOGFSFODF (JWFO B QBSUJBMMZ MBCFMFE OFUXPSL D .V; E ;E ;R ; W / BOE B MBCFMJOH CVEHFU b OVNCFS PG VTFS JOUFSBDUJPOT PVS PCKFDUJWF A EU b JT UP TFMFDU B TVCTFU PG VOLOPXO SFMBUJPOTIJQT ! XJUIJO UIF DPOTUSBJOU PG UP MBCFM TP UIBU UIF QFSGPSNBODF PG QSFEJDUJWF GVODUJPO f DBO CF NBYJNBMMZ JNQSPWFE 0VS GPSNVMBUJPO PG JOGFSSJOH TPDJBM SFMBUJPOTIJQT JT WFSZ EJĊFSFOU GSPN FYJTUJOH XPSLT PO SFMBUJPO NJOJOH <> XIJDI GPDVTFT PO EFUFDUJOH UIF SFMBUJPOTIJQT GSPN UIF DPOUFOU JOGPSNBUJPO XIJMF XF GPDVT PO NJOJOH SFMBUJPOTIJQ TFNBOUJDT JO TPDJBM OFUXPSLT %JFIM FU BM <> BOE 8BOH FU BM <> JOWFTUJHBUFE UIF QSPCMFN PG SFMBUJPOTIJQ JEFOUJmDBUJPO )PXFWFS UIFZ TUVEJFE UIF QSPC MFN JO TQFDJmD EPNBJOT &NBJM OFUXPSL PS 1VCMJDBUJPO OFUXPSL #BDLTUSPN FU BM <> QSPQPTFE BO BMHPSJUIN CBTFE PO TVQFSWJTFE SBOEPN XBMLT GPS MJOL QSFEJDUJPO $SBOEBMM FU BM <> JODPSQP SBUFE HFPHSBQIJD DPJODJEFODFT UP JOGFS TPDJBM UJFT %JĊFSFOU GSPN UIFTF XPSLT XIJDI BJN BU MJOL QSFEJDUJPO PVS HPBM JT UP JOGFS UIF UZQFT PG SFMBUJPOTIJQT ɩFSF BSF BMTP XPSLT PO JOGFSSJOH UIF */'&33*/( 40$*"- 5*&4 UZQFT PG SFMBUJPOTIJQT )PQDSPGU FU BM <> FYQMPSFE UIF QSPCMFN PG SFDJQSPDBM SFMBUJPOTIJQ QSFEJD UJPO BOE 5BOH FU BM <> EFWFMPQFE B GSBNFXPSL GPS DMBTTJGZJOH UIF UZQF PG TPDJBM SFMBUJPOTIJQT CZ MFBSOJOH BDSPTT IFUFSPHFOFPVT OFUXPSLT :BOH FU BM <> TUVEJFE UIF SFUXFFUJOH CFIBWJPS -FTLPWFD FU BM <> GPDVTFE PO UIF QSFEJDUJPO PG FEHF TJHOT QPTJUJWF PS OFHBUJWF )PXFWFS UIFZ EP OPU DPOTJEFS IPX UP NBLF PQUJNBM VTF PG VTFS JOUFSBDUJPO 'PSNBMMZ GPS BDUJWFMZ TFMFDUJOH IFMQGVM SFMBUJPOTIJQT UP RVFSZ UIF VTFS XF EFmOF B RVBMJUZ GVODUJPO Q.A/ XIJDI NFBTVSFT UIF FYQFDUFE JNQSPWFNFOU PG UIF QSFEJDUJPO QFSGPSNBODF CZ MBCFMJOH SFMBUJPOTIJQT JO TFU A ɩF QSPCMFN DBO CF UIFO EFmOFE BT BO PQUJNJ[BUJPO QSPCMFN PG Q.A/ JF A# Q.A/; A b; b > 0: D BSHA NBYY U j jD % 5P RVBOUJGZ Q.A/ XF DPVME DPOTJEFS IPX B TFMFDUFE OPEF DBO JOnVFODF UIF PUIFST 'PS FYBNQMF DPSSFDUJPO PG B DFOUFSFE SFMBUJPOTIJQ NBZ USJHHFS B TQSFBE PG UIF DPSSFDUJPO UIVT IFMQJOH JOGFS DPSSFMBUFE SFMBUJPOTIJQT #BTFE PO UIF BCPWF JOUVJUJPOT XF EFWFMPQ BO *OnVFODF.BYJNJ[BUJPO 4FMFDUJPO *.4 NPEFM BOE B #FMJFG.BYJNJ[BUJPO 4FMFDUJPO #.4 NPEFM GPS BDUJWFMZ JOGFSSJOH UIF UZQFT PG TP DJBM SFMBUJPOTIJQT ɩF *.4 NPEFM TFMFDUT UIF NPTU JOnVFOUJBM OPEFT CZ MFWFSBHJOH UIF OFUXPSL TUSVDUVSF BOE UIF VODFSUBJOUZ PCUBJOFE GSPN 1-1'(. ɩF #.4 NPEFM GVSUIFS JODPSQPSBUFT UIF BDUJWF TFMFDUJPO QSPDFTT JOUP UIF MFBSOJOH QSPDFTT PG 1-1'(. #BTFMJOF .FUIPET ɩF RVBMJUZ GVODUJPO Q.A/ DBO CF EFmOFE JO EJĊFSFOU GPSNT 8JUIPVU BOZ DPOTUSBJOUT PQUJNJ[JOH Q.A/ A Y U UIF RVBMJUZ GVODUJPO OFFET UP FOVNFSBUF BMM QPTTJCMF TVCTFUT ! XIJDI JT PCWJPVTMZ /1IBSE 8F mSTU SFWJFX UXP CBTFMJOF HSFFEZ BMHPSJUINT .BYJNVN 6ODFSUBJOUZ .6 " NPTU DPNNPO TFMFDUJPO TUSBUFHZ GPS BDUJWF MFBSOJOH JT UP TFMFDU UIF NPTU VODFSUBJO SFMBUJPOTIJQT ɩF VODFSUBJOUZ PG BO VOMBCFMFE SFMBUJPOTIJQ yi JT NFBTVSFE CZ H.yi / y p.yi y/ p.yi y/ UIF FOUSPQZ D$ 2Y D MPH D #BTFE PO UIJT JOUVJUJPO XF DBO EFmOF UIF RVBMJUZ GVODUJPO BT P Q .A/ H.A/ MU D H.A/ H.y / yi A i XIFSF D 2 *OGPSNBUJPO %FOTJUZP *% " ESBXCBDL PG UIF .BYJNVN 6ODFSUBJOUZ TUSBUFHZ JT JUT UFOEFODZ UP DIPPTF PVUMJFST ɩVT XF FNQMPZ BOPUIFS TUSBUFHZ *OGPSNBUJPO %FOTJUZ U QSPQPTFE JO 4FUUMFT BOE $SBWFO <> ɩF JEFB JT UP DIPPTF UIF NPTU SFQSFTFOUBUJWF OPEFT JO Y XIJDI BSF TVQQPTFE UP CF UIF NPTU JOGPSNBUJWF POFT #BTFE PO UIJT JOUVJUJPO XF NFBTVSF UIF JOGPSNBUJWFOFTT PG B OPEF 40$*"- 5*& "/"-:4*4 CZ JUT DPTJOF TJNJMBSJUZ UP BMM PUIFS VOMBCFMFE OPEFT JO UIF TFOTF PG UIF BUUSJCVUFT BUUBDIFE UP B OPEF 'PSNBMMZ XF EFmOF UIF RVBMJUZ GVODUJPO BT 1 QID.A/ H.yi / Œ .xi ; xj / D " Y U TJN i A j j j Y U X2 X2 xi xj .xi ; xj / " XIFSF TJN xi xj /PUF UIBU XF BHBJO FNQMPZ UIF FOUSPQZ PG B SFMBUJPOTIJQ OPEF D k k$k k H.yi / UP MFWFSBHF UIF iCBTFw JOGPSNBUJWFOFTT 1SPQPTFE .FUIPET GPS "DUJWFMZ -FBSOJOH 1-1'(. 8F QSPQPTF UXP OFX BMHPSJUINT JF *OnVFODF.BYJNJ[BUJPO 4FMFDUJPO NPEFM *.4 BOE #FMJFG .BYJNJ[BUJPO 4FMFDUJPO NPEFM #.4 GPS BDUJWFMZ MFBSOJOH UIF QSFTFOUFE 1-1'(. NPEFM *OnVFODF.BYJNJ[BUJPO 4FMFDUJPO *.4 "MM UIF TUSBUFHJFT NFOUJPOFE BCPWF EP OPU DPOTJEFS UIF OFUXPSL TUSVDUVSF JOGPSNBUJPO "T SFMBUJPOTIJQ OPEFT JO 1-1'(. BSF DPSSFMBUFE UIF NPTU JOnVFOUJBM OPEFT BSF NPSF MJLFMZ UP IFMQ JNQSPWF UIF PWFSBMM QFSGPSNBODF PG UIF NPEFM &YJTUJOH XPSL IBT TUVEJFE TFWFSBM JOnVFODF QSPQBHBUJPO NPEFMT JODMVEJOH UIF -JOFBS ɩSFTIPME .PEFM -5. JO ,FNQF FU BM <> ɩF -5. NPEFM TFUT B UISFTIPME WBMVF "i GPS FBDI OPEF BOE XFJHIUT bi;j bi;j 1 bi;j "i GPS JUT FEHFT TBUJTGZJOH j NB.i/ Ä *O FBDI UJNF TUBNQ JG j NB.i/ activated.j / ' i 2 2 ^ UIFO UIF OPEF XJMM CF BDUJWBUFEP 8F EFWFMPQ B WBSJBUJPO PG UIF -5.P CZ JODPSQPSBUJOH B TDPSF GPS FBDI OPEF SFnFDUJOH UIF TUSFOHUI PG UIF JOnVFODF TQSFBEJOH JO PVS NPEFM ɩF QSPQBHBUJPO QSPDFTT JT EFTDSJCFE BT GPMMPXT t ɩF HSBQI JT UIF TBNF BT UIF 1-1'(. NPEFM *O BEEJUJPO XF DBMM B SFMBUJPOTIJQL OPEF BT iBDUJWBUFEw XIFO JUT MBCFM yi JT EFUFSNJOFE ɩF JOJUJBM BDUJWBUFE TFU PG OPEFT JT Y 8F " p.y y G; Y L/ 1 BTTJHO B UISFTIPME i y i GPS FBDI OPEF ɩVT B OPEF XJUI D 2Y j D j $ jYj j IJHIFS VODFSUBJOUZ XJMM CFP FBTJFS UP CF BDUJWBUFE i gi "i t 8IFO B OPEF JT BDUJWBUFE JU TQSFBET JUT HBJOFE TDPSF JODSFNFOU $ UP JUT OFJHI j NB.i/ bi;j gj gj bi;j .gi "i / CPS OPEFT 2 XJUI B XFJHIU JF C $ ɩF HBJOFE TDPSF JODSFNFOU SFnFDUT UIF JNQSPWFNFOU PG DPOmEFODF CSPVHIU CZ VTFS MBCFMJOH UIFSFGPSF UIF JOnVFODF CZ MBCFMJOH BO VODFSUBJO SFMBUJPOTIJQ XJMM CF HSFBUFS UIBO MBCFMJOH B NPSF DFSUBJO bi;j 1= NB.j / SFMBUJPOTIJQ 5P TJNQMJGZ UIF QSPCMFN XF TFU XFJHIU D j j t *G B OPEF JT MBCFMFE CZ UIF VTFS XF TFU JU BT BDUJWBUFE BOE BTTJHO JUT HBJOFE TDPSF BT ɩF HBJOFE TDPSF GPS PUIFS OPEFT JT TFU UP BU UIF CFHJOOJOH 0ODF BO JOBDUJWBUFE OPEF k HBJOT B TDPSF XIJDI FYDFFET UIF UISFTIPME JF gk >"i JU XJMM CFDPNF BDUJWBUFE BOE TQSFBE JUT HBJOFE TDPSF TJNJMBSMZ "O BDUJWBUFE OPEF POMZ TQSFBET JUT HBJOFE TDPSF PODF BOE SFNBJOT JUT TUBUVT 8F EFmOF UIF RVBMJUZ GVODUJPO QIMS.A/ BT UIF UPUBM OVNCFS PG BDUJWBUFE OPEFT BGUFS UIF QSPQBHBUJPO QSPDFTT 'JOEJOH UIF TFU A UIBU NBYJNJ[FT UIF RVBMJUZ GVODUJPO QIMS.A/ JT /1IBSE */'&33*/( 40$*"- 5*&4 4JNJMBS UP <> JO UIJT DIBQUFS XF VTF B HSFFEZ TUSBUFHZ UP BQQSPYJNBUF UIF TPMVUJPO /PUF UIBU VOMJLF UIF -5. XF EP OPU HVBSBOUFF B MPXFS CPVOE PG FSSPS GPS UIF HSFFEZ PQUJNJ[BUJPO NFUIPE #FMJFG.BYJNJ[BUJPO 4FMFDUJPO #.4 5P RVBOUJGZ UIF JOnVFODF PG POF OPEF PO UIF PUIFST XF FNQMPZ UIF CFMJFG PG FBDI OPEF PCUBJOFE CZ -PPQZ #FMJFG 1SPQBHBUJPO JO PVS NPEFM 8F EFmOFL .yi G; Y / B IFVSJTUJD CZ SFNPWJOH UIF FĊFDU PG BUUSJCVUFT GSPN UIF CFMJFG TDPSF EFOPUFE CZ B j .PSF QSFDJTFMZ L T T .yi G; Y / ' s.yi / & ˆˆ.yi ; xi / : B j D FYQf $ g #Z OPSNBMJ[JOH UIF CFMJFG PG POF SFMBUJPOTIJQ OPEF XF PCUBJO UIF CFMJFG NBSHJOBM QSPCBCJMJUZ L 1 L p .yi G; Y / .yi G;Y /; B j D Z B j B Z XIFSF B JT UIF OPSNBMJ[BUJPO GBDUPS *U FTUJNBUFT UIF NBSHJOBM QSPCBCJMJUZ EJTUSJCVUJPO PG B SFMB UJPOTIJQ OPEF XIFSF UIF JOGPSNBUJPO PG JUT BUUSJCVUF WFDUPS JT BCTFOU " CBTJD JOUVJUJPO JT UIF CFMJFG PG B SFMBUJPOTIJQ OPEF JT NPOPUPOJDBMMZ JODSFBTJOHL XJUI SFTQFDU .yi y G; Y / UP UIF OVNCFS PG SFMBUJPOTIJQ OPEFT PG UIF TBNF UZQF JF B D j JT NPOPUPOJDBMMZ JODSFBTJOH XJUI SFTQFDU UP UIF OVNCFS PG SFMBUJPOTIJQT XJUI MBCFM yŊ 8JUIPVU MPTT PG HFOFSBMJUZ XF mSTU DPOTJEFS UIF CJOBSZ SFMBUJPOTIJQ NJOJOH QSPCMFN JF UIFSF BSF POMZ UXP QPTTJCMF MBCFMT PG 0; 1 SFMBUJPOTIJQT Y Df g *O UIF CJOBSZ TFUUJOH XF GVSUIFS DPOTJEFS UIF BDUJWF TFMFDUJPO GPS FBDI UZQF TFQBSBUFMZ ɩJT JT CFDBVTF XIFO NJYJOH UIF EJĊFSFOU UZQFT PG SFMBUJPOTIJQT UPHFUIFS JU DBOOPU CF HVBSBOUFFE UP IBWF B DMPTFEGPSN TPMVUJPO ɩVT XIFO VTFST QSPWJEF POMZ QPTJUJWF GFFECBDL PVS PCKFDUJWF JT UP mOE B TFU PG QPTJUJWF OPEFT "DDPSEJOHMZ XF EFmOF UIF RVBMJUZ GVODUJPO PG UIF QPTJUJWFPSJFOUFE #.4 TUSBUFHZ BT L Q .A/ p .yi 1 G; Y A/; BMSC B D U D j [ yi Y X2 .1/ U U L L Y yi yi Y .yi 1 G; Y / .yi 0 G; Y / XIFSF .1/ Df j 2 ^ B D j ' B D j g 4ZNNFUSJDBMMZ JG UIF VTFST QSPWJEF POMZ OFHBUJWF GFFECBDL XF DBO BEPQU B OFHBUJWFPSJFOUFE #.4 TUSBUFHZ XJUI UIF GPMMPXJOH RVBMJUZ GVODUJPO L QBMS .A/ p .yi 0 G; Y A/: ! B D U D j [ yi Y X2 .0/ T y0 ;y0 y ˛ g.y; y/ Ŋ8FT QSFTFOU B TVċDJFOUT DPOEJUJPO GPST UIJT BTTVNQUJPO *G GPS BMM L2 Y ¤ XF DBO IBWF FYQf C ˇ h.y; y/ ˛ g.y; y / ˇ h.y; y / .yi y G; Y / FYQ 0 0 UIFO B JT NPOPUPOJDBMMZ JODSFBTJOH XJUI SFTQFDU UP UIF yg& f C Y L g D j OVNCFS PG MBCFMFE SFMBUJPOTIJQT JO 40$*"- 5*& "/"-:4*4 *OQVU G b 0VUQVU B TFU PG TFMFDUFE SFMBUJPOTIJQT A ' 5SBJO 1-1'(. BOE HFU UIF QBSBNFUFS DPOmHVSBUJPO ' A ;A C ! ; GPS b=2 UJNFT EP 6TF -PPQZ #FMJFG 1SPQBHBUJPO -#1 UP PCUBJO UIF QSPCBCJMJUZ EJTUSJCVUJPO GPS FBDI SFMBUJPOTIJQ L y U p.yi 1 G; Y /.Q .AC yi / Q .AC// 'JOE NBYC BSHNBYyi Y BMSC BMSC D U 2 D j [ $ y Y AC .PWF NBYC GSPN UP Y L Y L A [ C 6TF -PPQZ #FMJFG 1SPQBHBUJPO -#1 UP PCUBJO UIF QSPCBCJMJUZ EJTUSJCVUJPO GPS FBDI SFMBUJPOTIJQ L y U p.yi 0 G; Y /.QBMS .A yi / QBMS .A // 'JOE NBY! D BSHNBYyi Y D j ! ! [ $ ! ! y Y U 2 A .PWF NBY! GSPN UP ! Y L Y L A [ ! FOE "MHPSJUIN #FMJFGNBYJNJ[BUJPO TFMFDUJPO Q .A/ QBMS .A/ ɩF PQUJNJ[BUJPO PG CPUI RVBMJUZ GVODUJPOT BMSC BOE ! JT /1IBSE )PX FWFS BT CPUI RVBMJUZ GVODUJPOT BSF TVCNPEVMBS UIFPSFUJDBM BOBMZTJT JT HJWFO JO 4FDUJPO B .1 1=e/ TPMVUJPO XJUI BO BQQSPYJNBUJPO SBUJP PG $ DBO CF PCUBJOFE VTJOH B HSFFEZ BMHPSJUIN BU FBDI UJNF JU TFMFDUT UIF SFMBUJPOTIJQ XIJDI JT FYQFDUFE UP QSPWJEF UIF NBYJNVN NBSHJOBM JODSFBTF PG UIF RVBMJUZ GVODUJPO /PUJDF UIBU XF USFBU UIF FYBNJOJOH SFMBUJPOTIJQ OPEF yi BT JG JU JT QPTJUJWF Q .A/ QBMS .A/ MBCFMFE XIFO PQUJNJ[JOH BMSC PS OFHBUJWFMBCFMFE GPS ! TJODF UIF BDUJWF MFBSOJOH BMHPSJUIN JT MBCFMVOBXBSF JO UIF TFMFDUJPO TUBHF *O PSEFS UP MFWFSBHF UIF SJTL UIBUL B TFMFDUFE SF p.yi G; Y / MBUJPOTIJQ JT OPU MBCFMFE BT FYQFDUFE XF FNQMPZ B XFJHIUJOH GBDUPS j UP SFnFDU IPX MJLFMZ UIF SFMBUJPOTIJQ XPVME CF MBCFMFE BT QPTJUJWF OFHBUJWF Q b=2 5P QSFWFOU NBLJOH BO JNCBMBODF TFMFDUJPO XF JOUVJUJWFMZ VTF BMSC UP DIPPTF OPEFT XIFSF b JT UIF OVNCFS PG SFMBUJPOTIJQT XF FYQFDU UP RVFSZ UIF VTFS FBDI UJNF BOE UIFO VTF Q BMS! GPS UIF SFTU "MHPSJUIN GPSNBMMZ EFTDSJCFT UIF TFMFDUJPO QSPDFTT ɩJT TFMFDUJPO TUSBUFHZ JT EFOPUFE CZ #.4 /PUF UIBU #.4 DPNCJOFT CPUI #.4 BOE #.4 ɩVT JU DBOOPU HVBSBOUFF B MPXFS FSSPS CPVOE PG UIF BQQSPYJNBUJPO DzFPSFUJDBM "OBMZTJT 8F HJWF B UIFPSFUJDBM BOBMZTJT PG QSPQPTFE BDUJWF MFBSOJOH NPEFMT ɩF BQQSPYJNBUJPO SBUJP PG UIF *.4 NPEFM JT HJWFO JO ,FNQF FU BM <> )FSF XF GPDVT PO UIF QSPPG PG BQQSPYJNBUJPO HVBSBOUFFT PG UIF #.4 NPEFM ɩF QSPPG JT CBTFE PO UIF TVCNPEVMBS QSPQFSUZ XIJDI JOEJDBUFT */'&33*/( 40$*"- 5*&4 UIBU UIF NBSHJOBM HBJO GSPN BEEJOH BO FMFNFOU UP B TFU S JT BU MFBTU BT IJHI BT UIF NBSHJOBM HBJO GSPN BEEJOH UIF TBNF FMFNFOU UP B TVQFSTFU PG S ɩF GPMMPXJOH JT B GPSNBM EFmOJUJPO PG UIF TVCNPEVMBS TFU GVODUJPO %FmOJUJPO 4VCNPEVMBS " TFU GVODUJPO F EFmOFE PO TFU S JT DBMMFE TVCNPEVMBS JG GPS BMM A B S s B F .A s / F.A/ F .B s / F.B/ ! ! BOE … JU TBUJTmFT [f g $ ' [f g $ (JWFO B TVCNPEVMBS GVODUJPO F XIJDI JT BMTP NPOPUPOF BOE OPOOFHBUJWF JU JT BO /1 IBSE QSPCMFN UP mOE B kFMFNFOU TVCTFU S UP PQUJNJ[F F #VU B HSFFEZ BMHPSJUIN DBO SFTVMU JO .1 1=e/ BO BQQSPYJNBUJPO SBUJP PG $ *U DPOTUSVDUT UIF TVCTFU CZ TFMFDUJOH FMFNFOUT POF BU B UJNF FBDI UJNF DIPPTJOH BO FMFNFOU UIBU QSPWJEFT UIF MBSHFTU NBSHJOBM JODSFBTF JO UIF GVODUJPO WBMVF ɩVT XF IBWF UIF GPMMPXJOH DzFPSFN 'PS B OPOOFHBUJWF NPOPUPOF TVCNPEVMBS GVODUJPO F MFU S CF UIF kFMFNFOU TVCTFU EFDJEFE CZ UIF GPMMPXJOH BMHPSJUIN GPS k UJNFT FBDI UJNF DIPPTF BO FMFNFOU XIJDI HJWFT UIF NBYJNVN F S S F .S/ NBSHJOBM JODSFBTF PG BOE NPWF JU UP -FU # EFOPUFT UIF PQUJNBM TPMVUJPO DzFO XF IBWF ' .1 1 /F.S / $ e # Q #FGPSF XF QSPWF UIF TVCNPEVMBSJUZ PG UIF RVBMJUZ GVODUJPO BMSC XF mSTU QSPWF UIF NPOP p .yi 1 S/ UPOJDJUZ PG GVODUJPO B D j U yi Y p .yi 1 S/ S -FNNB 'PS BMM 2 GVODUJPO B D j JT NPOPUPOJD XJUI SFTQFDU UP 4VQQPTF x JT BOPUIFS VOMBCFMFE SFMBUJPOTIJQ 8F IBWF .yi 1 S x / p .yi 1 S x / B D j [f g B D j [f g D .yi 1 S x / .yi 0 S x / B D 1j [ f g C B D j [f g : .yi 0 S x / D 1 B D j [f g .yi 1 S x / C B D j [f g .yi 0 S x / k1 B D j [f g -FU .yi 1 S x / UIFO D B D j [f g 1 p .yi 1 S x / : B D j [f g D 1 k1 C .yi 0 S/ k2 B D j 4JNJMBSMZ MFU .yi 1 S/ UIFO D B D j 1 p .yi 1 S/ : B D j D 1 k2 C k1 k2 "DDPSEJOH UP UIF BTTVNQUJPO JO JU JT PCWJPVT UIBU Ä 0CWJPVTMZ 40$*"- 5*& "/"-:4*4 p .yi 1 S x / p .yi 1 S/: B D j [f g ' B D j Q /PX XF QSPWF UIF TVCNPEVMBSJUZ PG UIF RVBMJUZ GVODUJPO BMSC EFmOFE CZ &RVBUJPO Q .S/ S Y U DzFPSFN DzF RVBMJUZ GVODUJPO BMSC TBUJTmFT UIF TVCNPEVMBS QSPQFSUZ XIFO ! .1/ L F .S/ p.yi 1 G; Y S/ 1SPPG ɩF mSTU TUFQ JT UP QSPWF UIBU GVODUJPO D D j [ JT TVCNPEVMBS XJUI S A B Y U x B SFTQFDU UP 4VQQPTF ! ! .1/ BOE UIFSF JT BOPUIFS VOMBCFMFE SFMBUJPOTIJQ … 4JNJMBSMZ XF EFmOF k1 k2 k3 k4 CFMPX L L .yi 0 G; Y A x / .yi 0 G; Y A/ k1 B D j L [ [f g ;k2 B D j L [ D .yi 1 G;Y A x / D .yi 1 G;Y A/ B D j L [ [f g B D j L [ .yi 0 G; Y B x / .yi 0 G; Y B/ k3 B D j L [ [f g ;k4 B D j L [ : D .yi 1 G;Y B x / D .yi 1 G;Y B/ B D j [ [f g B D j [ U A B Y k1;k2;k3;k4 1 4JODF ! ! .1/ XF IBWF Ä *O BEEJUJPO ŋ TJODF PVS GBDUPS GVODUJPOT k1=k2 k3=k4 ˛ ˇ BSF EFmOFE BT FYQPOFOUJBMMJOFBS GVODUJPOT XF DBO IBWF D 8F EFmOF BOE BT GPMMPXT k k k k ˛ 1 3 1;ˇ 3 4 1: D k2 D k4 Ä D k1 D k2 Ä ɩFO XF DBO PCUBJO UIF GPMMPXJOH JOFRVBMJUZ L L ıı.A; x/ p .yi 1 G; Y A x / p .yi 1 G; Y A/ D B 1 D j 1 [ [f g $ B D j [ D 1 k1 $ 1 k2 C .1 ˛/kC2 $ D .1 ˛k2/.1 k2/ C C L L ıı.B; x/ p .yi 1 G; Y B x / p .yi 1 G; Y B/ D B D j [ [f g $ B D j [ .1 ˛˛/k4 $ D .1 ˛k4/.1 k4/ C .1 C˛/ˇk ˇ k 2 ıı.A; x/ 2 2 : C C C 2 2 D .1 ˛/ˇk2 1 k2 ıı.A; x/ C C C Ä L x yi .yi G; Y S ŋ*G UIFSF JT OPL GBDUPS GVODUJPO CFUXFFO BOE UIF DPODMVTJPO JT PCWJPVT PUIFSXJTF B j [ [ x /= .yi G; Y S/ x yi S f g B j [ JT POMZ SFMFWBOU UP UIF GBDUPS GVODUJPO CFUXFFO BOE TJODF SFMBUJPOTIJQT JO SFNBJO UIFJS MBCFMT BOE UIF DPODMVTJPO DBO CF EFSJWFE BDDPSEJOHMZ */'&33*/( 40$*"- 5*&4 Q A B BMSC U ɩFO XF HJWF UIF QSPPG PG UIF TVCNPEVMBSJUZ PG RVBMJUZ GVODUJPO 4VQQPTF ! ! Y yx B BOE UIFSF JT BOPUIFS VOMBCFMFE SFMBUJPOTIJQ … .A; x/ Q .A yx / Q .A/ BMSC BMSC D [f g $ L L p .yi 1 G; Y A yx / p .yi 1 G; Y A/ B B D U D j [ [f g $ U D j [ yi Y yi Y X2 .1/ X2 .1/ L Œııı.A; yx/ 1 p .yx 1 G; Y A/ B D U C $ D j [ yi Y .A yx / 2 .1/Xn [f g L Œııı.B; yx/ 1 p .yx 1 G; Y B/ B ' U C $ D j [ yi Y .B yx / 2 .1/Xn [f g .B; x/: D Q QBMS ɩFSFGPSF XF IBWF QSPWFE UIBU BMSC JT TVCNPEVMBS ɩF TVCNPEVMBSJUZ PG ! DBO CF QSPWFE JO B TJNJMBS XBZ "DDPSEJOH UP ɩFPSFN JU HVBSBOUFFT B MPXFS CPVOE PG UIF HSFFEZ BMHPSJUIN FNQMPZFE GPS UIF #.4 NPEFM ! &WBMVBUJPO 8F TUJMM VTF UIF EBUB TFUT VTFE JO 4FDUJPO UP FWBMVBUF UIF EJĊFSFOU BDUJWF MFBSOJOH BMHPSJUINT .PSF TQFDJmDBMMZ JO FBDI EBUB TFU XF mSTU SBOEPNMZ TFMFDU SFMBUJPOTIJQT BT UIF JOJUJBM MBCFMFE Y L b 10 TFU "OE UIFO XF JUFSBUJWFMZ QFSGPSN UIF BDUJWF TFMFDUJPO BMHPSJUIN FBDI UJNF TFMFDUJOH D SFMBUJPOTIJQT UP RVFSZ "GUFS FBDI SPVOE PG TFMFDUJPO XF MFBSO UIF 1-1'(. NPEFM BOE FWBMVBUF UIF QSFEJDUJPO QFSGPSNBODF 8F JNQMFNFOU UIF FYQFSJNFOU GPS UFO UJNFT PO FBDI EBUB TFU BOE VTF UIF NFBO PG 'TDPSF GPS FWBMVBUJPO $PNQBSJTPO .FUIPET 8F DPOTJEFS UIF GPMMPXJOHU CBTFMJOF NFUIPETŅ 3BOEPN *U SBOEPNMZ TFMFDUT b OPEFT JO Y BU FBDI UJNF b .BYJNVNU 6ODFSUBJOUZ .6 *U DIPPTFT UIF NPTU VODFSUBJO OPEFT BNPOH VOMBCFMFE SF MBUJPOTIJQT Y b *OGPSNBUJPOU %FOTJUZ *% *U DIPPTFT OPEFT XJUI UIF NBYJNVN BWFSBHF TJNJMBSJUZ UP BMM PUIFS OPEFT JO Y QSPQPTFE JO 4FUUMFT BOE $SBWFO <> &ąFDU PG "DUJWF -FBSOJOH 8F QMPU UIF MFBSOJOH DVSWFT PO FBDI EBUB TFU JO 'JHVSF BOE MJTU UIF BWFSBHF 'TDPSF CZ BMM TFMFDUJPO TUSBUFHJFT JO 5BCMF ɩF SFTVMUT DMFBSMZ EFNPOTUSBUF UIF FĊFD UJWFOFTT PG UIF BDUJWF TFMFDUJPO TUSBUFHJFT *O UIF 1VCMJDBUJPO EBUB TFU UIF PWFSBMM 'TDPSF PG UIF *.4 TUSBUFHZ XJUI TBNQMFT MBCFMFE PVUQFSGPSNT UIF 3BOEPN BMHPSJUIN CZ *O &NBJM Ņ8F EJE OPU DPOTJEFS UIF DPBEWJTFF DPSSFMBUJPO JO UIF NPEFM XIFO EFBMJOH XJUI UIF 1VCMJDBUJPO EBUB TFU BOE UIF DPTVCPSEJOBUF DPSSFMBUJPO GPS UIF &NBJM EBUB TFU TJODF UIFZ DPOnJDU XJUI UIF BTTVNQUJPO PG NPOPUPOJD CFMJFG JO 4FDUJPO 40$*"- 5*& "/"-:4*4 0.75 0.94 0.92 0.7 0.9 0.65 0.88 0.86 F1 − score F1 − score 0.6 Random 0.84 Random ID ID 0.82 0.55 MU MU BMS 0.8 BMS IMS IMS 0.5 0.78 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 Number of Labeled Samples Number of Labeled Samples B 1VCMJDBUJPO C &NBJM 0.9 0.85 0.8 F1 − score 0.75 Random ID 0.7 MU BMS IMS 0.65 10 20 30 40 50 60 70 80 90 100 Number of Labeled Samples D .PCJMF 'JHVSF -FBSOJOH DVSWFT JO UFSNT PG 'TDPSF BOE .PCJMF EBUB TFU UIF #.4 TUSBUFHZ BDIJFWFT UIF CFTU QFSGPSNBODF XJUI BO JNQSPWFNFOU PG BOE SFTQFDUJWFMZ 1FSGPSNBODF $PNQBSJTPO *O UIF QVCMJDBUJPO EBUB TFU CPUI UIF QSPQPTFE #.4 BOE *.4 TUSBUFHZ TJHOJmDBOUMZ QFSGPSN CFUUFS UIBO BMM UIF CBTFMJOF NFUIPET QBJSFE tUFTUT XJUI TJHOJmDBODF #.4 BMTP TJHOJmDBOUMZ PVUQFSGPSNT 3BOEPN BOE *% TUSBUFHZ JO .PCJMF EBUB TFU XIJMF JUT QFS GPSNBODF JT DMPTF UP .6 ɩF QFSGPSNBODF PG *.4 JT TIPXO CFUUFS UIBO *% JO .PCJMF EBUB TFU CVU JT DMPTF UP PUIFS CBTFMJOF NFUIPET *O &NBJM EBUB TFU #.4 TJHOJmDBOUMZ PVUQFSGPSNT 3BO EPN XIJMF UIF QFSGPSNBODF PG PUIFS NFUIPET TFFNT DMPTF UP FBDI PUIFS (FOFSBMMZ UIF QSPQPTFE #.4 TUSBUFHZ QFSGPSNT NPSF DPOTJTUFOUMZ BOE PCUBJOT CFUUFS SFTVMUT JO UXP PG UIF UISFF EBUB TFUT */'&33*/( 40$*"- 5*&4 5BCMF "WFSBHF 'TDPSF CZ BMM TFMFDUJPO TUSBUFHJFT ɩF SFTVMUT XFSF PCUBJOFE CZ SBOEPNMZ L TFMFDUJOH SFMBUJPOTIJQT BT UIF JOJUJBM MBCFMFE TFU Y BOE UIFO JUFSBUJWFMZ QFSGPSN UIF BDUJWF TFMFDUJPO b 10 BMHPSJUINT FBDI UJNF XJUI D SFMBUJPOTIJQT UP RVFSZ Data set Random MU ID BMS IMS Publication 60.6 63.7 64.8 66.4 66.8 Email 85.6 86.2 87.3 87.6 86.3 Mobile 79.2 80.0 74.3 80.4 79.9 ɩF QFSGPSNBODF PG *.4 TUSBUFHZ JT UIF CFTU JO 1VCMJDBUJPO EBUB TFU CVU TFFNT DMPTF UP CBTFMJOF NFUIPET JO UIF PUIFS UXP EBUB TFUT /FUXPSL *OGPSNBUJPO )FMQT "DDPSEJOH UP GBDUPS DPOUSJCVUJPO BOBMZTJT NFOUJPOFE CFGPSF DP BEWJTPS GBDUPS JO 1VCMJDBUJPO EBUB TFU DPOUSJCVUFT UIF NPTU ɩJT FYQMBJOT XIZ UIF QSPQPTFE NFUI PET BDIJFWF CFUUFS QFSGPSNBODF UIBO UIF BMUFSOBUJWF CBTFMJOF NFUIPET JO 1VCMJDBUJPO EBUB TFU ɩF BWFSBHF 'TDPSF PG #.4 BOE *.4 SFBDIFT XJUI MFTT UIBO MBCFMFE TBNQMFT XIJMF *% VTFT NPSF UIBO BOE .6 VTFT NPSF UIBO *O &NBJM BOE .PCJMF EBUB TFU #.4 TUJMM UBLFT BEWBO UBHF PG UIF OFUXPSL JOGPSNBUJPO CVU UIF JNQSPWFNFOU TISJOLT EVF UP UIF DPOTJEFSBCMF EFDSFBTF PG GBDUPS DPOUSJCVUJPO *O%FQUI "OBMZTJT PG #.4 ɩFSF BSF BMTP TPNF WBSJBUJPOT PG #.4 BOE XF DPOEVDU B DPNQBSJTPO b Q .A/ QBMS .A/ CFUXFFO UIFN #.4 TFMFDUT BMM OPEFT PQUJNJ[JOH BMSC XIJMF #.4 FNQMPZT ! 'JHVSF TIPXT UIF BWFSBHF 'TDPSF PG UIF EJĊFSFOU WFSTJPOT *O 1VCMJDBUJPO BOE &NBJM EBUB TFU UIF EJĊFSFODF CFUXFFO #.4 BOE #.4 JT NJOPS XIJMF UIF QFSGPSNBODF PG #.4 ESPQT *U NJHIU CF SFTVMUFE GSPN EJĊFSFOU DSJUFSJB PG UIFTF UISFF TUSBUFHJFT #.4 UFOET UP PCUBJO USVF QPTJUJWF TBNQMFT XIFSFBT #.4 JT NPSF MJLFMZ UP BDRVJSF USVFOFHBUJWF TBNQMFT 'TDPSF FYDMVEFT UIF JNQBDU PG USVFOFHBUJWF TBNQMFT BOE UIFSFGPSF VOEFSNJOFT UIF QFSGPSNBODF PG #.4 ɩF HBQ EJTBQQFBST JO .PCJMF EBUB TFU QSPCBCMZ EVF UP UIF XFBL DPOUSJCVUJPO PG JUT DPSSFMBUJPO BOE DPOTUSBJOU GBDUPST 4VNNBSZ *O UIJT TFDUJPO XF FYQMBJO IPX UP VUJMJ[F BDUJWF MFBSOJOH UP IFMQ JOGFS TPDJBM UJFT 8F QSPQPTF UXP BDUJWF MFBSOJOH TUSBUFHJFT *OnVFODF.BYJNJ[BUJPO 4FMFDUJPO BOE #FMJFG.BYJNJ[BUJPO 4FMFDUJPO CPUI BJNJOH UP DBQUVSF UIF JOUFSSFMBUJPOTIJQ JOnVFODF &YQFSJNFOUBM SFTVMUT TIPX UIBU #.4 BOE *.4 PGUFO BDIJFWF TJHOJmDBOU CFUUFS QFSGPSNBODF UIBO CBTFMJOF NFUIPET */'&33*/( 40$*"- 5*&4 "$3044 )&5&30(&/&064 /&5803,4 *O UIF QSFWJPVT TFDUJPOT XF JOUSPEVDFE NFUIPEPMPHJFT UP JOGFS QBSUJDVMBS UZQFT PG SFMBUJPOTIJQT JO EJĊFSFOU TQFDJmD TPDJBM OFUXPSLT /PX XF EJTDVTT IPX UP HFOFSBMJ[F UIF QSPCMFN UP JOGFS TPDJBM UJFT BDSPTT NVMUJQMF IFUFSPHFOFPVT OFUXPSLT 40$*"- 5*& "/"-:4*4 90 BMS 80 BMS+ BMS− 70 60 50 40 30 20 AverageF1 − scorelearning of curves 10 0 Publication Email Mobile 'JHVSF 1FSGPSNBODF DPNQBSJTPO CFUXFFO WBSJBUJPOT PG #.4 *O USBEJUJPOBM NFUIPET TVċDJFOU MBCFMFE SFMBUJPOTIJQT BSF VTVBMMZ OFDFTTBSZ UP MFBSO B HPPE QSFEJDUJWF NPEFM GPS JOGFSSJOH TPDJBM UJFT )PXFWFS UIF BWBJMBCJMJUJFT PG MBCFMFE SFMBUJPOTIJQT JO EJĊFSFOU OFUXPSLT BSF WFSZ VOCBMBODFE *O TPNF OFUXPSLT TVDI BT 4MBTIEPU JU NJHIU CF FBTZ UP DPMMFDU UIF MBCFMFE SFMBUJPOTIJQT FH USVTUEJTUSVTU SFMBUJPOTIJQT CFUXFFO VTFST XIJMF JO NPTU PUIFS OFUXPSLT JU NBZ CF EJċDVMU PS FWFO JOGFBTJCMF UP PCUBJO UIF MBCFMFE JOGPSNBUJPO " DIBM MFOHJOH RVFTUJPO JT DBO XF MFWFSBHF UIF MBCFMFE SFMBUJPOTIJQT GSPN POF OFUXPSL UP JOGFS UIF UZQF PG SFMBUJPOTIJQT JO BOPUIFS UPUBMMZ EJĊFSFOU OFUXPSL 1SPCMFN 'PSNVMBUJPO 'JHVSF HJWFT BO FYBNQMF PG JOGFSSJOH TPDJBM UJFT BDSPTT B QSPEVDU SFWJFXFS OFUXPSL BOE B NPCJMF DPNNVOJDBUJPO OFUXPSL *O 'JHVSF UIF MFGU TVCmHVSF JT UIF JOQVU UP PVS QSPCMFN B SFWJFXFS OFUXPSL XIJDI DPOTJTUT PG SFWJFXFST BOE SFMBUJPOTIJQT CFUXFFO SFWJFXFST BOE B NPCJMF OFUXPSL XIJDI DPOTJTUT PG NPCJMF VTFST BOE UIFJS DPNNVOJDBUJPO SFMB UJPOTIJQT WJB DBMMJOH PS UFYUJOH NFTTBHF ɩF SJHIU TVCmHVSF TIPXT UIF PVUQVU PG PVS QSPCMFN UIF JOGFSSFE TPDJBM UJFT JO UIF UXP OFUXPSLT *O UIF SFWJFXFS OFUXPSL XF JOGFS UIF USVTUEJTUSVTU SFMBUJPOTIJQT BOE JO UIF DPNNVOJDBUJPO OFUXPSL XF JEFOUJGZ GSJFOETIJQT DPMMFBHVFT BOE GBNJ MJFT ɩF NJEEMF PG 'JHVSF JT UIF DPNQPOFOU PG LOPXMFEHF USBOTGFS GPS JOGFSSJOH TPDJBM UJFT JO EJĊFSFOU OFUXPSLT ɩJT JT UIF LFZ PCKFDUJWF PG UIJT XPSL ɩF GVOEBNFOUBM DIBMMFOHF JT IPX UP CSJEHF UIF BWBJMBCMF LOPXMFEHF GSPN EJĊFSFOU OFUXPSLT UP IFMQ JOGFS UIF EJĊFSFOU UZQFT PG TPDJBM SFMBUJPOTIJQT G .V; EL;EU ; / EL 'PSNBMMZ MFU D 9 EFOPUF B QBSUJBMMZ MBCFMFE TPDJBM OFUXPSL XIFSF JT B EU EL EU E TFU PG MBCFMFE SFMBUJPOTIJQT BOE JT B TFU PG VOMBCFMFE SFMBUJPOTIJQT XJUI [ D 9 JT E d E BO j j" BUUSJCVUF NBUSJY BTTPDJBUFE XJUI FEHFT JO XJUI FBDI SPX DPSSFTQPOEJOHth UP BO FEHF FBDI DPMVNO BO BUUSJCVUF BOE BO FMFNFOU xij EFOPUJOH UIF WBMVF PG UIF j BUUSJCVUF PG FEHF ei */'&33*/( 40$*"- 5*&4 +HWHURJHQHRXV1HWZRUNV ,QIHUUHGVRFLDOWLHVLQ GLIIHUHQWQHWZRUNV 5HYLHZHUQHWZRUN Adam review Adam review distrust trust Bob Product 1 Bob distrust Chris trust Chris review Danny review Danny Product 2 .QRZOHGJH 7UDQVIHUIRU ,QIHUULQJ &RPPXQLFDWLRQQHWZRUN 6RFLDO7LHV From Home Both in office 08:40 08:00 – 18:00 Colleague Family From Office 11:35 Colleague From Office From Office 15:20 17:55 Colleague Friend From Outside 21:30 Friend 'JHVSF &YBNQMF PG JOGFSSJOH TPDJBM UJFT BDSPTT UXP IFUFSPHFOFPVT OFUXPSLT B QSPEVDUSFWJFXFS OFUXPSL BOE B NPCJMF DPNNVOJDBUJPO OFUXPSL ei yi ɩF MBCFM PG FEHF JT EFOPUFE BT 2 Y XIFSF Y JT UIF QPTTJCMF TQBDF PG UIF MBCFMT FH GBNJMZ DPMMFBHVF DMBTTNBUF GS (JWFO UIJT UIF JOQVU UP PVS QSPCMFNL DPOTJTUTL PG UXP QBSUJBMMZ MBCFMFE OFUXPSLTL TPVSDF GT E E E 0 OFUXPSL BOE UBSHFU OFUXPSL XJUI j S j(j T j XJUI BO FYUSFNF DBTF PG j T jD 1MFBTF VS OPUF UIBU UIF UXP OFUXPSLT NJHIU CF UPUBMMZ EJĊFSFOU XJUI EJĊFSFOU TFUT PG WFSUFYFT JF \ VT ¿ D BOE EJĊFSFOU BUUSJCVUFT EFmOFE PO FEHFT *O SFBM TPDJBM OFUXPSLT UIF SFMBUJPOTIJQ DPVME CF VOEJSFDUFE FH GSJFOETIJQT JO B NPCJMF OFUXPSL PS EJSFDUFE FH NBOBHFSTVCPSEJOBUF SFMBUJPOTIJQT JO BO FOUFSQSJTF FNBJM OFUXPSL 5P LFFQ UIJOHT DPOTJTUFOU XF XJMM DPODFOUSBUF PO UIF VOEJSFDUFE OFUXPSL *O BEEJUJPO UIF MBCFM PG B SFMBUJPOTIJQ NBZ CF TUBUJD FH UIF GBNJMZNFNCFS SFMBUJPOTIJQ PS DIBOHF PWFS UJNF FH UIF NBOBHFSTVCPSEJOBUF SFMBUJPOTIJQ *O UIJT XPSL XF GPDVT PO TUBUJD SFMBUJPOTIJQT (JWFO B TPVSDF OFUXPSL GS XJUI BCVOEBOUMZ MBCFMFE SFMBUJPOTIJQT BOE B UBSHFU OFUXPSL GT f XJUI B MJNJUFE OVNCFS PG MBCFMFE SFMBUJPOTIJQT UIF HPBM JT UP MFBSO B QSFEJDUJWF GVODUJPO W .GT GS / YT j ! GPS JOGFSSJOH UIF UZQF PG SFMBUJPOTIJQT JO UIF UBSHFU OFUXPSL CZ MFWFSBHJOH UIF TVQFSWJTFE JOGPSNBUJPO MBCFMFE SFMBUJPOTIJQT GSPN UIF TPVSDF OFUXPSL 40$*"- 5*& "/"-:4*4 8JUIPVU MPTT PG HFOFSBMJUZ XF BTTVNF UIBU GPS FBDI QPTTJCMF UZQF yi PG SFMBUJPOTIJQ ei UIF p.yi ei / QSFEJDUJWF GVODUJPO XJMM PVUQVU B QSPCBCJMJUZ j UIVT PVS UBTL DBO CF WJFXFE BT PCUBJOJOH B .ei ;yi ; p.yi ei // ei USJQMF j UP DIBSBDUFSJ[F FBDI MJOL JO UIF TPDJBM OFUXPSL %BUB 4FUT 5P TUVEZ UIJT QSPCMFN XF USZ UP mOE B OVNCFS PG EJĊFSFOU UZQFT PG OFUXPSLT UP JOWFTUJHBUF UIF QSPCMFN PG JOGFSSJOH TPDJBM UJFT BDSPTT IFUFSPHFOFPVT OFUXPSLT *O UIJT TUVEZ XF DPOTJEFS mWF EJĊFSFOU UZQFT PG OFUXPSLT &QJOJPOT 4MBTIEPU .PCJMF $PBVUIPS BOE &OSPO 5B CMF MJTUT TUBUJTUJDT PG UIF mWF OFUXPSLT "MM EBUB TFUT BOE DPEFT VTFE JO UIJT XPSL BSF QVCMJDMZ BWBJMBCMF &QJOJPOT JT B OFUXPSL PG QSPEVDU SFWJFXFST &BDI VTFS PO UIF TJUF DBO QPTU B SFWJFX PO BOZ QSPEVDU BOE PUIFS VTFST XPVME SBUF UIF SFWJFX XJUI USVTU PS EJTUSVTU *O UIJT EBUB XF DSFBUFE B OFU XPSL PG SFWJFXFST DPOOFDUFE XJUI USVTU BOE EJTUSVTU SFMBUJPOTIJQT ɩF EBUB TFU DPOTJTUT PG OPEFT VTFST BOE FEHFT PG XIJDI BCPVU BSF USVTU MJOLT VTFST SFDFJWFE BU MFBTU POF USVTU PS EJTUSVTU FEHF 0VS HPBM PO UIJT EBUB TFU JT UP JOGFS UIF USVTU SFMBUJPOTIJQT CFUXFFO VTFST 4MBTIEPU JT B OFUXPSL PG GSJFOET 4MBTIEPU JT B TJUF GPS TIBSJOH UFDIOPMPHZ SFMBUFE OFXT *O 4MBTIEPU JOUSPEVDFE UIF 4MBTIEPU ;PP XIJDI BMMPXT VTFST UP UBH FBDI PUIFS BT iGSJFOETw MJLF PS iGPFTw EJTMJLF ɩF EBUB TFU JT DPNQSJTFE PG VTFST BOE FEHFT PG XIJDI BSF iGSJFOEw SFMBUJPOTIJQT 0VS HPBM PO UIJT EBUB TFU JT UP JOGFS UIF iGSJFOEw SFMBUJPOTIJQT CFUXFFO VTFST .PCJMF JT B OFUXPSL PG NPCJMF VTFST ɩF EBUB TFU JT GSPN &BHMF FU BM <> *U DPOTJTUT PG UIF MPHT PG DBMMT CMVFUPPUI TDBOOJOH EBUB BOE DFMM UPXFS *%T PG VTFST EVSJOH BCPVU NPOUIT *G UXP VTFST DPNNVOJDBUFE CZ NBLJOH B DBMM BOE TFOEJOH B UFYU NFTTBHF XJUI FBDI PUIFS PS DPPDDVSSFE JO UIF TBNF QMBDF XF DSFBUF BO FEHF CFUXFFO UIFN *O UPUBM UIF EBUB DPOUBJOT FEHFT 0VS HPBM JT UP JOGFS XIFUIFS UXP VTFST IBWF B GSJFOE SFMBUJPOTIJQ 'PS FWBMVBUJPO BMM VTFST BSF SFRVJSFE UP DPNQMFUF BO POMJOF TVSWFZ JO XIJDI QBJST PG VTFST BSF MBCFMFE BT GSJFOET $PBVUIPS JT B OFUXPSL PG BVUIPST ɩF EBUB TFU DSBXMFE GSPN "SOFU.JOFSPSH <> JT DPNQSJTFE PG BVUIPST BOE DPBVUIPS SFMBUJPOTIJQT *O UIJT EBUB TFU XF BUUFNQU UP JOGFS BEWJTPSBEWJTFF SFMBUJPOTIJQT CFUXFFO DPBVUIPST 'PS FWBMVBUJPO XF DSFBUFE B TNBMMFS HSPVOE USVUI EBUB JO UIF GPMMPXJOH XBZT DPMMFDUJOH UIF BEWJTPSBEWJTFF JOGPSNBUJPO GSPN UIF .BUIFNBUJDT (FOFBMPHZ QSPKFDU ¤ BOE UIF "* (FOFBMPHZ QSPKFDU© NBOVBMMZ DSBXMJOH UIF BEWJTPSBEWJTFF JOGPSNBUJPO GSPN SFTFBSDIFST IPNFQBHFT 'JOBMMZ XF IBWF DSFBUFE B EBUB TFU XJUI DPBVUIPS SFMBUJPOTIJQT PG XIJDI BSF BEWJTPSBEWJTFF SFMBUJPOTIJQT ɩF EBUB TFU XBT VTFE JO 8BOH FU BM <> &OSPO JT BO FNBJM DPNNVOJDBUJPO OFUXPSL *U DPOTJTUT PG FNBJMT CFUXFFO &OSPO FNQMPZFFT 5XP UZQFT PG SFMBUJPOTIJQT JF NBOBHFSTVCPSEJOBUF BOE DPMMFBHVF XFSF BO OPUBUFE CFUXFFO UIFTF FNQMPZFFT ɩF EBUB TFU XBT QSPWJEFE CZ %JFIM FU BM <> 0VS HPBM PO IUUQBSOFUNJOFSPSHTPDJBMUJFBDSPTT ¤IUUQXXXHFOFBMPHZNBUIOETVOPEBLFEV ©IUUQBJHQFFDTVNJDIFEV */'&33*/( 40$*"- 5*&4 UIJT EBUB TFU JT UP JOGFS NBOBHFSTVCPSEJOBUF SFMBUJPOTIJQT CFUXFFO VTFST ɩFSF BSF JO UPUBM FEHFT PG XIJDI BSF NBOBHFSTVCPSEJOBUF SFMBUJPOTIJQT 1MFBTF OPUF UIBU GPS UIF mSTU UISFF EBUB TFUT JF &QJOJPOT 4MBTIEPU BOE .PCJMF PVS HPBM JT UP JOGFS VOEJSFDUFE SFMBUJPOTIJQT GSJFOETIJQT PS USVTUGVM SFMBUJPOTIJQT XIJMF GPS UIF PUIFS UXP EBUB TFUT JF $PBVUIPS BOE &OSPO PVS HPBM JT UP JOGFS EJSFDUFE SFMBUJPOTIJQT UIF TPVSDF FOE IBT B IJHIFS TPDJBM TUBUVT UIBO UIF UBSHFU FOE FH BEWJTPSBEWJTFF SFMBUJPOTIJQT BOE NBOBHFS TVCPSEJOBUF SFMBUJPOTIJQT 5BCMF 4UBUJTUJDT PG mWF EBUB TFUT Relationship Dataset #Nodes #Edges Trust Epinions 131,828 841,372 Friendship Slashdot 77,357 516,575 Friendship Mobile 107 5,436 Advisor-advisee Coauthor 815,946 2,792,833 Manager- Enron 151 3,572 subordinate 0CTFSWBUJPOT "T B mSTU TUFQ XF FOHBHF JO TPNF IJHIMFWFM JOWFTUJHBUJPO PG IPX EJĊFSFOU GBDUPST JOnVFODF UIF GPSNBUJPO PG EJĊFSFOU TPDJBM UJFT JO EJĊFSFOU OFUXPSLT (FOFSBMMZ JG XF DPOTJEFS JOGFSSJOH QBSUJD VMBS TPDJBM UJFT JO B TQFDJmD OFUXPSL FH NJOJOH BEWJTPSBEWJTFF SFMBUJPOTIJQT GSPN UIF $PBVUIPS OFUXPSL XF DBO EFmOF EPNBJOTQFDJmD GFBUVSFT BOE MFBSO B QSFEJDUJWF NPEFM CBTFE PO MBCFMFE USBJOJOH EBUB ɩF QSPCMFN CFDPNFT WFSZ EJĊFSFOU XIFO IBOEMJOH NVMUJQMF IFUFSPHFOFPVT OFU XPSLT BT UIF EFmOFE GFBUVSFT JO EJĊFSFOU OFUXPSLT NBZ CF TJHOJmDBOUMZ EJĊFSFOU 5P TPMWF UIJT QSPCMFN XF DPOOFDU PVS QSPCMFN UP TFWFSBM CBTJD TPDJBM QTZDIPMPHJDBM UIFPSJFT BOE GPDVT PVS BOBMZTJT PO UIF OFUXPSL CBTFE DPSSFMBUJPOT WJB UIF GPMMPXJOH TUBUJTUJDT 4PDJBM CBMBODF <> )PX JT UIF TPDJBM CBMBODF QSPQFSUZ TBUJTmFE BOE DPSSFMBUFE JO EJĊFSFOU OFUXPSLT 4USVDUVSBM IPMF <> 8PVME TUSVDUVSBM IPMFT IBWF B TJNJMBS CFIBWJPS QBUUFSO JO EJĊFSFOU OFU XPSLT 4PDJBM TUBUVT < > )PX EP EJĊFSFOU OFUXPSLT TBUJTGZ UIF QSPQFSUJFT PG TPDJBM TUBUVT i5XPTUFQ nPXw <> )PX EP EJĊFSFOU OFUXPSLT GPMMPX UIF iUXPTUFQ nPXw PG JOGPSNBUJPO QSPQBHBUJPO 4PDJBM #BMBODF 4PDJBM CBMBODF UIFPSZ TVHHFTUT UIBU QFPQMF JO B TPDJBM OFUXPSL UFOE UP GPSN JOUP B CBMBODFE OFUXPSL TUSVDUVSF 'JHVSF TIPXT UIF QSPCBCJMJUJFT PG CBMBODFE USJBET PG UIF UISFF 40$*"- 5*& "/"-:4*4 1 Epinions Slashdot 0.8 Mobile 0.6 0.4 0.2 0 relationships communication links 'JHVSF 4PDJBM CBMBODF 1SPCBCJMJUJFT PG CBMBODFE USJBET JO EJĊFSFOU OFUXPSLT CBTFE PO DPNNVOJDBUJPO MJOLT BOE GSJFOETIJQT PS USVTUGVM SFMBUJPOTIJQT #BTFE PO DPNNVOJDBUJPO MJOLT EJĊFSFOU OFUXPSLT IBWF WFSZ EJĊ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mOE JU JOUFSFTUJOH UIBU EJĊFSFOU OFUXPSLT IBWF WFSZ EJĊFSFOU CBMBODF QSPCBCJMJUJFT CBTFE PO UIF DPNNVOJDBUJPO MJOLT FH UIF CBMBODF QSPCBCJM JUZ JO UIF NPCJMF OFUXPSL JT OFBSMZ TFWFO UJNFT IJHIFS UIBO UIBU PG UIF TMBTIEPU OFUXPSL XIJMF CBTFE PO GSJFOETIJQT PS USVTUGVM SFMBUJPOTIJQT UIF UISFF OFUXPSLT IBWF SFMBUJWFMZ TJNJMBS CBMBODF QSPCBCJMJUJFT XJUI B NBYJNVN PG EJĊFSFODF 4USVDUVSBM )PMF " QFSTPO JT TBJE UP TQBO B TUSVDUVSBM IPMF JO B TPDJBM OFUXPSL JG IF PS TIF JT MJOLFE UP QFPQMF JO QBSUT PG UIF OFUXPSL UIBU BSF PUIFSXJTF OPU XFMM DPOOFDUFE UP POF BOPUIFS <> "SHVNFOUT CBTFE PO TUSVDUVSBM IPMFT TVHHFTU UIBU UIFSF JT BO JOGPSNBUJPOBM BEWBOUBHF UP IBWJOH GSJFOET JO B OFUXPSL XIP EP OPU LOPX FBDI PUIFS 0VS JEFB IFSF JT UP UFTU JG B TUSVDUVSBM IPMF UFOET UP IBWF UIF TBNF UZQF PG SFMBUJPOTIJQ XJUI UIF PUIFS VTFST 8F mSTU FNQMPZ B TJNQMF BMHPSJUIN UP JEFOUJGZ TUSVDUVSBM IPMF VTFST JO B OFUXPSL 'PMMPXJOH UIF JOGPSNBM EFTDSJQUJPO PG TUSVDUVSBM IPMFT <> GPS FBDI OPEF XF DPVOU UIF OVNCFS PG QBJST PG OFJHICPST XIP BSF OPU EJSFDUMZ DPOOFDUFE "MM VTFST BSF SBOLFE CBTFE PO UIF OVNCFS PG QBJST BOE UIF UPQ VTFSTņ XJUI UIF IJHIFTU OVNCFST BSF WJFXFE BT TUSVDUVSBM IPMFT JO UIF OFUXPSL 'JHVSF TIPXT UIF QSPCBCJMJUJFT UIBU UXP VTFST " BOE # IBWF UIF TBNF UZQF PG SFMBUJPOTIJQ XJUI BOPUIFS VTFS TBZ $ DPOEJUJPOFE PO XIFUIFS ņɩJT JT CBTFE PO UIF PCTFSWBUJPO UIBU MFTT UIBO PG UIF 5XJUUFS VTFST QSPEVDF PG JUT DPOUFOU <> */'&33*/( 40$*"- 5*&4 1 Random SH−not connected 0.8 SH−connected 0.6 0.4 0.2 0 Epinions Slashdot Mobile 'JHVSF 4USVDUVSBM IPMF 1SPCBCJMJUJFT UIBU UXP DPOOFDUFE PS EJTDPOOFDUFE VTFST " BOE # IBWF UIF TBNF UZQF PG SFMBUJPOTIJQ XJUI VTFS $ DPOEJUJPOFE PO XIFUIFS VTFS $ TQBOT B TUSVDUVSBM IPMF PS OPU *U JT DMFBS UIBU VTFST BSF NPSF MJLFMZ BWFSBHFMZ IJHIFS UIBO DIBODF UP IBWF UIF TBNF UZQF PG SFMBUJPOTIJQ XJUI $ JG $ TQBOT B TUSVDUVSBM IPMF BOE EJTDPOOFDUFE VTFST BSF NPSF MJLFMZ UIBO DPOOFDUFE VTFST UP IBWF UIF TBNF UZQF PG SFMBUJPOTIJQ XJUI B VTFS XIP TQBOT B TUSVDUVSBM IPMF FYDFQU UIF NPCJMF OFUXPSL VTFS $ TQBOT B TUSVDUVSBM IPMF PS OPU 8F IBWF UXP JOUFSFTUJOH PCTFSWBUJPOT VTFST BSF NPSF MJLFMZ PO BWFSBHF IJHIFS UIBO DIBODF UP IBWF UIF TBNF UZQF PG SFMBUJPOTIJQ XJUI $ JG $ TQBOT B TUSVDUVSBM IPMF BOE EJTDPOOFDUFE VTFST BSF NPSF MJLFMZ UIBO DPOOFDUFE VTFST UP IBWF UIF TBNF UZQF PG SFMBUJPOTIJQ XJUI B VTFS DMBTTJmFE BT TQBOOJOH B TUSVDUVSBM IPMF 0OF FYDFQUJPO JT UIF NPCJMF OFUXPSL XIFSF NPTU NPCJMF VTFST JO UIF EBUB TFU BSF VOJWFSTJUZ TUVEFOUT BOE UIVT GSJFOET GSFRVFOUMZ DPNNVOJDBUF XJUI FBDI PUIFS 4PDJBM 4UBUVT 4PDJBM TUBUVT UIFPSZ < > JT CBTFE PO UIF EJSFDUFE SFMBUJPOTIJQ OFUXPSL 8F DPOEVDUFE BO BOBMZTJT PO UIF $PBVUIPS BOE &OSPO OFUXPSLT XIFSF XF BJN UP mOE EJSFDUFE SFMBUJPOTIJQT BEWJTPSBEWJTFF BOE NBOBHFSTVCPSEJOBUF 8F GPVOE OFBSMZ PG USJBET JO UIF UXP OFUXPSLT TBUJTGZ UIF TPDJBM TUBUVT UIFPSZ XIJDI XBT BMTP WBMJEBUFE JO -FTLPWFD FU BM <> 8F JOWFTUJHBUF NPSF CZ MPPLJOH BU UIF EJTUSJCVUJPO PG EJĊFSFOU GPSNT PG USJBET JO UIF UXP OFUXPSLT 4QFDJmDBMMZ UIFSF BSF JO UPUBM EJĊFSFOU GPSNT PG USJBET <> 8F TFMFDU mWF NPTU GSFRVFOU GPSNT PG USJBET JO UIF UXP OFUXPSLT 'PS FBTZ VOEFSTUBOEJOH HJWFO B USJBE .A; B; C / XF VTF UP EFOPUF UIF BEWJTPSBEWJTFF SFMBUJPOTIJQ BOE DPMMFBHVF SFMBUJPOTIJQ BOE UISFF DPOTFDVUJWF OVNCFST 011 UP EFOPUF A BOE B BSF DPMMFBHVFT B JT C T BEWJTPS BOE A JT C T BEWJTPS *U JT TUSJLJOH UIBU BMUIPVHI UIF UXP OFUXPSLT $PBVUIPS BOE &OSPO BSF UPUBMMZ EJĊFSFOU UIFZ TIBSF B TJNJMBS EJTUSJCVUJPO PO UIF mWF GSFRVFOU GPSNT PG USJBET BT QMPUUFE JO 'JHVSF 40$*"- 5*& "/"-:4*4 0.5 011 101 0.4 110 100 0.3 000 0.2 0.1 0 Enron Coauthor 'JHVSF 4PDJBM TUBUVT %JTUSJCVUJPO PG mWF NPTU GSFRVFOU GPSNBUJPOT PG USJBET XJUI TPDJBM TUBUVT (JWFO B USJBE .A; B; C / MFU VT VTF UP EFOPUF UIF BEWJTPSBEWJTFF SFMBUJPOTIJQ BOE DPMMFBHVF SFMBUJPOTIJQ ɩVT UIF OVNCFS 011 UP EFOPUF A BOE B BSF DPMMFBHVFT B JT C T BEWJTPS BOE A JT C T BEWJTPS 0QJOJPO -FBEFS ɩF UXPTUFQ nPX UIFPSZ <> TVHHFTUT UIBU JEFBT JOOPWBUJPOT VTVBMMZ nPX mSTU UP PQJOJPO MFBEFST BOE UIFO GSPN UIFN UP B XJEFS QPQVMBUJPO 0VS CBTJD JEFB IFSF JT UP FYBNJOF XIFUIFS iPQJOJPO MFBEFSTw BSF NPSF MJLFMZ UP IBWF B IJHIFS TPDJBM TUBUVT NBOBHFS PS BEWJTPS UIBO PSEJOBSZ VTFST 5P EP UIJT XF mSTU DBUFHPSJ[F VTFST JOUP UXP HSPVQT PQJOJPO MFBEFST BOE PSEJOBSZ VTFST CZ 1BHF3BOLŇ 8JUI 1BHF3BOL BDDPSEJOH UP UIF OFUXPSL TUSVDUVSF XF TFMFDU BT PQJOJPO MFBEFST UIF UPQ VTFST XIP IBWF UIF IJHIFTU 1BHF3BOL TDPSFT BOE UIF SFTU BT PSEJOBSZ VTFST ɩ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ɩF SFBTPO NJHIU CF JO UIF FOUFSQSJTF FNBJM OFUXPSL &OSPO TPNF NBOBHFST NBZ CF JOBDUJWF BOE NPTU NBOBHFNFOUSFMBUFE DPNNVOJDBUJPOT XFSF EPOF CZ UIFJS BTTJTUBOUT 4VNNBSZ "DDPSEJOH UP UIF TUBUJTUJDT BCPWF XF IBWF UIF GPMMPXJOH JOUVJUJPOT 1SPCBCJMJUJFT PG CBMBODFE USJBET CBTFE PO DPNNVOJDBUJPO MJOLT BSF WFSZ EJĊFSFOU JO EJĊFSFOU OFUXPSLT XIJMF UIF CBMBODF QSPCBCJMJUJFT CBTFE PO GSJFOETIJQT PS USVTUGVM SFMBUJPOTIJQT BSF TJNJMBS XJUI FBDI PUIFS Ň1BHF3BOL JT BO BMHPSJUIN UP FTUJNBUF UIF JNQPSUBODF PG FBDI OPEF JO B OFUXPSL <> */'&33*/( 40$*"- 5*&4 1 from OU to OU from OL to OU 0.8 from OU to OL from OL to OL 0.6 0.4 0.2 0 Enron Coauthor 'JHVSF 0QJOJPO MFBEFS 0- 0QJOJPO MFBEFS 06 0SEJOBSZ VTFS 1SPCBCJMJUZ UIBU UXP UZQFT PG VTFST IBWF B EJSFDUFE SFMBUJPOTIJQ GSPN IJHIFS TPDJBM TUBUVT UP MPXFS TUBUVT JF NBOBHFSTVCPSEJOBUF SFMBUJPOTIJQ JO &OSPO BOE BEWJTPSBEWJTFF SFMBUJPOTIJQ JO $PBVUIPS *U JT DMFBS UIBU PQJOJPO MFBEFST EFUFDUFE CZ 1BHF3BOL BSF NPSF MJLFMZ UP IBWF B IJHIFS TPDJBM TUBUVT UIBO PSEJOBSZ VTFST 6TFST BSF NPSF MJLFMZ C$C IJHIFS UIBO DIBODF UP IBWF UIF TBNF UZQF PG SFMB UJPOTIJQ XJUI B VTFS XIP TQBOT B TUSVDUVSBM IPMF .PTU USJBET TBUJTGZ QSPQFSUJFT PG UIF TPDJBM TUBUVT UIFPSZ 'PS UIF mWF NPTU GSFRVFOU GPSNBUJPOT PG USJBET UIF $PBVUIPS BOE UIF &OSPO OFUXPSLT TIBSF B TJNJMBS EJTUSJCVUJPO 0QJOJPO MFBEFST BSF NPSF MJLFMZ C$C IJHIFS UIBO DIBODF UP IBWF B IJHIFS TPDJBM TUBUVT UIBO PSEJOBSZ VTFST .PEFM 'SBNFXPSL 8F QSPQPTF B USBOTGFSCBTFE GBDUPS HSBQI 5SBO'( NPEFM GPS MFBSOJOH BOE QSFEJDUJOH UIF UZQF PG TPDJBM SFMBUJPOTIJQT BDSPTT OFUXPSLT 8F mSTU EFTDSJCF UIF NPEFM JO UIF DPOUFYU PG B TJOHMF OFUXPSL BOE UIFO FYQMBJO IPX UP USBOTGFS UIF TVQFSWJTFE JOGPSNBUJPO QSPWJEFE CZ POF OFUXPSL UP BOPUIFS OFUXPSL G .V; EL;EU ; / -FBSOJOH PWFS 4JOHMF /FUXPSL (JWFO B OFUXPSL D 9 FBDI SFMBUJPOTIJQ FEHF ei JT BTTPDJBUFE XJUI BO BUUSJCVUF WFDUPS xi BOE B MBCFM yi JOEJDBUFT UIF UZQF PG UIF SFMBUJPOTIJQ xi Y yi -FU 9 Df g BOE Df g ɩFO XF IBWF UIF GPMMPXJOH GPSNVMBUJPO P.X;G Y /P.Y / P.Y X;G/ j : j D P.X;G/ 40$*"- 5*& "/"-:4*4 )FSF G EFOPUFT BMM GPSNT PG OFUXPSL JOGPSNBUJPO ɩJT QSPCBCJMJTUJD GPSNVMBUJPO JOEJDBUFT UIBU MBCFMT PG FEHFT EFQFOE PO OPU POMZ MPDBM BUUSJCVUFT BTTPDJBUFE XJUI FBDI FEHF CVU BMTP UIF TUSVDUVSF PG UIF OFUXPSL "DDPSEJOH UP #BZFT SVMF XF IBWF P.X;G Y /P.Y / P.Y X;G/ j ; P.X Y/ P.Y G/ j D P.X;G/ / j # j P.Y G/ P.X Y/ XIFSF j SFQSFTFOUT UIF QSPCBCJMJUZ PG MBCFMT HJWFO UIF TUSVDUVSF PG UIF OFUXPSL BOE j EFOPUFT UIF QSPCBCJMJUZ PG HFOFSBUJOH BUUSJCVUFT X BTTPDJBUFE UP BMM FEHFT HJWFO UIFJS MBCFMT Y 8F BTTVNF UIBU UIF HFOFSBUJWF QSPCBCJMJUZ PG BUUSJCVUFT HJWFO UIF MBCFM PG FBDI FEHF JT DPOEJUJPOBMMZ JOEFQFOEFOU UIVT XF IBWF P.Y X;G/ P.Y G/ P.xi yi / j / j j Yi P.xi yi / xi yi XIFSF j JT UIF QSPCBCJMJUZ PG HFOFSBUJOH BUUSJCVUFT HJWFO UIF MBCFM /PX UIF QSPCMFN P.Y G/ P.xi yi / JT IPX UP JOTUBOUJBUF UIF QSPCBCJMJUZ j BOE j *O QSJODJQMF UIFZ DBO CF JOTUBOUJBUFE JO EJĊFSFOU XBZT GPS FYBNQMF CZ UIF #BZFTJBO UIFPSZ PS .BSLPW SBOEPN mFMET *O UIJT CPPL XF DIPPTF UIF MBUUFS #BTFE PO .BSLPW SBOEPN mFMET GPS BOZ OPEF vi UIF DPOEJUJPOBM QSPQ P.yi G vi / P.yi NB.i// NB.i/ yi G FSUZ IPMET j n D j XIFSF BSF OFJHICPSIPPE PG JO UIF HSBQI ɩF )BNNFSTMFZ$MJĊPSE UIFPSFN <> UFMMT VT UIBU UIF QSPCBCJMJUZ PG B .BSLPW SBOEPN mFME JT FRVJWBMFOU UP B (JCCT EJTUSJCVUJPO XIJDI JT GBDUPSJ[FE JOUP QPTJUJWF GVODUJPO EFmOFE PO DMJRVFT Yc G f g UIBU DPWFS BMM UIF OPEFT BOE FEHFT PG ɩVT UIF UXP QSPCBCJMJUJFT JO &R DBO CF SFXSJUUFO BT 1 d P.xi yi / ˛j gj .xij ;yi / j D Z1 FYQf g j 1 1 XD P.Y G/ + h .Y / Z FYQ k k c j D 2 f c g X Xk Z1 Z2 XIFSF BOE BSF OPSNBMJ[BUJPO GBDUPST &RVBUJPO JOEJDBUFT UIBU XF EFmOF B GFBUVSFth GVODUJPO gj .xij ;yi / GPS FBDI BUUSJCVUF xij BTTPDJBUFE XJUI FEHF ei BOE ˛j JT UIF XFJHIU PG UIF j BUUSJCVUF *U DBO CF EFmOFE BT FJUIFS B CJOBSZ GVODUJPO PS B SFBMWBMVFE GVODUJPO 'PS FYBNQMF GPS JOGFSSJOH BEWJTPSBEWJTFF SFMBUJPOTIJQT GSPN UIF QVCMJDBUJPO OFUXPSL XF DBO EFmOF B SFBMWBMVFE GFBUVSF GVODUJPO BT UIF EJĊFSFODF PG ZFBST XIFO BVUIPST vi BOE vj SFTQFDUJWFMZ QVCMJTIFE IJT mSTU hk.Yc/ k QBQFS *O &R XF EFmOF B TFU PG DPSSFMBUJPO GFBUVSFth GVODUJPOT f g PWFS FBDI DMJRVF Yc JO UIF OFUXPSL )FSF +k JT UIF XFJHIU PG UIF k DPSSFMBUJPO GFBUVSF GVODUJPO ɩF TJNQMFTU DMJRVF JT BO FEHF UIVT B GFBUVSF GVODUJPO hk.yi ;yj / DBO CF EFmOFE BT UIF DPSSFMBUJPO CFUXFFO UXP FEHFT .ei ;ej / JG UIF UXP FEHFT TIBSF B DPNNPO FOE OPEF 8F BMTP DPOTJEFS USJBET BT DMJRVFT JO UIF 5SBO'( NPEFM JO UIBU TFWFSBM TPDJBM UIFPSJFT XF EJTDVTTFE JO 4FDUJPO BSF CBTFE PO USJBET */'&33*/( 40$*"- 5*&4 *G XF BSF HJWFO B TJOHMF OFUXPSL G XJUI MBCFMFE JOGPSNBUJPO Y MFBSOJOH UIF QSFEJDUJWF ' . ˛ ; + / NPEFM JT UP FTUJNBUF B QBSBNFUFS DPOmHVSBUJPO D f g f g UP NBYJNJ[F UIF MPHMJLFMJIPPE .'/ P# .Y X;G/ PCKFDUJWF GVODUJPO O D MPH j JF ' ? .'/: D BSH NBY O -FBSOJOH BDSPTT )FUFSPHFOFPVT /FUXPSLT 8F OPX UVSO UP EJTDVTT IPX UP MFBSO UIF QSFEJD UJWF NPEFM XJUI UXP IFUFSPHFOFPVT OFUXPSLT B TPVSDF OFUXPSL GS BOE B UBSHFU OFUXPSL GT 4USBJHIUGPSXBSEMZ XF DBO EFmOF UXP TFQBSBUF PCKFDUJWF GVODUJPOT GPS UIF UXP OFUXPSLT ɩF DIBM MFOHF JT UIFO IPX UP CSJEHF UIF UXP OFUXPSLT TP UIBU XF DBO USBOTGFS UIF MBCFMFE JOGPSNBUJPO GSPN UIF TPVSDF OFUXPSL UP UIF UBSHFU OFUXPSL "T UIF TPVSDF BOE UBSHFU OFUXPSLT NBZ CF GSPN BSCJUSBSZ EPNBJOT JU JT EJċDVMU UP EFmOF DPSSFMBUJPOT CFUXFFO UIFN CBTFE PO QSJPS LOPXMFEHF 5P UIJT FOE XF QSPQPTF B USBOTGFSCBTFE GBDUPS HSBQI 5SBO'( NPEFM 0VS JEFB JT CBTFE PO UIF GBDU UIBU UIF TPDJBM UIFPSJFT XF EJTDVTTFE JO 4FDUJPO BSF HFOFSBM PWFS BMM OFUXPSLT *OUVJUJWFMZ XF DBO MFWFSBHF UIF DPSSFMBUJPO UP UIF FYUFOU UP XIJDI EJĊFSFOU OFUXPSLT TBUJTGZ FBDI PG UIF TPDJBM UIFPSJFT UP USBOTGFS UIF LOPXMFEHF BDSPTT OFUXPSLT *O QBSUJDVMBS GPS TPDJBM CBMBODF XF EFmOF USJBECBTFE GFBUVSFT UP EFOPUF UIF QSPQPSUJPO PG EJĊFSFOU CBMBODFE USJBOHMFT JO B OFU XPSL GPS TUSVDUVSBM IPMF XF EFmOF FEHF DPSSFMBUJPO CBTFE GFBUVSFT JF DPSSFMBUJPO CFUXFFO UXP SFMBUJPOTIJQT ei BOE ej GPS TPDJBM TUBUVT XF EFmOF GFBUVSFT PWFS USJBET UP SFTQFDUJWFMZ SFQSFTFOU UIF QSPCBCJMJUJFT PG UIF TFWFO NPTU GSFRVFOU GPSNBUJPOT PG USJBET GPS PQJOJPO MFBEFST XF EFmOF GFBUVSFT PWFS FBDI FEHF 'JOBMMZ CZ JODPSQPSBUJOH UIF TPDJBM UIFPSJFT JOUP PVS QSFEJDUJWF NPEFM XF EFmOF UIF GPM MPXJOH MPHMJLFMJIPPE PCKFDUJWF GVODUJPO PWFS UIF TPVSDF BOE UIF UBSHFU OFUXPSLT .˛; ˇ; +/ S .˛; +/ T .ˇ; +/ O D O C O VS d VT d 0 j j S S j j T T ˛j gj .x ;y / ˇj g .x ;y / D ij i C j0 ij i i 1 j 1 i 1 j 1 XD XD XD XD + . h .Y S / h .Y T //; C k k c C k c k c GS c GT X X2 X2 Z $ MPH XIFSF d BOE d 0 BSF OVNCFST PG BUUSJCVUFT JO UIF TPVSDF OFUXPSL BOE UIF UBSHFU OFUXPSL SF TQFDUJWFMZ *O UIJT PCKFDUJWF GVODUJPO UIF mSTU UFSN BOE UIF TFDPOE UFSN SFTQFDUJWFMZ EFmOF UIF MJLFMJIPPE PWFS UIF TPVSDF OFUXPSL BOE UIF UBSHFU OFUXPSL XIJMF UIF UIJSE UFSN EFmOFT UIF MJLF MJIPPE PWFS DPNNPO GFBUVSFT EFmOFE JO UIF UXP OFUXPSLT ɩF DPNNPO GFBUVSF GVODUJPOT BSF EFmOFE BDDPSEJOH UP UIF TPDJBM UIFPSJFT 4VDI B EFmOJUJPO JNQMJFT UIBU BUUSJCVUFT PG UIF UXP OFU ˛ ˇ XPSLT DBO CF FOUJSFMZ EJĊFSFOU BT UIFZ BSF PQUJNJ[FE XJUI EJĊFSFOU QBSBNFUFST f g BOE f g XIJMF UIF JOGPSNBUJPO USBOTGFSSFE GSPN UIF TPVSDF OFUXPSL UP UIF UBSHFU OFUXPSL JT UIF JNQPSUBODF PG DPNNPO GFBUVSFT UIBU BSF EFmOFE BDDPSEJOH UP UIF TPDJBM UIFPSJFT 'JOBMMZ XF EFmOF GPVS SFBM 40$*"- 5*& "/"-:4*4 *OQVU B TPVSDF OFUXPSL GS B UBSHFU OFUXPSL GT BOE UIF MFBSOJOH SBUF ( ' . ˛ ; ˇ ; + / 0VUQVU FTUJNBUFE QBSBNFUFST D f g f g f g ' 0 *OJUJBMJ[F 1FSGPSN TUBUJTUJDT BDDPSEJOH UP TPDJBM UIFPSJFT $POTUSVDU TPDJBM UIFPSJFT CBTFE GFBUVSFT hk.Yc/ SFQFBU 4UFQ 1FSGPSN -#1 UP DBMDVMBUF NBSHJOBM EJTUSJCVUJPO PG VOLOPXO WBSJBCMFT JO UIF TPVSDF P.yi xi ;GS / OFUXPSL j 4UFQ 1FSGPSN -#1 UP DBMDVMBUF NBSHJOBM EJTUSJCVUJPO PG VOLOPXO WBSJBCMFT JO UIF UBSHFU P.yi xi ;GT / OFUXPSL j 4UFQ c S1FSGPSNT -#1 UP DBMDVMBUF UIF NBSHJOBM EJTUSJCVUJPO PG DMJRVF JF P.yc ; ;G ;G / j9c 9c S T 4UFQ $BMDVMBUF UIF HSBEJFOU PG +k BDDPSEJOH UP &R GPS ˛j BOE ˇj XJUI B TJNJMBS GPSNVMB 4UFQ 6QEBUF QBSBNFUFS ' XJUI UIF MFBSOJOH SBUF ( .'/ ' ' ( O OFX D PME C # ' VOUJM $POWFSHFODF "MHPSJUIN -FBSOJOH BMHPSJUIN GPS 5SBO'( WBMVFE CBMBODF CBTFE GFBUVSFT TFWFO SFBMWBMVFE TUBUVT CBTFE GFBUVSFT GPVS CJOBSZ GFBUVSFT GPS PQJOJPO MFBEFS BOE TJY SFBMWBMVFE DPSSFMBUJPO GFBUVSFT GPS TUSVDUVSBM IPMF .PSF EFUBJMT BCPVU GFBUVSF GVODUJPO BSF HJWFO JO UIF "QQFOEJY .PEFM -FBSOJOH BOE *OGFSSJOH ɩF MBTU JTTVF JT UP MFBSO UIF 5SBO'( NPEFM BOE UP JOGFS UIF UZQF PG VOLOPXO SFMBUJPOTIJQT JO UIF UBSHFU OFUXPSL -FBSOJOH UIF 5SBO'( NPEFM JT UP FTUJNBUF ' . ˛ ; ˇ ; + / B QBSBNFUFS DPOmHVSBUJPO D f g f g f g UP NBYJNJ[F UIF MPHMJLFMJIPPE PCKFDUJWF GVODUJPO .˛; ˇ; +/ O 8F VTF B HSBEJFOU EFDFOU NFUIPE PS B /FXUPO3BQITPO NFUIPE UP TPMWF UIF PC KFDUJWF GVODUJPO 8F VTF + BT UIF FYBNQMF UP FYQMBJO IPX XF MFBSO UIF QBSBNFUFST 4QFDJmDBMMZ XF mSTU XSJUF UIF HSBEJFOU PG FBDI +k XJUI SFHBSE UP UIF PCKFDUJWF GVODUJPO .'/ S T O EŒhk.Yc / hk.Yc / +k D C S T EP# .Yc S ; T ;GS ;GT /Œhk.Yc / hk.Yc /; $ k j9 9 C S T S T EŒhk.Y / hk.Y / hk.Y / hk.Y / XIFSF c C c JT UIF FYQFDUBUJPO PG GBDUPS GVODUJPO c C c HJWFO UIF EBUB EJTUSJCVUJPO JF UIF BWFSBHF WBMVF PG UIF GBDUPS GVODUJPO hk.Yc/ PWFS BMM USJBET JO UIF TPVSDF EP# .Yc S ; T ;GS ;GT /Œ: BOE UIF UBSHFU OFUXPSLT UIF TFDPOE UFSN k j9 9 JT UIF FYQFDUBUJPO VOEFS UIF P$ .Yc S ; T ;GS ;GT / EJTUSJCVUJPO k j9 9 HJWFO CZ UIF FTUJNBUFE NPEFM 4JNJMBS HSBEJFOUT DBO CF EFSJWFE GPS QBSBNFUFST ˛j BOE ˇj */'&33*/( 40$*"- 5*&4 "T UIF HSBQIJDBM TUSVDUVSF DBO CF BSCJUSBSZ BOE NBZ DPOUBJO DZDMFT XF VTF MPPQZ CFMJFG QSPQBHBUJPO -#1 <> UP BQQSPYJNBUF UIF HSBEJFOUT *U JT XPSUI OPUJOH UIBU JO PSEFS UP MFWFSBHF UIF VOMBCFMFE SFMBUJPOTIJQT XF OFFE UP QFSGPSN UIF -#1 QSPDFTT UXJDF JO FBDI JUFSBUJPO POF yi ‹ UJNF GPS FTUJNBUJOH UIF NBSHJOBM EJTUSJCVUJPO PG VOLOPXO WBSJBCMFT D BOE UIF PUIFS UJNF GPS NBSHJOBM EJTUSJCVUJPO PWFS BMM DMJRVFT 'JOBMMZ XJUI UIF HSBEJFOU XF VQEBUF FBDI QBSBNFUFS XJUI B MFBSOJOH SBUF ( ɩF MFBSOJOH BMHPSJUIN JT TVNNBSJ[FE JO "MHPSJUIN 8F TFF UIBU JO UIF MFBSOJOH QSPDFTT UIF BMHPSJUIN VTFT BO BEEJUJPOBM MPPQZ CFMJFG QSPQBHBUJPO UP JOGFS UIF MBCFM PG VOLOPXO SFMBUJPOTIJQT "GUFS MFBSOJOH BMM VOLOPXO SFMBUJPOTIJQT BSF BTTJHOFE XJUI MBCFMT UIBU NBYJNJ[F UIF NBSHJOBM QSPCBCJMJUJFT &WBMVBUJPO ɩF QSPQPTFE GSBNFXPSL JT WFSZ HFOFSBM BOE DBO CF BQQMJFE UP NBOZ EJĊFSFOU OFUXPSLT 'PS FY QFSJNFOUT XF DPOTJEFS mWF EJĊFSFOU UZQFT PG OFUXPSLT &QJOJPOT 4MBTIEPU .PCJMF $PBVUIPS BOE &OSPO 0O UIF mSTU UISFF OFUXPSLT &QJOJPOT 4MBTIEPU BOE .PCJMF PVS HPBM JT UP JOGFS VOEJSFDUFE SFMBUJPOTIJQT FH GSJFOETIJQT XIJMF PO UIF PUIFS UXP OFUXPSLT $PBVUIPS BOE &O SPO UIF HPBM JT UP JOGFS EJSFDUFE SFMBUJPOTIJQT FH BEWJTPSBEWJTFF SFMBUJPOTIJQT &WBMVBUJPO .FBTVSFT 5P RVBOUJUBUJWFMZ FWBMVBUF UIF QFSGPSNBODF PG JOGFSSJOH UIF UZQF PG TPDJBM SFMBUJPOTIJQT XF DPOEVDUFE FYQFSJNFOUT XJUI EJĊFSFOU QBJST PG TPVSDF BOE UBSHFU OFUXPSLT BOE FWBMVBUFE UIF QSPQPTFE BQQSPBDIFT JO UFSNT PG 1SFDJTJPO 3FDBMM BOE '.FBTVSF 8F DPNQBSF UIF GPMMPXJOH NFUIPET GPS JOGFSSJOH UIF UZQF PG TPDJBM SFMBUJPOTIJQT 47. 4JNJMBS UP UIF MPHJTUJD SFHSFTTJPO NPEFM VTFE JO -FTLPWFD FU BM <> 47. VTFT BUUSJCVUFT BTTPDJBUFE XJUI FBDI FEHF BT GFBUVSFT UP USBJO B DMBTTJmDBUJPO NPEFM BOE UIFO FNQMPZT UIF DMBTTJmDBUJPO NPEFM UP QSFEJDU FEHFT MBCFMT JO UIF UFTU EBUB TFU 'PS 47. XF FNQMPZ 47. MJHIU $3' *U USBJOT B DPOEJUJPOBM SBOEPN mFME <> XJUI BUUSJCVUFT BTTPDJBUFE XJUI FBDI FEHF BOE DPSSFMBUJPOT CFUXFFO FEHFT 1'( ɩF NFUIPE JT BMTP CBTFE PO $3' CVU JU FNQMPZT UIF VOMBCFMFE EBUB UP IFMQ MFBSO UIF QSFEJDUJWF NPEFM ɩF NFUIPE JT QSPQPTFE JO 5BOH FU BM <> 5SBO'( ɩF QSPQPTFE BQQSPBDI XIJDI MFWFSBHFT UIF MBCFM JOGPSNBUJPO GSPN UIF TPVSDF OFUXPSL UP IFMQ JOGFS UIF UZQF PG SFMBUJPOTIJQ JO UIF UBSHFU OFUXPSL 8F BMTP DPNQBSF XJUI UIF NFUIPE 51'( QSPQPTFE JO 8BOH FU BM <> GPS NJOJOH BEWJTPS BEWJTFF SFMBUJPOTIJQT JO UIF QVCMJDBUJPO OFUXPSL ɩJT NFUIPE JT EPNBJOTQFDJmD BOE UIVT XF POMZ DPNQBSF XJUI JU PO UIF $PBVUIPS OFUXPSL *O BMM FYQFSJNFOUT XF VTF UIF TBNF GFBUVSF EFmOJUJPOT GPS BMM NFUIPET 0O UIF $PBVUIPS OFUXPSL XF EP OPU DPOTJEFS TPNF EPNBJOTQFDJmD DPSSFMBUJPO GFBUVSFTň "MM DPEFT XFSF JNQMF NFOUFE JO $ BOE BMM FYQFSJNFOUT XFSF QFSGPSNFE PO B 1$ SVOOJOH 8JOEPXT XJUI *OUFM 3 $PSF 5. $16 ()[ BOE (# NFNPSZ *U UPPL BCPVU o NJO UP USBJO UIF 5SBO'( NPEFM PWFS EJĊFSFOU EBUB TFUT FH NJO GPS MFBSOJOH PWFS UIF &QJOJPOT BOE UIF 4MBTI ň8F DPOEVDUFE FYQFSJNFOUT CVU GPVOE UIBU UIPTF GFBUVSFT XJMM MFBE UP PWFSmUUJOH 40$*"- 5*& "/"-:4*4 EPU OFUXPSLT 'PS JODPSQPSBUJOH TPDJBM CBMBODF BOE TPDJBM TUBUVT JOUP UIF 5SBO'( NPEFM XF OFFE1 DPVOU BMM USJBET JO UIF TPVSDF BOE UIF UBSHFU OFUXPSLT 8F EFTJHO BO FċDJFOU MJOFBS BMHPSJUIN XIJDI UBLFT o NJO UP FOVNFSBUF BMM USJBET GPS UIF mWF OFUXPSLT 5BCMF 1FSGPSNBODF DPNQBSJTPO PG EJĊFSFOU NFUIPET GPS JOGFSSJOH GSJFOETIJQT PS USVTUGVM SFMB UJPOTIJQT 4 JOEJDBUFT UIF TPVSDF OFUXPSL BOE 5 UIF UBSHFU OFUXPSL 'PS UIF UBSHFU OFUXPSL XF VTF PG UIF MBCFMFE EBUB JO USBJOJOH BOE UIF SFTU GPS UFTU Data Set Method Prec. Rec. F1-score SVM 0.7157 0.9733 0.8249 Epinions (S) to CRF 0.8919 0.6710 0.7658 Slashdot (T) PFG 0.9300 0.6436 0.7607 (40%) TranFG 0.9414 0.9446 0.9430 SVM 0.9132 0.9925 0.9512 Slashdot (S) to CRF 0.8923 0.9911 0.9393 Epinions (T) PFG 0.9954 0.9787 0.9870 (40%) TranFG 0.9954 0.9787 0.9870 SVM 0.8983 0.5955 0.7162 Epinions (S) to CRF 0.9455 0.5417 0.6887 Mobile (T) PFG 1.0000 0.5924 0.7440 (40%) TranFG 0.8239 0.8344 0.8291 SVM 0.8983 0.5955 0.7162 Slashdot (S) to CRF 0.9455 0.5417 0.6887 Mobile (T) PFG 1.0000 0.5924 0.7440 (40%) TranFG 0.7258 0.8599 0.7872 *OGFSSJOH "DDVSBDZ "OBMZTJT 8F DPNQBSF UIF QFSGPSNBODF PG UIF GPVS NFUIPET GPS JOGFSSJOH GSJFOETIJQT PS USVTUGVM SFMBUJPOTIJQT PO GPVS QBJST PG OFUXPSLT &QJOJPOT 4 UP 4MBTIEPU 5 4MBTIEPU 4 UP &QJOJPOT 5 &QJOJPOT 4 UP .PCJMF 5 BOE 4MBTIEPU 4 UP .PCJMF 5 ʼn *O BMM FYQFSJNFOUT XF VTF PG UIF MBCFMFE EBUB JO UIF UBSHFU OFUXPSL GPS USBJOJOH BOE UIF SFTU GPS UFTU 'PS USBOTGFS XF DPOTJEFS UIF MBCFMFE JOGPSNBUJPO JO UIF TPVSDF OFUXPSL 5BCMF MJTUT UIF QFSGPSNBODF PG UIF EJĊFSFOU NFUIPET PO UIF GPVS UFTU DBTFT 0VS BQQSPBDI TIPXT CFUUFS QFSGPSNBODF UIBO UIF UISFF BMUFSOBUJWF NFUIPET 8F DPOEVDUFE TJHO UFTUT GPS FBDI SFTVMU XIJDI TIPXT UIBU BMM UIF JNQSPWFNFOUT PG PVS BQQSPBDI 5SBO'( PWFS UIF UISFF NFUIPET BSF TUBUJTUJDBMMZ p 0:01 TJHOJmDBOU ) 5BCMF TIPXT UIF QFSGPSNBODF PG UIF GPVS NFUIPET GPS JOGFSSJOH EJSFDUFE SFMBUJPOTIJQT UIF TPVSDF FOE IBT B IJHIFS TPDJBM TUBUVT UIBO UIF UBSHFU FOE PO UXP QBJST PG OFUXPSLT $PBVUIPS ʼn8F EJE USZ UP VTF .PCJMF BT UIF TPVSDF OFUXPSL BOE 4MBTIEPU&QJOJPOT BT UIF UBSHFU OFUXPSL )PXFWFS BT UIF TJ[F PG .PCJMF JT NVDI TNBMMFS UIBO UIF PUIFS UXP OFUXPSLT UIF QFSGPSNBODF XBT DPOTJEFSBCMZ XPSTF */'&33*/( 40$*"- 5*&4 5BCMF 1FSGPSNBODF DPNQBSJTPO PG EJĊFSFOU NFUIPET GPS JOGFSSJOH EJSFDUFE SFMBUJPOTIJQT UIF TPVSDF FOE IBT B IJHIFS TPDJBM TUBUVT UIBO UIF UBSHFU FOE 4 JOEJDBUFT UIF TPVSDF OFUXPSL BOE 5 UIF UBSHFU OFUXPSL 'PS UIF UBSHFU OFUXPSL XF VTF PG MBCFMFE EBUB JO USBJOJOH BOE UIF SFTU GPS UFTU Data Set Method Prec. Rec. F1-score SVM 0.9524 0.5556 0.7018 Coauthor (S) to CRF 0.9565 0.5366 0.6875 Enron (T) PFG 0.9730 0.6545 0.7826 (40%) TranFG 0.9556 0.7818 0.8600 SVM 0.6910 0.3727 0.4842 Enron (S) to CRF 1.0000 0.3043 0.4666 Coauthor (T) PFG 0.9916 0.4591 0.6277 (40%) TPFG 0.5936 0.7611 0.6669 Tran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ɩF NFUIPE 1'( DBO CF WJFXFE BT B OPOUSBOTGFSBCMF DPVOUFSQBSU PG PVS NFUIPE XIJDI EPFT OPU DPOTJEFS UIF MBCFMFE JOGPSNBUJPO GSPN UIF TPVSDF OFUXPSL 'SPN CPUI 5BCMF BOE 5BCMF XF DBO TFF UIBU XJUI UIF USBOTGFSSFE JOGPSNBUJPO PVS NFUIPE DBO DMFBSMZ JNQSPWF UIF SFMBUJPOTIJQ DBUFHPSJ[BUJPO QFSGPSNBODF "OPUIFS QIFOPNFOPO JT UIBU 1'( IBT B CFUUFS QFS GPSNBODF UIBO UIF PUIFS UXP NFUIPET 47. BOE $3' JO NPTU DBTFT 1'( DPVME MFWFSBHF UIF VOMBCFMFE JOGPSNBUJPO JO UIF UBSHFU OFUXPSL UIVT FOIBODFT UIF JOGFSSJOH QFSGPSNBODF ɩF POMZ FYDFQUJPO JT UIF DBTF PG &QJOJPOT 4 UP 4MBTIEPU 5 XIFSF JU TFFNT UIBU VTFST JO 4MBTIEPU IBWF B SFMBUJWFMZ DPOTJTUFOU QBUUFSO UIVT B DMBTTJmDBUJPO CBTFE NFUIPE 47. XJUI POMZ HFOFSBM GFBUVSFT FH JOEFHSFF PVUEFHSFF BOE OVNCFS PG DPNNPO OFJHICPST DBO BDIJFWF WFSZ IJHI QFSGPS NBODF 'BDUPS $POUSJCVUJPO "OBMZTJT 8F OPX BOBMZ[F IPX EJĊFSFOU TPDJBM UIFPSJFT TPDJBM CBMBODF TPDJBM TUBUVT TUSVDUVSBM IPMF BOE UXPTUFQ nPX PQJOJPO MFBEFS DBO IFMQ JOGFS TPDJBM UJFT 'PS JOGFSSJOH GSJFOETIJQT XF DPOTJEFS TPDJBM CBMBODF 4# BOE TUSVDUVSBM IPMF 4) CBTFE USBOTGFS BOE GPS JOGFSSJOH EJSFDUFE GSJFOETIJQT XF DPOTJEFS TPDJBM TUBUVT 44 BOE PQJOJPO MFBEFS 0- CBTFE USBOTGFS )FSF XF FYBNJOF UIF DPOUSJCVUJPO PG UIF EJĊFSFOU GBDUPST EFmOFE JO PVS 5SBO'( NPEFM 'JHVSF TIPXT UIF BWFSBHF '.FBTVSF TDPSF PWFS UIF EJĊFSFOU OFUXPSLT PCUBJOFE CZ UIF 5SBO'( NPEFM GPS JOGFSSJOH GSJFOETIJQT BOE EJSFDUFE SFMBUJPOTIJQT *O QBSUJDVMBS 5SBO'(4# 40$*"- 5*& "/"-:4*4 1 1 TranFG TranFG 0.95 TranFG − SH 0.95 TranFG − OL TranFG − SB TranFG − SS 0.9 0.9 TranFG − ALL TranFG − ALL 0.85 0.85 0.8 0.8 F1 − Measure 0.75 F1 − Measure 0.75 0.7 0.7 0.65 0.65 B 'SJFOETIJQ C %JSFDUFE 'JHVSF 'BDUPS DPOUSJCVUJPO BOBMZTJT 5SBO'(4) EFOPUFT PVS 5SBO'( NPEFM CZ JHOPSJOH UIF TUSVD UVSBM IPMFCBTFE USBOTGFS 5SBO'(4# TUBOET GPS JHOPSJOH UIF TUSVDUVSBM CBMBODFCBTFE USBOTGFS 5SBO'(0- TUBOET GPS JHOPSJOH UIF PQJOJPO MFBEFSCBTFE USBOTGFS BOE 5SBO'(44 TUBOET GPS JHOPSJOH TPDJBM TUBUVTCBTFE USBOTGFS SFQSFTFOUT 5SBO'( XJUIPVU TPDJBM CBMBODF CBTFE GFBUVSFT BOE 5SBO'("MM EFOPUFT UIBU XF SFNPWF BMM UIF USBOTGFS GFBUVSFT *U DBO CF DMFBSMZ PCTFSWFE UIBU UIF QFSGPSNBODF ESPQT XIFO JHOPSJOH FBDI PG UIF GBDUPST 8F DBO BMTP TFF UIBU GPS JOGFSSJOH GSJFOETIJQT UIF TPDJBM CBMBODF JT B CJU NPSF VTFGVM UIBO TUSVDUVSBM IPMF BOE GPS JOGFSSJOH EJSFDUFE SFMBUJPOTIJQT UIF TPDJBM TUBUVT GBDUPS JT NPSF JNQPSUBOU UIBO UIF GBDUPS PG PQJOJPO MFBEFS ɩF BOBMZTJT BMTP DPOmSNT UIBU PVS NFUIPE XPSLT XFMM GVSUIFS JNQSPWFNFOU JT PCUBJOFE XIFO DPNCJOJOH EJĊFSFOU TPDJBM UIFPSJFT 4PDJBM #BMBODF BOE 4USVDUVSBM )PMF #BTFE 5SBOTGFS 8F QSFTFOU BO JOEFQUI BOBMZTJT PO IPX UIF TPDJBM CBMBODF BOE TUSVDUVSBM IPMF CBTFE USBOTGFS DBO IFMQ CZ WBSZJOH UIF QFSDFOU PG MBCFMFE USBJOJOH EBUB JO UIF UBSHFU OFUXPSL 8F TFF UIBU JO BMM DBTFT FYDFQU 4MBTIEPUUP&QJOJPOT DMFBS JNQSPWFNFOUT DBO CF PCUBJOFE CZ VTJOH UIF TPDJBM CBMBODF BOE TUSVDUVSBM IPMFCBTFE USBOTGFS XIFO UIF MBCFMFE EBUB JO UIF UBSHFU OFUXPSL JT MJNJUFE Ä *OEFFE JO TPNF DBTFT TVDI BT &QJOJPOTUP4MBTIEPU XJUI NFSFMZ PG UIF MBCFMFE SFMBUJPOTIJQT JO 4MBTIEPU PVS NFUIPE DBO PCUBJO B HPPE QFSGPSNBODF CZ 'TDPSF 8JUIPVU USBOTGFS UIF CFTU QFSGPSNBODF JT POMZ PCUBJOFE CZ 47. 8F BMTP mOE UIBU TUSVDUVSBM CBMBODFCBTFE USBOTGFS JT NPSF IFMQGVM UIBO TUSVDUVSBM IPMFCBTFE USBOTGFS GPS JOGFSSJOH GSJFOETIJQT JO NPTU DBTFT XJUI WBSJPVT QFSDFOUT PG MBCFMFE SFMBUJPOTIJQT ɩJT SFTVMU JT DPOTJTUFOU XJUI XIBU XF PCUBJOFE JO UIF GBDUPS DPOUSJCVUJPO BOBMZTJT " EJĊFSFOU QIFOPNFOPO JT GPVOE JO UIF DBTF PG 4MBTIEPUUP&QJOJPOT XIFSF BMM NFUIPET DBO PCUBJO B 'TDPSF PG XJUI POMZ PG UIF MBCFMFE EBUB ɩF LOPXMFEHF USBOTGFS TFFNT OPU IFMQGVM #Z B DBSFGVM JOWFTUJHBUJPO XF GPVOE TJNQMZ XJUI UIPTF GFBUVSFT DG "QQFOEJY GPS */'&33*/( 40$*"- 5*&4 1 1 0.9 SVM 0.9 SVM CRF CRF 0.8 PFG 0.8 PFG TranFG−SB TranFG−SB 0.7 TranFG−SH 0.7 TranFG−SH TranFG TranFG 0.6 0.6 F1 − Measure F1 − Measure 0.5 0.5 0.4 0.4 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 percentage percentage B &QJOJPOTUP4MBTIEPU C 4MBTIEPUUP&QJOJPOT 1 1 0.9 0.9 0.8 0.8 SVM SVM CRF CRF 0.7 PFG 0.7 PFG TranFG−SB TranFG−SB 0.6 0.6 F1 − Measure TranFG−SH F1 − Measure TranFG−SH TranFG TranFG 0.5 0.5 0.4 0.4 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 percentage percentage D &QJOJPOTUP.PCJMF E 4MBTIEPUUP.PCJMF 'JHVSF 1FSGPSNBODF PG JOGFSSJOH GSJFOETIJQT XJUI BOE XJUIPVU UIF CBMBODFCBTFE USBOTGFS CZ WBSZJOH UIF QFSDFOU PG MBCFMFE EBUB JO UIF UBSHFU OFUXPSL EFUBJMT EFmOFE PO UIF FEHFT XF DPVME BDIJFWF B IJHI QFSGPSNBODF BCPVU ɩF TUSVDUVSF JOGPSNBUJPO JOEFFE IFMQT CVU UIF HBJOFE JNQSPWFNFOU JT MJNJUFE 4PDJBM 4UBUVT BOE 0QJOJPO -FBEFS #BTFE 5SBOTGFS 'JHVSF TIPXT BO BOBMZTJT GPS JOGFSSJOH EJSFDUFE SFMBUJPOTIJQT PO UIF UXP DBTFT &OSPOUP$PBVUIPS BOE $PBVUIPSUP&OSPO )FSF XF GPDVT PO UFTUJOH IPX TPDJBM TUBUVT BOE PQJOJPO MFBEFS CBTFE USBOTGFS DBO IFMQ JOGFS UIF UZQF PG SFMBUJPOTIJQT CZ WBSZJOH UIF QFSDFOU PG MBCFMFE SFMBUJPOTIJQT JO UIF UBSHFU OFUXPSL *O CPUI DBTFT $PBVUIPSUP&OSPO BOE &OSPOUP$PBVUIPS UIF 5SBO'( NPEFM BDIJFWFT DPOTJTUFOU JNQSPWF NFOUT 'PS FYBNQMF XIFO UIFSF JT POMZ PG MBCFMFE BEWJTPSBEWJTFF SFMBUJPOTIJQT JO UIF $PBV UIPS OFUXPSL XJUIPVU DPOTJEFSJOH UIF TUBUVT BOE PQJOJPO MFBEFS CBTFE USBOTGFS UIF 'TDPSF JT POMZ #Z MFWFSBHJOH UIF TUBUVT BOE PQJOJPO MFBEFSCBTFE USBOTGFS GSPN UIF FNBJM OFUXPSL 40$*"- 5*& "/"-:4*4 1 1 0.8 0.8 SVM CRF SVM 0.6 0.6 PFG CRF TranFG−SS PFG F1 − Measure TranFG−OL F1 − Measure TranFG−SS 0.4 0.4 TranFG TranFG−OL TranFG 0.2 0.2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 percentage percentage B $PBVUIPSUP&OSPO C &OSPOUP$PBVUIPS 'JHVSF 1FSGPSNBODF PG JOGFSSJOH EJSFDUFE SFMBUJPOTIJQ XJUI BOE XJUIPVU UIF TUBUVTCBTFE USBOT GFS CZ WBSZJOH UIF QFSDFOU PG MBCFMFE EBUB JO UIF UBSHFU OFUXPSL &OSPO UIF TDPSF JT EPVCMFE .PSFPWFS XF mOE UIBU UIF TPDJBM TUBUVTCBTFE USBOTGFS JT NPSF IFMQGVM UIBO UIF PQJOJPO MFBEFSCBTFE USBOTGFS XJUI WBSJPVT QFSDFOUT PG UIF MBCFMFE EBUB 2VBMJUBUJWF $BTF 4UVEZ /PX XF QSFTFOU B DBTF TUVEZ UP EFNPOTUSBUF UIF FĊFDUJWFOFTT PG UIF QSPQPTFE NPEFM 'JHVSF TIPXT BO FYBNQMF HFOFSBUFE GSPN PVS FYQFSJNFOUT *U SFQSFTFOUT B QPSUJPO PG UIF $PBVUIPS OFUXPSL #MBDL FEHFT BOE BSSPXT SFTQFDUJWFMZ EFOPUF MBCFMFE DPMMFBHVF SFMBUJPOTIJQT BOE BEWJTPSBEWJTFF SFMBUJPOTIJQT JO UIF USBJOJOH EBUB $PMPSFE BSSPXT BOE FEHFT JOEJDBUF BEWJTPSBEWJTFF BOE DPMMFBHVFT SFMBUJPOTIJQT EFUFDUFE CZ UISFF NFUIPET 47. 1'( BOE 5SBO'( XJUI SFE DPMPS JOEJDBUJOH NJTUBLF POFT ɩF OVNCFST BTTPDJBUFE XJUI FBDI BVUIPS SFTQFDUJWFMZ EFOPUF UIF OVNCFS PG QBQFST BOE UIF TDPSF PG IJOEFY 8F JOWFTUJHBUF NPSF CZ MPPLJOH BU B TQFDJmD FYBNQMF 47. NJTUBLFOMZ DMBTTJmFT UISFF BEWJTPSBEWJTFF SFMBUJPOTIJQT BOE UXP DPMMFBHVF SFMBUJPOTIJQT 47. USBJOT B MPDBM DMBTTJmDBUJPO NPEFM XJUIPVU DPOTJEFSJOH UIF OFUXPSL JOGPSNBUJPO 1'( DPOTJEFST UIF OFUXPSL JOGPSNBUJPO BT XFMM BT UIF VOMBCFMFE EBUB UIVT PCUBJOT B CFUUFS SFTVMU 0VS QSPQPTFE 5SBO'( NPEFM GVSUIFS DPSSFDUT UXP NJTUBLFT i'BJU-FPOBSEJw BOE i"VTJFMMP-BVSBw CZ MFWFSBHJOH QSPQFSUJFT PG TPDJBM TUBUVT BOE PQJOJPO MFBEFS 'PS FYBNQMF UIF SFTVMUT PCUBJOFE CZ 1'( BNPOH i"[BS w i"NPT w BOE i-FPOBSEJw GPSN B USJBE PG iw "MUIPVHI JU TBUJTmFT UIF QSPQFSUZ PG TPDJBM TUBUVT UIF QSPCBCJM JUZ PG TVDI USJBE JT NVDI MPXFS .0:4 WT 24:6/ UIBO UIF GPSN iw )PXFWFS UIF MJNJUBUJPO PG UIF USBJOJOH EBUB MFBET 1'( UP SFTVMU JO B CJBT NJTUBLF 5:8 WT 12:6 5SBO'( TNPPUIFT UIF SFTVMUT CZ USBOTGFSSJOH LOPXMFEHF GSPN UIF TPVSDF &OSPO OFUXPSL 4VNNBSZ *O UIJT TFDUJPO XF TUVEZ UIF QSPCMFN PG JOGFSSJOH TPDJBM UJFT BDSPTT IFUFSPHFOFPVT OFUXPSLT 8F QSFDJTFMZ EFmOF UIF QSPCMFN BOE QSPQPTF B USBOTGFSCBTFE GBDUPS HSBQI 5SBO'( NPEFM ɩF */'&33*/( 40$*"- 5*&4 B 47. C 1'( D 0VS BQQSPBDI 5SBO'( 'JHVSF $BTF TUVEZ *MMVTUSBUJPO PG JOGFSSJOH BEWJTPSBEWJTFF SFMBUJPOTIJQT PO UIF $PBVUIPS OFUXPSL %JSFDUFE FEHFT JOEJDBUF BEWJTPS SFMBUJPOTIJQT BOE VOEJSFDUFE POFT JOEJDBUF DPBVUIPS SFMBUJPOTIJQT #MBDL FEHFT JOEJDBUF MBCFMFE EBUB 3FE DPMPSFE FEHFT JOEJDBUF XSPOH QSFEJDUJPOT 40$*"- 5*& "/"-:4*4 NPEFM JODPSQPSBUFT TPDJBM UIFPSJFT JOUP B TFNJTVQFSWJTFE MFBSOJOH GSBNFXPSL XIJDI JT VTFE UP USBOTGFS TVQFSWJTFE JOGPSNBUJPO GSPN UIF TPVSDF OFUXPSL UP IFMQ JOGFS TPDJBM UJFT JO UIF UBSHFU OFUXPSL 8F FWBMVBUF UIF QSPQPTFE NPEFM PO mWF EJĊFSFOU HFOSFT PG OFUXPSLT 8F TIPX UIBU UIF QSPQPTFE NPEFM DBO TJHOJmDBOUMZ JNQSPWF UIF QFSGPSNBODF GPS JOGFSSJOH TPDJBM UJFT BDSPTT EJĊFSFOU OFUXPSLT DPNQBSJOH XJUI TFWFSBM BMUFSOBUJWF NFUIPET 0VS TUVEZ BMTP SFWFBMT TFWFSBM JOUFSFTUJOH QIFOPNFOB $0/$-64*0/4 *O UIJT DIBQUFS XF HJWF B DPNQSFIFOTJWF JOUSPEVDUJPO UP UIF TUVEZ PG TPDJBM UJF BOBMZTJT 8F QSFTFOU UIF TUBUFPGUIFBSU BMHPSJUINT GPS QSFEJDUJOH NJTTJOH MJOLT BOE EFTDSJCF NFUIPEPMPHJFT GPS JOGFS SJOH TPDJBM UJFT JODMVEJOH VOTVQFSWJTFE MFBSOJOHCBTFE NFUIPE TVQFSWJTFE MFBSOJOHCBTFE NFUIPE BDUJWF MFBSOJOHCBTFE NFUIPE BOE USBOTGFS MFBSOJOHCBTFE NFUIPE $ )"15&3 4PDJBM *OnVFODF "OBMZTJT 4PDJBM JOnVFODF PDDVST XIFO POFT PQJOJPOT FNPUJPOT PS CFIBWJPST BSF BĊFDUFE CZ PUIFST JO UFOUJPOBMMZ PS VOJOUFOUJPOBMMZ <> 4PDJBM JOnVFODF JT B QSFWBMFOU DPNQMFY BOE TVCUMF GPSDF UIBU HPWFSOT UIF EZOBNJDT PG BMM TPDJBM OFUXPSLT 07&37*&8 4PDJBM JOnVFODF IBT CFFO B XJEFMZ BDDFQUFE QIFOPNFOPO JO TPDJBM OFUXPSLT GPS EFDBEFT .BOZ BQQMJDBUJPOT IBWF CFFO CVJMU CBTFE BSPVOE UIF JNQMJDJU OPUBUJPO PG TPDJBM JOnVFODF CFUXFFO QFP QMF 'PS FYBNQMF NPSF BOE NPSF QFPQMF NBLF EFDJTJPOT CBTFE PO UIFJS JOUFSBDUJPOT GSPN TPDJBM OFUXPSLT 1FPQMF PGUFO QJDL XIBU SFTUBVSBOUT UP HP UP CBTFE PO SFDPNNFOEBUJPOT BOE SFWJFXT GSPN :FMQ "T UIF VTF PG TPDJBM OFUXPSLT HSPXT JO BMM EPNBJOT TVDI CFIBWJPST PG TPDJBM JOnVFODF CFDPNF NPSF BOE NPSF QSFWBMFOU .PSF BOE NPSF QFPQMF NBLF EFDJTJPOT BOE DIBOHFT JOnVFODFE CZ UIFJS TPDJBM OFUXPSLT 8JUI UIF FYQPOFOUJBM HSPXUI PG POMJOF TPDJBM OFUXPSL TFSWJDFT TVDI BT 'BDFCPPL BOE 5XJUUFS TPDJBM JOnVFODF DBO GPS UIF mSTU UJNF CF NFBTVSFE PWFS B MBSHF QPQVMBUJPO %FVUTDI BOE (FSBSE <> DBUFHPSJ[FE TPDJBM JOnVFODF JOUP JOGPSNBUJWF TPDJBM JOnVFODF BOE OPSNBUJWF TPDJBM JOnVFODF GSPN UIF QFSTQFDUJWF PG QTZDIPMPHJDBM OFFET ɩF GPSNFS JT BO JOnVFODF UP BDDFQU PS EJTBHSFF XJUI JOGPSNBUJPO GSPN PUIFST BOE UIF MBUUFS JT BO JOnVFODF UP DPOGPSN UP UIF FYQFDUBUJPOT PG PUIFST 8JUI UIF QPXFS PG JOnVFODF B DPNQBOZ DBO NBSLFU B OFX QSPEVDU CZ mSTU DPOWJODJOH B TNBMM OVNCFS PG JOnVFOUJBM VTFST UP BEPQU UIF QSPEVDU BOE UIFO USJHHFSJOH B DBTDBEF PG GVSUIFS BEPQUJPOT UISPVHI UIF FĊFDU PG iXPSE PG NPVUIw JO UIF TPDJBM OFUXPSL *O BO BDBEFNJD OFUXPSL XJUI UIF JOnVFODF CFUXFFO SFTFBSDI DPMMBCPSBUPST OPWFM JEFBT PS JOOPWB UJPOT DBO RVJDLMZ TQSFBE BOE MFBE UP UIF CMPPNJOH PG OFX BDBEFNJD EJSFDUJPOT $ISJTUBLJT BOE 'PXMFS <> DSFBUFE UIF UIFPSZ PG ɩSFF%FHSFFPG*OnVFODF XIJDI QPTJUT UIBU iFWFSZUIJOH XF EP PS TBZ UFOET UP SJQQMF UISPVHI PVS OFUXPSL IBWJOH BO JNQBDU FWFO PO PVS UISFF EFHSFF PG GSJFOET GSJFOET GSJFOET GSJFOET w 3FDFOUMZ TPDJBM JOnVFODF BOBMZTJT IBT BUUSBDUFE DPOTJEFSBCMF SFTFBSDI JOUFSFTU 3PVHIMZ TQFBLJOH FYJTUJOH XPSLT DBO CF HSPVQFE JOUP UISFF DBUFHPSJFT ɩF mSTU DBUFHPSZ PG SFTFBSDI GP DVTFE PO RVBMJUBUJWFMZ WBMJEBUJOH UIF FYJTUFODF PG JOnVFODF < > 'PS FYBNQMF #POE FU BM <> VTFE B SBOEPNJ[FE DPOUSPMMFE USJBM UP WFSJGZ UIF TPDJBM JOnVFODF PO QPMJUJDBM WPUJOH CFIBWJPST CZ EFMJWFSJOH QPMJUJDBM NPCJMJ[BUJPO NFTTBHFT UP NJMMJPO 'BDFCPPL VTFST EVSJOH UIF 64 DPOHSFTTJPOBM FMFDUJPOT ɩFZ GPVOE UIBU UIF NFTTBHFT EJSFDUMZ JOnVFODF QPMJUJDBM TFMGFYQSFTTJPO BOE SFBMXPSME WPUJOH CFIBWJPS PG NJMMJPOT PG QFPQMF #BLTIZ FU BM <> BMTP DPOEVDUFE UXP WFSZ MBSHF mFME FYQFSJNFOUT PO 'BDFCPPL UP UFTU UIF FĊFDU PG TPDJBM JOnVFODF PO DPOTVNFS SFTQPOTFT UP 40$*"- */'-6&/$& "/"-:4*4 Probability of B influence A 0.8 C 0.5 0.1 0.4 0.6 0.1 0.6 D E F 0.1 'JHVSF *OnVFODF NBYJNJ[BUJPO GPS WJSBM NBSLFUJOH BEWFSUJTJOH ɩFZ BMTP GPVOE TJHOJmDBOU JOnVFODF FYJTUT GPS VTFST BEWFSUJTJOH CFIBWJPST BOE UIF UIF HSFBUFTU JOnVFODF PDDVST XJUI TUSPOH UJFT ɩF TFDPOE DBUFHPSZ PG SFTFBSDI PO TPDJBM JOnVFODF JT UP NFBTVSF UIF JOnVFOUJBM TUSFOHUI CFUXFFO VTFST 5BOH FU BM <> mSTU TUVEJFE UIF QSPCMFN PG UPQJDMFWFM TPDJBM JOnVFODF BOBMZTJT BOE QSFTFOUFE B 5PQJDBM "ĆOJUZ 1SPQBHBUJPO 5"1 BQQSPBDI UP RVBOUJGZ UIF TPDJBM JOnVFODF CFUXFFO VTFST GSPN EJĊFSFOU BOHMFT (PZBM FU BM <> QSPQPTFE B NFUIPE UP MFBSO UIF JOnVFODF QSPCBCJMJUZ CZ DPOTJEFSJOH UIF DPSSFMBUJPO CFUXFFO VTFST BDUJPOT -JV FU BM <> FYUFOEFE UIF JOnVFODF MFBSOJOH UP IFUFSPHFOFPVT TPDJBM OFUXPSLT BOE GVSUIFS TUVE JFE UIF JOnVFODF QSPQBHBUJPO BOE BHHSFHBUJPO NFDIBOJTNT ɩF UIJSE DBUFHPSZ PG TPDJBM JOnVFODF SFTFBSDI JT TPDJBM JOnVFODF NPEFM 5XP QPQVMBS TPDJBM JOnVFODF NPEFMT BSF MJOFBS UISFTIPME NPEFM BOE JOEFQFOEFOU DBTDBEFE NPEFM < > *O CPUI NPEFMT UIF PCKFDUJWF JT UP mOE B TNBMM TVCTFU PG VTFST TFFE VTFST UP BEPQU B CFIBWJPS FH BEPQU B QSPEVDU BOE UIF HPBM JT UP USJHHFS B MBSHF DBTDBEF PG GVSUIFS BEPQUJPOT UISPVHI UIF JOnVFODF EJĊVTJPO NPEFM ɩF QSPCMFN JT SFGFSSFE UP BT JOnVFODF NBYJNJ[BUJPO 3JDIBSETPO <> BOE ,FNQF FU BM <> GPSNBMMZ EFmOFE UIF QSPCMFN PG JOnVFODF NBYJNJ[BUJPO $IFO FU BM <> QSFTFOUFE BO FċDJFOU BMHPSJUIN UP TPMWF UIF QSPCMFN (PZBM FU BM <> MFWFSBHFE SFBM QSPQBHBUJPO USBDFT UP EFSJWF NPSF BDDVSBUF JOnVFODF NBYJNJ[BUJPO NPEFMT 'JHVSF TIPXT BO FYBNQMF PG VTJOH TPDJBM JOnVFODF GPS WJSBM NBSLFUJOH " NPCJMF QIPOF DPNQBOZ XBOUT UP BEWFSUJTF UIFJS OFX NPCJMF QIPOF JO UIF TPDJBM OFUXPSL ɩFJS TUSBUFHZ JT UP mOE B TNBMM OVNCFS PG JOnVFOUJBM TFFE VTFST JO B TPDJBM OFUXPSL UP GSFFMZ VTF UIF OFX QSPEVDU ɩF PCKFDUJWF JT UIBU UIF BEPQUJPO PG UIF TNBMM OVNCFS PG JOnVFOUJBM VTFST DBO USJHHFS UIFJS GSJFOET BOE GVSUIFS DPOUJOVF UP USJHHFS UIFJS GSJFOET GSJFOET UP BMTP VTF UIF NPCJMF QIPOF ɩF SFBM OVNCFS BTTPDJBUFE XJUI FBDI BSSPX JOEJDBUFT UIF JOnVFODF PG UIF TPVSDF VTFS PO UIF UBSHFU VTFS 'SPN UIF FYBNQMF XF TFF UIBU UIFSF BSF TFWFSBM DIBMMFOHFT GPS mOEJOH UIF PQUJNBM TVCTFU PG TFFE VTFST ɩF mSTU POF JT IPX UP PCUBJO PS RVBOUJGZ UIF JOnVFODF CFUXFFO VTFST BOE UIF TFDPOE POF JT IPX UP EFTJHO BO BMHPSJUIN UP TFMFDU UIF TFFE VTFST *O BEEJUJPO UIF FĊFDU PG UIF TPDJBM JOnVFODF GSPN EJĊFSFOU BOHMFT UPQJDT NBZ CF EJĊFSFOU 'PS FYBNQMF JO UIF SFTFBSDI DPNNVOJUZ TVDI JOnVFODFT BSF XFMM LOPXO .PTU SFTFBSDIFST BSF .*/*/( 501*$-&7&- 40$*"- */'-6&/$& "/"-:4*4 JOnVFODFE CZ PUIFST JO UFSNT PG DPMMBCPSBUJPO BOE DJUBUJPOT "O FYQFSU JO iEBUB NJOJOHw XPVME IBWF B TUSPOH JOnVFODF PO IJT DPMMBCPSBUPST XIJMF PO TPNF PUIFS UPQJD TVDI BT iDPNQVUFS HSBQI JDT w IF NBZ CF NBJOMZ JOnVFODFE CZ IJT DPMMBCPSBUPST ɩVT UIF LFZ RVFTUJPO JT IPX UP FĊFDUJWFMZ BOE FċDJFOUMZ RVBOUJGZ UIF JOnVFODF BNPOH VTFST PO EJĊFSFOU UPQJDT *O UIJT DIBQUFS XF XJMM GPDVT PO JOUSPEVDJOH NFUIPEPMPHJFT GPS RVBOUJGZJOH UIF UPQJDMFWFM JOnVFOUJBM TUSFOHUI CFUXFFO VTFST GPS MBSHF TPDJBM OFUXPSLT BOE UIFO JOUSPEVDF JUT BQQMJDBUJPO UP TPDJBM BDUJPO QSFEJDUJPO .*/*/( 501*$-&7&- 40$*"- */'-6&/$& "/"-:4*4 ɩF HPBM PG TPDJBM JOnVFODF BOBMZTJT JT UP EFSJWF UIF UPQJDMFWFM TPDJBM JOnVFODFT CBTFE PO UIF JOQVU OFUXPSL BOE UPQJD EJTUSJCVUJPO PO FBDI OPEF 'JSTU XF JOUSPEVDF TPNF UFSNJOPMPHZ BOE UIFO EFmOF UIF TPDJBM JOnVFODF BOBMZTJT QSPCMFN 5PQJD %JTUSJCVUJPO *O TPDJBM OFUXPSLT B VTFS VTVBMMZT IBT JOUFSFTUT PO NVMUJQMF UPQJDT 'PS v V 'v R T NBMMZ FBDI OPEF 2 JT BTTPDJBUFE XJUI B WFDUPS 2 PG EJNFOTJPOBM UPQJD EJTUSJCVUJPO 'vz 1 'vz z z D &BDI FMFNFOU JT UIF QSPCBCJMJUZ JNQPSUBODF PG UIF OPEF PO UPQJD s t + P 5PQJD#BTFE 4PDJBM *OnVFODFT 4PDJBM JOnVFODF GSPN OPEF UP EFOPUFE BT st JT B OV NFSJDBM XFJHIU BTTPDJBUFE XJUI UIF FEHF est *O NPTU DBTFT UIF TPDJBM JOnVFODF TDPSF JT BTZNNFUSJD +st +ts s t JF ¤ 'VSUIFSNPSF UIF TPDJBM JOnVFODF GSPN OPEF UP XJMM WBSZ PO EJĊFSFOU UPQJDT ɩVT CBTFE PO UIF BCPWF DPODFQUT XF DBO EFmOF UIF UBTLT PG UPQJDCBTFE TPDJBM JOnVFODF G .V; E/ BOBMZTJT (JWFO B TPDJBM OFUXPSL D BOE B UPQJD EJTUSJCVUJPO GPS FBDI OPEF UIF HPBM JT UP mOE UIF UPQJDMFWFM JOnVFODF TDPSFT PO FBDI FEHF 1SPCMFN G .V; E/ V (JWFO B OFUXPSL D XIFSF JT UIF TFU PG OPEFT VTFST FOUJUJFT T BOE E T 'v R JT UIF TFU PG EJSFDUFEVOEJSFDUFE FEHFT BOE EJNFOTJPOBM UPQJD EJTUSJCVUJPO 2 GPS v V Gz .Vz;Ez/ BMM OPEF JO IPX EPFT POF mOE UIF UPQJDMFWFM JOnVFODF OFUXPSL D GPS BMM UPQJDT 1 z T Vz z Ez Ä Ä )FSF JT B TVCTFU PG OPEFT UIBU BSF SFMBUFE UP UPQJD BOE JT UIF TFUz PG QBJSXJTF Vz .vs;vt ;+st/ XFJHIUFEz JOnVFODF SFMBUJPOT PWFS FBDI FEHF JT UIF GPSN PG B USJQMFU z PS TIPSUMZ .est;+st/ XIFSF UIF FEHF JT GSPN OPEF vs UP OPEF vt XJUI UIF XFJHIU +st ɩF JOQVU UP PVS TPDJBM JOnVFODF BOBMZTJT JODMVEFT OFUXPSLT BOE UPQJD EJTUSJCVUJPO PO BMM OPEFT ɩF mSTU JOQVU JT UIF OFUXPSL CBDLCPOF PCUBJOFE CZ BOZ TPDJBM OFUXPSL TVDI BT POMJOF TPDJBM OFUXPSLT MJLF 'BDFCPPL BOE 5XJUUFS ɩF TFDPOE JOQVU JT UIF UPQJD EJTUSJCVUJPO GPS BMM OPEFT *O HFOFSBM UIF UPQJD JOGPSNBUJPO DBO CF PCUBJOFE JO NBOZ EJĊFSFOU XBZT 'PS FYBNQMF JO B TPDJBM OFUXPSL POF DBO VTF UIF QSFEFmOFE DBUFHPSJFT BT UIF UPQJD JOGPSNBUJPO PS VTF VTFS BTTJHOFE UBHT BT UIF UPQJD JOGPSNBUJPO *O BEEJUJPO XF DBO VTF TUBUJTUJDBM UPQJD NPEFMJOH < > UP BVUPNBUJDBMMZ FYUSBDU UPQJDT GSPN UIF TPDJBM OFUXPSLJOH EBUB *O UIJT EFmOJUJPO UP NBLF JU HFOFSBM XF EP OPU DPOTJEFS VTFST BDUJPOT 8F XJMM FYUFOE UIF QSPCMFN GPSNVMBUJPO JO UIF OFYU TFDUJPO ɩF TPDJBM JOnVFODF BOBMZTJT QSPCMFN QPTFT B VOJRVF TFU PG DIBMMFOHFT 40$*"- */'-6&/$& "/"-:4*4 'JSTU IPX EPFT POF MFWFSBHF CPUI OPEFTQFDJmD UPQJD EJTUSJCVUJPO BOE OFUXPSL TUSVDUVSF UP RVBOUJGZ TPDJBM JOnVFODF *O BOPUIFS XPSET B VTFST JOnVFODF PO PUIFST OPU POMZ EFQFOET PO UIFJS PXO UPQJD EJTUSJCVUJPO CVU BMTP SFMJFT PO XIBU LJOET PG TPDJBM SFMBUJPOTIJQT UIFZ IBWF XJUI PUIFST ɩF HPBM JT UP EFTJHO B VOJmFE BQQSPBDI UP VUJMJ[F CPUI UIF MPDBM BUUSJCVUFT UPQJD EJTUSJCVUJPO BOE UIF HMPCBM TUSVDUVSF OFUXPSL JOGPSNBUJPO GPS TPDJBM JOnVFODF BOBMZTJT 4FDPOE IPX EPFT POF TDBMF UIF QSPQPTFE BOBMZTJT UP B SFBM MBSHF TPDJBM OFUXPSL 'PS FY BNQMF UIF BDBEFNJD DPNNVOJUZ PG $PNQVUFS 4DJFODF IBT NPSF UIBO NJMMJPO SFTFBSDIFST BOE NPSF UIBO NJMMJPO DPBVUIPS SFMBUJPOT 'BDFCPPL IBT NPSF UIBO NJMMJPOT VTFST BOE IVOESFET PG NJMMJPOT PG EJĊFSFOU TPDJBM UJFT )PX UP FċDJFOUMZ JEFOUJGZ UIF UPQJDCBTFE JOnVFOUJBM TUSFOHUI GPS FBDI TPDJBM UJF JT SFBMMZ B DIBMMFOHJOH QSPCMFN 4PMVUJPO 5P BEESFTT UIF BCPWF DIBMMFOHFT XF QSPQPTF 5PQJDBM "ċOJUZ 1SPQBHBUJPO 5"1 UP NPEFM UIF UPQJDMFWFM TPDJBM JOnVFODF PO MBSHF OFUXPSLT *O QBSUJDVMBS HJWFO B TPDJBM OFUXPSL G .V; E/ V D BOE B UPQJD NPEFM PO UIF OPEFT 5"1 DPNQVUFT UPQJDMFWFM TPDJBM JOnVFODF HSBQIT Gz .Vz;Ez/ 1 z T D GPS BMM UPQJD Ä Ä ɩF LFZ GFBUVSFT PG 5"1 BSF UIF GPMMPXJOH t 5"1 QSPWJEFT UPQJDBM JOnVFODF HSBQIT UIBU RVBOUJUBUJWFMZ NFBTVSF UIF JOnVFODF PO B mOF HSBJO MFWFM t UIF JOnVFODF HSBQIT GSPN 5"1 DBO CF VTFE UP TVQQPSU PUIFS BQQMJDBUJPOT TVDI BT mOEJOH SFQSFTFOUBUJWF OPEFT PS DPOTUSVDUJOH UIF JOnVFOUJBM TVCHSBQIT BOE t BO FċDJFOU EJTUSJCVUFE MFBSOJOH BMHPSJUIN JT EFWFMPQFE GPS 5"1 CBTFE PO UIF .BQ3FEVDF GSBNFXPSL JO PSEFS UP TDBMF UP SFBM MBSHF OFUXPSLT 501*$"- "''*/*5: 1301"("5*0/ #BTFE PO UIF JOQVU OFUXPSL BOE UPQJD EJTUSJCVUJPO PO UIF OPEFT XF GPSNBMJ[F UIF TPDJBM JOnVFODF QSPCMFN JO B UPQJDBM GBDUPS HSBQI NPEFM BOE QSPQPTF B UPQJDBM BċOJUZ QSPQBHBUJPO PO UIF GBDUPS HSBQI UP BVUPNBUJDBMMZ JEFOUJGZ UIF UPQJDTQFDJmD TPDJBM JOnVFODF 0VS NBJO JEFB JT UP MFWFSBHF BO BċOJUZ QSPQBHBUJPO BU UIF UPQJDMFWFM GPS TPDJBM JOnVFODF JEFOUJmDBUJPO ɩF BQQSPBDI JT CBTFE PO UIF UIFPSZ PG GBDUPS HSBQI <> JO XIJDI UIF PCTFSWBUJPO EBUB BSF DPIFTJWF PO CPUI MPDBM BUUSJCVUFT BOE SFMBUJPOTIJQT *O PVS TFUUJOH UIF OPEF DPSSFTQPOET UP UIF PCTFSWBUJPO EBUB JO UIF GBDUPS HSBQI BOE UIF TPDJBM SFMBUJPOTIJQ DPSSFTQPOET UP FEHF CFUXFFO UIF PCTFSWFE OPEFT BOE UIF PCTFSWBUJPO EBUB JO UIF HSBQI 'JOBMMZ XF QSPQPTF UXP EJĊFSFOU QSPQBHBUJPO SVMFT POF CBTFE PO NFTTBHF QBTTJOH PO HSBQIJDBM NPEFMT UIF PUIFS B QBSBMMFM VQEBUF SVMF UIBU JT TVJUBCMF GPS .BQ3FEVDF GSBNFXPSL 5PQJDBM 'BDUPS (SBQI 5'( NPEFM /PX XF mSTU FYQMBJO UIF QSPQPTFEN 5'( NPEFM ɩF 5'( vi i 1 NPEFM IBTN UIF GPMMPXJOH DPNQPOFOUT B TFU PG PCTFSWFE WBSJBCMFT f g D BOE B TFU PG IJEEFO WFD yi i 1 N UPST f g D XIJDI DPSSFTQPOET UP UIF OPEFT JO UIF JOQVU OFUXPSL /PUBUJPOT BSF TVNNBSJ[FE JO 5BCMF .*/*/( 501*$-&7&- 40$*"- */'-6&/$& "/"-:4*4 v1;:::;v4 'JHVSF (SBQIJDBM SFQSFTFOUBUJPO PG UIF UPQJDBM GBDUPS HSBQI NPEFM f g BSF PCTFSWBCMF ;:::; OPEFT JO UIF TPDJBM OFUXPSL fZ1 Z4g BSF IJEEFO WFDUPST EFmOFE PO BMM OPEFT XJUI FBDI FMFNFOU SFQSFTFOUJOH XIJDI OPEF IBT UIF IJHIFTU QSPCBCJMJUZ UP JOnVFODF UIF DPSSFTQPOEJOH OPEF g.:/ SFQSF TFOUT B GFBUVSF GVODUJPO EFmOFE PO B OPEF f .:/ SFQSFTFOUT B GFBUVSF GVODUJPO EFmOFE PO BO FEHF BOE h.:/ k 1; : : : ; N SFQSFTFOUT B HMPCBM GFBUVSF GVODUJPO EFmOFE GPS FBDI OPEF JF 2f g T i 1; : : : ; N ɩF IJEEFO WFDUPS zZ 2f g NPEFMT UIF UPQJDMFWFM JOnVFODFT GSPN PUIFS OPEFT UP vi y 1; : : : ; N OPEF &BDI FMFNFOU i UBLJOH UIF WBMVF GSPN UIF TFU f g SFQSFTFOUT UIF OPEF UIBU IBT UIF IJHIFTU QSPCBCJMJUZ UP JOnVFODF OPEF vi PO UPQJD z 'PS FYBNQMF 'JHVSF TIPXT B TJNQMF FYBNQMF PG BO 5'( ɩF PCTFSWFE EBUB DPOTJTUT PG v1;:::;v4 ;:::; GPVS OPEFT f g XIJDI IBWF DPSSFTQPOEJOH IJEEFO WFDUPST : DfZ1 Z4g ɩF FEHFT CFUXFFO UIF IJEEFO OPEFT JOEJDBUF UIF GPVS TPDJBM SFMBUJPOTIJQT JO UIF PSJHJOBM OFUXPSL BLB UIF FEHFT PG UIF JOQVU OFUXPSL ɩFSF BSF UISFF LJOET PG GFBUVSF GVODUJPOT g.v ; ;z/ v t /PEF GFBUVSF GVODUJPO i Zi JT B GFBUVSF GVODUJPO EFmOFE PO OPEF i TQFDJmD UP UPQJD z f. ; ;z/ t &EHF GFBUVSF GVODUJPO Zi Zj JT B GFBUVSF GVODUJPO EFmOFE PO UIF FEHF PG UIF JOQVU OFUXPSL TQFDJmD UP UPQJD z BOE h. ;:::; ;k;z/ t (MPCBM GFBUVSF GVODUJPO Z1 ZN JT B GFBUVSF GVODUJPO EFmOFE PO BMM OPEFT PG UIF JOQVU OFUXPSL XSU UPQJD z #BTJDBMMZ OPEF GFBUVSF GVODUJPO g EFTDSJCFT MPDBM JOGPSNBUJPO PO OPEFT FEHF GFBUVSF GVOD UJPO f EFTDSJCFT EFQFOEFODJFT CFUXFFO OPEFT WJB UIF FEHF PO UIF HSBQI NPEFM BOE HMPCBM GFBUVSF GVODUJPO DBQUVSFT DPOTUSBJOUT EFmOFE PO UIF OFUXPSL 40$*"- */'-6&/$& "/"-:4*4 5BCMF /PUBUJPOT SYMBOL DESCRIPTION N number of nodes in the social network M number of edges in the social network T number of topics V the set of nodes in the social network E the set of edges vi a single node z yi node-vi’s representative on topic z yi the hidden vector of representatives for all topics on node vi z θi the probability for topic z to be generated by the node vi est an edge connecting node vs and node vt z wst the similarity weight of the edge est w.r.t. topic z z µst the social influence of node vs on node vt w.r.t. topic z *O UIJT CPPL XF EFmOF UIF OPEF GFBUVSF GVODUJPO g BT wz iyz i z z z yi i j NB.i/.wij wji/ g.vi ; i ;z/ 2 Cz ¤ ; Z 8 j NB.i/ wji z D P 2 ˆ .wz wz / yi i < j PNB.i/ ij ji 2 C D P z z NB.i/ :ˆ vi w ' ˛ij XIFSF SFQSFTFOUT UIF JOEJDFT PG UIF OFJHICPSJOH OPEFT PG OPEF ij D j SFnFDUT UIF v v ' z UPQJDBM TJNJMBSJUZ PS JOUFSBDUJPO TUSFOHUI CFUXFFO i BOE j XJUI j EFOPUJOH UIF JNQPSUBODF PG OPEFj UP UPQJD z BOE ˛ij EFOPUJOH UIF XFJHIU PG UIF FEHF eij ˛ij DBO CF EFmOFE CZ EJĊFSFOU XBZT 'PS FYBNQMF JO B DPBVUIPS OFUXPSL ˛ij DBO CF EFmOFE BT UIF OVNCFS PG QBQFST DPBVUIPSFE CZ vi BOE vj ɩF BCPWF EFmOJUJPO PG UIF OPEF GFBUVSF GVODUJPO IBT UIF GPMMPXJOH JOUVJUJPO JG OPEF v v v v i IBT B IJHI TJNJMBSJUZXFJHIU XJUI OPEF yi UIFO yi NBZ IBWF B IJHI JOnVFODF PO OPEF i PS JG OPEF vi JT USVTUFE CZ PUIFS VTFST JF PUIFS VTFST UBLF IJN BT BO IJHI JOnVFOUJBM OPEF PO UIFN UIFO JU NVTU BMTP iUSVTUw IJNTFMG IJHIMZ UBLJOH IJNTFMG BT B NPTU JOnVFOUJBM VTFS PO IJN f. ; ;z/ 1 "T GPS UIF FEHF GFBUVSF GVODUJPO XF EFmOF B CJOBSZ GFBUVSF GVODUJPO JF Zi Zj D JG BOE POMZ JG UIFSF JT BO FEHF eij CFUXFFO OPEF vi BOE OPEF vj PUIFSXJTF 8F BMTP EFmOF B HMPCBM FEHF GFBUVSF GVODUJPO h PO BMM OPEFT JF 0 yz k yz k i k h. ;:::; ;k;z/ JG k D BOE i ¤ GPS BMM ¤ Z1 ZN D 1 ! PUIFSXJTF h. / *OUVJUJWFMZ # DPOTUSBJOT UIF NPEFM UP CJBT UPXBSET UIF iUSVFw SFQSFTFOUBUJWF OPEFT .PSF z z TQFDJBMMZ z B SFQSFTFOUBUJWF OPEF PO UPQJD NVTU CF UIF SFQSFTFOUBUJWF PG JUTFMGz PO UPQJD JF y k vi y k; i k k D "OE JU NVTU CF B SFQSFTFOUBUJWF PG BU MFBTU BOPUIFS OPEF JF 9 i D ¤ .*/*/( 501*$-&7&- 40$*"- */'-6&/$& "/"-:4*4 /FYU B GBDUPS HSBQI NPEFM JT DPOTUSVDUFE CBTFE PO UIJT GPSNVMBUJPO 5ZQJDBMMZ XF IPQF UIBU B NPEFM DBO CFTU mU SFDPOTUSVDU UIF PCTFSWBUJPO EBUB XIJDI JT VTVBMMZ SFQSFTFOUFE CZ NBYJNJ[JOH UIF MJLFMJIPPE PG UIF PCTFSWBUJPO ɩVT XF DBO EFmOF UIF PCKFDUJWF MJLFMJIPPE GVODUJPO BT 1 N T P. ; / h. ; :::; ;k;z/ W : D Z Z1 ZN k 1 z 1 N T YD YD T g.v ; ;z/ f. ; ; z/; i Zi Zk Zl i 1 z 1 ekl E z 1 YD YD Y2 YD Œv1;:::;vN Œ ;:::; XIFSF W D BOE : D Z1 ZN DPSSFTQPOET UP BMM PCTFSWFE BOE IJEEFO WBSJBCMFT SFTQFDUJWFMZ g BOE f BSF UIF OPEF BOE FEHF GFBUVSF GVODUJPOT h JT UIF HMPCBM GFBUVSF GVODUJPO Z JT B OPSNBMJ[JOH GBDUPS ɩF GBDUPS HSBQI JO 'JHVSF EFTDSJCFT UIJT GBDUPSJ[BUJPO &BDI CMBDL CPY DPSSFTQPOET UP B UFSN JO UIF GBDUPSJ[BUJPO BOE JU JT DPOOFDUFE UP UIF WBSJBCMFT PO XIJDI UIF UFSN EFQFOET #BTFE PO UIJT GPSNVMBUJPO UIF UBTL PG TPDJBM JOnVFODF JT DBTU BT JEFOUJGZJOH XIJDI OPEF IBT UIF IJHIFTU QSPCBCJMJUZ UP JOnVFODF BOPUIFS OPEF PO B TQFDJmD UPQJD BMPOH XJUI UIF FEHF ɩBU JT UP NBYJNJ[F UIF MJLFMJIPPE GVODUJPO P.W; :/ 0OF QBSBNFUFS DPOmHVSBUJPO JT TIPXO JO 'JHVSF 0O UPQJD CPUI OPEF v1 BOE OPEF v3 BSF TUSPOHMZ JOnVFODFE CZ OPEF v2 XIJMF OPEF v2 JT NBJOMZ JOnVFODFE CZ OPEF v4 0O UPQJD UIF TJUVBUJPO JT EJĊFSFOU "MNPTU BMM OPEFT BSF JOnVFODFE CZ OPEF v1 XIFSF OPEF v4 JT JOEJSFDUMZ JOnVFODFE CZ OPEF v1 WJB UIF OPEF v2 #BTJD 5"1 MFBSOJOH BMHPSJUIN 5P USBJO UIF 5'( NPEFM XF DBO UBLF &RVBUJPO BT UIF PC KFDUJWF GVODUJPO UP mOE UIF QBSBNFUFS DPOmHVSBUJPO UIBU NBYJNJ[FT UIF PCKFDUJWF GVODUJPO 8IJMF JU JT JOUSBDUBCMF UP mOE UIF FYBDU TPMVUJPO UP &RVBUJPO BQQSPYJNBUF JOGFSFODF BMHPSJUINT TVDI BT TVNQSPEVDU BMHPSJUIN <> DBO CF VTFE UP JOGFS UIF WBSJBCMFT Z *O TVNQSPEVDU BMHPSJUIN NFTTBHFT BSF QBTTFE CFUXFFO OPEFT BOE GVODUJPOT .FTTBHF QBTTJOH JT JOJUJBUFE BU UIF MFBWFT &BDI OPEF vi SFNBJOT JEMF VOUJM NFTTBHFT IBWF BSSJWFE PO BMM CVU POF PG UIF FEHFT JODJEFOU PO UIF OPEF vi 0ODF UIFTF NFTTBHFT IBWF BSSJWFE OPEF vi JT BCMF UP DPNQVUF B NFTTBHF UP CF TFOU POUP UIF POF SFNBJOJOH FEHF UP JUT OFJHICPS "GUFS TFOEJOH PVU B NFTTBHF OPEF vi SFUVSOT UP UIF JEMF TUBUF XBJUJOH GPS B iSFUVSO NFTTBHFw UP BSSJWF GSPN UIF FEHF 0ODF UIJT NFTTBHF IBT BSSJWFE UIF OPEF JT BCMF UP DPNQVUF BOE TFOE NFTTBHFT UP FBDI PG OFJHICPSIPPE OPEFT ɩJT QSPDFTT SVOT JUFSBUJWFMZ VOUJM DPOWFSHFODF )PXFWFS USBEJUJPOBM TVNQSPEVDU BMHPSJUIN DBOOPU CF EJSFDUMZ BQQMJFE GPS NVMUJQMF UPQJDT 8F mSTU DPOTJEFS B CBTJD FYUFOTJPO PG UIF TVNQSPEVDU BMHPSJUIN UPQJDBM TVNQSPEVDU ɩF BM HPSJUIN JUFSBUJWFMZ VQEBUFT B WFDUPS PG NFTTBHFT N CFUXFFO WBSJBCMF OPEFT BOE GBDUPS JF GFBUVSF GVODUJPO OPEFT )FODF UXP VQEBUF SVMFT DBO CF EFmOFE SFTQFDUJWFMZ GPS B UPQJDTQFDJmD NFTTBHF TFOU GSPN WBSJBCMF OPEF UP GBDUPS OPEF BOE GPS B UPQJDTQFDJmD NFTTBHF TFOU GSPN GBDUPS OPEF UP WBSJBCMF OPEF 40$*"- */'-6&/$& "/"-:4*4 .%z z / my f .y; z/ mf y.y; z/ mf y.y; z0/ 0 ! D 0! 0! f y f z zf y f 0'Yn Y0¤ 0'Yn mf y.y; z/ f .Y; z/ my f .y0;z/ ! D 0 0! 1 y y f y 'Xf g 0'Yn @ A ,z z f .Y; z0/ my f .y0;z0/ ; C 0 0 0! 1 z z y y f y X0¤ 'Xf g 0'Yn @ A XIFSF f y f f y t 0 & n SFQSFTFOUT 0 JT B OFJHICPS OPEF PG WBSJBCMF PO UIF GBDUPS HSBQI FYDFQU GBDUPS f t Y JT B TVCTFU PG IJEEFO WBSJBCMFT UIBU GFBUVSF GVODUJPO f JT EFmOFE PO GPS FYBNQMF B GFBUVSF f .yi ;yj / eij Y yi ;yj y JT EFmOFE PO FEHF UIFO XF IBWF Df g &f g SFQSFTFOUT BMM WBSJBCMFT JO Y FYDFQU y y y z t UIF TVN 'f g BDUVBMMZ DPSSFTQPOET UP B NBSHJOBM GVODUJPO GPS PO UPQJD BOE P t DPFċDJFOU , SFQSFTFOUT UIF DPSSFMBUJPO CFUXFFO UPQJDT XIJDI DBO CF EFmOFE JO NBOZ EJG GFSFOU XBZT *O UIJT CPPL GPS TJNQMJDJUZ XF BTTVNF UIBU UPQJDT BSF JOEFQFOEFOU ɩBU JT ,zz 1 z z ,zz 0 z z 0 D XIFO D 0 BOE 0 D XIFO ¤ 0 *O UIF GPMMPXJOH XF XJMM QSPQPTF UXP OFX MFBSOJOH BMHPSJUINT XIJDI BSF BMTP CBTFE UIJT JOEFQFOEFOU BTTVNQUJPO /FX 5"1 MFBSOJOH BMHPSJUIN )PXFWFS UIF TVNQSPEVDU BMHPSJUIN SFRVJSFT UIBU FBDI OPEF OFFE XBJU GPS BMM CVUPOF NFTTBHF UP BSSJWF UIVT UIF BMHPSJUIN DBO POMZ SVO JO B TFRVFOUJBM O.N 4 T/ NPEF ɩJT SFTVMUT JO B IJHI DPNQMFYJUZ PG " JO FBDI JUFSBUJPO 5P EFBM XJUI UIJT QSPC MFN XF QSPQPTF BO BċOJUZ QSPQBHBUJPO BMHPSJUIN XIJDI DPOWFSUT UIF NFTTBHF QBTTJOH SVMFT JOUP FRVJWBMFOU VQEBUF SVMFT QBTTJOH NFTTBHF EJSFDUMZ CFUXFFO OPEFT SBUIFS UIBO PO UIF GBDUPS HSBQI ɩF BMHPSJUIN JT TVNNBSJ[FE JO "MHPSJUIN *O UIF BMHPSJUIN XF mSTUz VTFT MPHBSJUINz UPT USBOT rij z 1 aij z 1 GPSN TVNQSPEVDU JOUP NBYTVN BOE JOUSPEVDF UXP TFUT PG WBSJBCMFT f g D BOE f g D GPS FBDI FEHF eij ɩF OFX VQEBUF SVMFT GPS UIF WBSJBCMFT BSF BT GPMMPXT z z z z rij bij bik aik D $ k NBYNB.j / f C g z 2 z ajj rkj ;0 D k NBYNB.j / NJO f g z 2 z z aij . rjj ;0 ; rjj ;0 D NJO NBY f g $zNJO f g rkj ;0 /; i NB.j /; $ k NBNBY.j / i NJO f g 2 2 nf g .*/*/( 501*$-&7&- 40$*"- */'-6&/$& "/"-:4*4 .j / j rz XIFSF NB EFOPUFT UIF OFJHICPSJOH OPEFT PG OPEF ij JT UIF JOnVFODF NFTTBHF TFOU GSPN i j az j i OPEF UP OPEF BOE ij JT UIF JOnVFODF NFTTBHF TFOU GSPN OPEF UP OPEF JOJUJBUFE CZ BOE bz ij JT UIF MPHBSJUIN PG UIF OPSNBMJ[FE GFBUVSF GVODUJPO z g.vi ; i ;z/y j z Z i D bij j : D MPH g.v ; ;z/ z k NB.i/ i i i yi k 2 [f g Z j D r a az ɩF JOUSPEVDFE WBSJBCMFT BOE PIBWF UIF GPMMPXJOH OJDF FYQMBOBUJPO .FTTBHF ij SFnFDUT GSPN UIF QFSTQFDUJWF PG OPEF vj IPX MJLFMZ OPEF vj UIJOLT IFTIF JOnVFODFT PO OPEF vi XJUI z rz v v SFTQFDU UP UPQJD XIJMF NFTTBHF ij SFnFDUT GSPN UIF QFSTQFDUJWF PG OPEF i IPX MJLFMZ OPEF i BHSFFT UIBU OPEF vj JOnVFODF PO IJNIFS XJUI SFTQFDU UP UPQJD z 'JOBMMZ XF DBO EFmOF UIF TPDJBM JOnVFODF TDPSF CBTFE PO UIF UXP WBSJBCMFT r BOE a VTJOH B TJHNPJE GVODUJPO z 1 +st z z : D 1 e .rts ats/ C ! C +z P.v; Y;z/ yz s ɩF TDPSF st BDUVBMMZ SFnFDUT UIF NBYJNVN PG GPS t D UIVT UIF NBYJNJ[B UJPO PG P.v; Y;z/DBO CF PCUBJOFE CZ z z yt +st: D BSHs NB NBY.t/ t 2 [f g z + 'v 'JOBMMZ BDDPSEJOH UP UIF PCUBJOFE JOnVFODF TDPSFT f stg BOE UIF UPQJD EJTUSJCVUJPO f g XF DBO FBTJMZ HFOFSBUF UIF UPQJDMFWFM TPDJBM JOnVFODF HSBQIT 4QFDJmDBMMZ GPS FBDI UPQJD z XF mSTU mMUFS PVU JSSFMFWBOU OPEFT JF OPEFT UIBU IBWF B MPXFS QSPCBCJMJUZ UIBO B QSFEFmOFE UISFTIPME "O BMUFSOBUJWF XBZ JT UP LFFQ POMZ B mYFE OVNCFS FH PG OPEFT GPS FBDI UPQJDCBTFE TPDJBM JOnVFODF HSBQI ɩJT mMUFSJOH QSPDFTT DBO CF BMTP UBLFO BT B QSFQSPDFTTJOH TUFQ PG PVS BQQSPBDI XIJDI JT UIF XBZ XF DPOEVDUFE PVS FYQFSJNFOUT ɩFO GPS B QBJS PG OPEFT .vs;vt / UIBU IBT BO G FEHF JO UIF PSJHJOBM OFUXPSLz XF DSFBUFz UXP EJSFDUFE FEHFT CFUXFFO UIF UXP OPEFT BOE BTTJHO UIF TPDJBM JOnVFODF TDPSFT +st BOE +ts SFTQFDUJWFMZ 'JOBMMZ XF PCUBJO B EJSFDUFE TPDJBM JOnVFODF HSBQI Gz GPS UIF UPQJD z O.N 4 T/ ɩF OFX BMHPSJUIN SFEVDFT UIF DPNQMFYJUZ PG FBDI JUFSBUJPO GSPN " JO UIF TVN O.M T/ QSPEVDU BMHPSJUIN UP " .PSF JNQPSUBOUMZ UIF OFX VQEBUF SVMFT DBO CF FBTJMZ QBSBM MFMJ[FE %JTUSJCVUFE 5"1 MFBSOJOH BMHPSJUIN "T B TPDJBM OFUXPSL NBZ DPOUBJO NJMMJPOT PG VTFST BOE IVOESFET PG NJMMJPOT PG TPDJBM UJFT CFUXFFO VTFST JU JT JNQSBDUJDBM UP MFBSO B 5'( GSPN TVDI B IVHF EBUB VTJOH B TJOHMF NBDIJOF 5P BEESFTT UIJT DIBMMFOHF XF EFQMPZ UIF MFBSOJOH UBTL PO B EJTUSJCVUFE TZTUFN VOEFS UIF NBQSFEVDF QSPHSBNNJOH NPEFM <> .BQ3FEVDF JT B QSPHSBNNJOH NPEFM GPS EJTUSJCVUFE QSPDFTTJOH PG MBSHF EBUB TFUT *O UIF NBQ TUBHF FBDI NBDIJOF DBMMFE B QSPDFTT OPEF SFDFJWFT B TVCTFU PG EBUB BT JOQVU BOE QSPEVDFT B TFU PG JOUFSNFEJBUF LFZWBMVF QBJST *O UIF SFEVDF TUBHF FBDI QSPDFTT OPEF NFSHFT BMM JOUFSNFEJBUF WBMVFT BTTPDJBUFE XJUI UIF TBNF JOUFSNFEJBUF LFZ BOE PVUQVUT UIF mOBM DPNQVUBUJPO SFTVMUT 6TFST 40$*"- */'-6&/$& "/"-:4*4 G .V; E/ 'v v V *OQVU D BOE UPQJD EJTUSJCVUJPOT f g 2 T Gz .Vz;Ez/ z 1 0VUQVU UPQJDMFWFM TPDJBM JOnVFODF HSBQIT f D g D g.v ; ;z/ $BMDVMBUF UIF OPEF GFBUVSF GVODUJPO i Zi bz $BMDVMBUF ij BDDPSEJOH UP &RVBUJPO rz 0 *OJUJBMJ[F BMM f ij g SFQFBU GPSFBDI FEHFUPQJD QBJS .eij ;z/EP rz 6QEBUF ij BDDPSEJOH UP &RVBUJPO FOE GPSFBDI OPEFUPQJD QBJS .vj ;z/EP az 6QEBUF jj BDDPSEJOH UP &RVBUJPO FOE GPSFBDI FEHFUPQJD QBJS .eij ;z/EP az 6QEBUF ij BDDPSEJOH UP &RVBUJPO FOE VOUJM DPOWFSHFODF GPSFBDI OPEF vt EP s NB.t/ t GPSFBDI OFJHICPSJOHz OPEF 2 [f g EP $PNQVUF +st BDDPSEJOH UP &RVBUJPO FOE FOE z Gz .Vz;Ez/ z + (FOFSBUF D GPS FWFSZ UPQJD BDDPSEJOH UP f stg "MHPSJUIN ɩF OFX 5"1 MFBSOJOH BMHPSJUIN TQFDJGZ B NBQ GVODUJPO UIBU QSPDFTTFT B LFZWBMVF QBJS UP HFOFSBUF B TFU PG JOUFSNFEJBUF LFZWBMVF QBJST BOE B SFEVDF GVODUJPO UIBU NFSHFT BMM JOUFSNFEJBUF WBMVFT BTTPDJBUFE XJUI UIF TBNF JOUFS NFEJBUF LFZ *O PVS BċOJUZ QSPQBHBUJPO QSPDFTT XF mSTU QBSUJUJPO UIF MBSHF TPDJBM OFUXPSL HSBQI JOUP TVCHSBQIT BOE EJTUSJCVUF FBDI TVCHSBQI UP B QSPDFTT OPEF *O FBDI TVCHSBQI UIFSF BSF UXP LJOET PG OPEFT JOUFSOBM OPEFT BOE NBSHJOBM OPEFT *OUFSOBM OPEFT BSF UIPTF BMM PG XIPTF OFJHICPST BSF JOTJEF UIF WFSZ TVCHSBQI NBSHJOBM OPEFT IBWF OFJHICPST JO PUIFS TVCHSBQIT 'PS FWFSZ TVCHSBQI G G BMM JOUFSOBM OPEFT BOE FEHFT CFUXFFO UIFN DPOTUSVDU UIF DMPTFE HSBQI N ɩF NBSHJOBM OPEFT DBO CF WJFXFE BT iUIF TVQQPSUJOH JOGPSNBUJPOw GPS VQEBUJOH UIF SVMFT 'PS FBTZ FYQMBOBUJPO XF DPOTJEFS UIF EJTUSJCVUFE MFBSOJOH BMHPSJUIN PO B TJOHMF UPQJD BOE UIVT UIF NBQ TUBHF BOE UIF SFEVDF TUBHF DBO CF EFmOFE BT GPMMPXT G G *O UIF NBQ TUBHF FBDI QSPDFTT OPEF TDBOT UIF DMPTFE HSBQI N PG UIF BTTJHOFE TVCHSBQI e az r /PUF UIBU FWFSZ FEHF ij IBT UXP WBMVFT ij BOE ij ɩVT UIF NBQ GVODUJPO JT EFmOFE BT GPS FWFSZ .*/*/( 501*$-&7&- 40$*"- */'-6&/$& "/"-:4*4 eij =aij ei =.bij aij / LFZWBMVF QBJS JU JTTVFT BO JOUFSNFEJBUF LFZWBMVF QBJS # C BOE GPS LFZWBMVF eij =rij e j =rij QBJS JU JTTVFT BO JOUFSNFEJBUF LFZWBMVF QBJS # *O UIF SFEVDF TUBHF FBDI QSPDFTT OPEF DPMMFDUT BMM WBMVFT BTTPDJBUFE XJUI BO JOUFSNFEJBUF ei ri LFZ # UP HFOFSBUF OFX # BDDPSEJOH UP &RVBUJPO BOE BMM JOUFSNFEJBUF WBMVFT BTTPDJBUFE e j a j XJUI UIF TBNF LFZ # UP HFOFSBUF OFX # BDDPSEJOH UP &RVBUJPOT BOE ɩVT UIF POF UJNF NBQSFEVDF QSPDFTT DPSSFTQPOET UP POF JUFSBUJPO JO PVS BċOJUZ QSPQBHBUJPO BMHPSJUIN 'JHVSF (SBQIJDBM SFQSFTFOUBUJPO PG UIF EZOBNJD GBDUPS HSBQI %:/".*$ 40$*"- */'-6&/$& "/"-:4*4 8F GVSUIFS FYUFOE UIF TPDJBM JOnVFODF BOBMZTJT UP UIF EZOBNJD TFUUJOH XIFSF UIF OFUXPSL TUSVD UVSF BOE UIF VTFST UPQJD EJTUSJCVUJPO NBZ DIBOHF PWFS UJNF *O HFOFSBM UIF JOQVU PG EZOBNJD Gt .V t ;Et / TPDJBMt JOnVFODF BOBMZTJT JT B TFSJBM PG UJNFEFQFOEFOU TPDJBM OFUXPSLT f gDf t g XIFSF V JT B TFU PG OPEFT VTFST FOUJUJFT BQQFBSJOH XJUIJO UIF UJNF XJOEPX t BOE E JT UIF TFU PG et Et wt EJSFDUFEVOEJSFDUFE FEHFT &BDI FEHF ij 2 JT BTTPDJBUFE XJUI B XFJHIUTJNJMBSJUZ ij XIJDI DBO CF EFmOFE JO EJĊFSFOU XBZT EFQFOEJOH PO UIF TQFDJmD BQQMJDBUJPO 8F TUJMM VTF UIF GBDUPS HSBQI NPEFM UP MFBSO UIF JOnVFODF TUSFOHUI CFUXFFO VTFST ɩF T UFDIOJDBM JTTVF XF OFFE UPt BEESFTT JTt IPXt T UP JODPSQPSBUF UIF UJNF JOGPSNBUJPO (JWFO UJNF G .V ;E / t 1 TQFDJmD TPDJBM OFUXPSLT f gDf g D %'( NPEFMT UIF OFUXPSLT BT B TFRVFODF PG UJNF EFQFOEFOU GBDUPS HSBQIT "U FBDI UJNF XJOEPX UIF GBDUPS HSBQI IBT B TJNJMBS TUSVDUVSF XJUI UIF 1'( NPEFM *O BEEJUJPO FBDI GBDUPS HSBQI BMTP EFQFOET PO UIF GBDUPS HSBQI PG UIF QSFWJPVT UJNF XJOEPX ɩVT UIF TFRVFODF PG UJNFEFQFOEFOU GBDUPS HSBQIT GPSNT B .BSLPW DIBJO 'BDUPS GVODUJPOT BSF EFmOFE CFUXFFO UIF WBSJBCMFT PG UXP DPOTFDVUJWF UJNFEFQFOEFOU GBDUPS HSBQIT 40$*"- */'-6&/$& "/"-:4*4 " GPSXBSECBDLXBSE NFTTBHF QBTTJOH QSPDFTT JT EFmOFE UP DBQUVSF UIF EFQFOEFODJFT CFUXFFO OFUXPSLT PG UXP UJNF XJOEPXT 'JHVSF TIPXT UIF HSBQIJDBM SFQSFTFOUBUJPO PG UIF %'( NPEFM 5P GPSNBMMZ EFmOF UIF %'( NPEFM XF BEE B TVQFSTDSJQU t UP UIF WBSJBCMFT vi yi ƒij k BOE +ij JO 1'( 8JUIJO UIF GBDUPS HSBQI PG FBDI UJNF XJOEPX UIF GBDUPS GVODUJPOT OPEF GBDUPS GVODUJPO BOE FEHF GBDUPS GVODUJPO BSF EFmOFE TJNJMBSMZ UP UIF 1'( NPEFM #FUXFFOt UXP DPOt 1 yi yi C TFDVUJWF UJNFEFQFOEFOU GBDUPSt HSBQIT t XF EFmOF B CSJEHF GBDUPS GVODUJPO CFUXFFO BOE + P.y j/ vj vi *O UIJT XBZ UIF JOnVFODF ji PS i D PG VTFS PO OPU POMZ JT EFUFSNJOFE CZ UIFJS MPDBM BOE OFUXPSL TUSVDUVSF JOGPSNBUJPO BU UJNF t CVU BMTP EFQFOET PO UIFJS IJTUPSJD JOnVFODF 4QFDJmDBMMZ UIF CSJEHF GBDUPS GVODUJPO BT q t t 1 y y C h.yt ;yt 1/ SC.j / j D j ; j j C j 1 q j t t 1 D ( SC.j / . !SC.j / 1/ yj yj C j j j j! ¤ q Œ0; 1 XIFSF 2 JT B XFJHIU JOEJDBUJOH UIF QSPCBCJMJUZ PG POF VTFST JOnVFODF PO BOPUIFS QSFTFSWFT XJUI UJNF DIBOHJOH ɩF XFJHIU q DBQUVSFT UIF UJNF EFQFOEFODJFT GPS UIF EZOBNJD TPDJBM JOnVFODF BOBMZTJT *U DBO CF MFBSOFE JO B TJNJMBS XBZ BT "MHPSJUIN /PX UIF KPJOU QSPCBCJMJUZ CFDPNFT t t P.y ;:::;y ;v1;:::;vN / 1 N D t t t t t 1 t t t g.y ;v / t f .y ;y / t h.y ;y /: v V i i eij E i j v V i ! i i 2 2 i 2 8F HFOFSBMJ[F 5"1Q MFBSOJOH BMHPSJUINQ UP TPMWF UIF MFBSOJOHQ QSPCMFN GPS UIF %'( NPEFM #Z JOUSPEVDJOH UXP OFX WBSJBCMFT ˛ BOE ˇ SFTQFDUJWFMZ SFQSFTFOUJOH UIF GPSXBSE BOE CBDLXBSE NFTTBHFT QBTTFE CFUXFFO UXP UJNFXJOEPXT XF DBO PCUBJO UIF GPMMPXJOH VQEBUF SVMFT t 1 t t ƒ fij .l; k/b ƒ ij k D Zt il sil i l SC.i/ s NB.i/ j 2X 2 Ynf g t 1 t 1 h.k0; k/˛k!i h.k;00 k/ˇ C 0 k00i k SC.i/ k SC.i/ 02X 002X t 1 t 1 t t ˛ h.l; k/˛ ! b ƒ ki D Zt li il sil i l SC.i/ s NB.i/ 2X 2Y t 1 t 1 t t ˇ h.l; k/ˇ C b ƒ ki D Zt li il sil i l SC.i/ s NB.i/ 2X 2Y t t 1 t 1 t Z ˛ ! ˇ C bjl ƒ : j D lj lj ij l l SC.j / i NB.j / 2X 2Y ɩVT UIF QSPCBCJMJTUJD JOnVFODF DBO CF DBMDVMBUFE CZ t 1 t 1 t 1 t + ˛ ! ˇ C bjk ƒ ; kj D Zt kj kj ij k j i NB.j / 2Y .*/*/( 501*$-&7&- 40$*"- */'-6&/$& "/"-:4*4 ˛t 1 ˇt 1 XIFSF kj! JT UIF NFTTBHF GSPN UIF QSFWJPVT UJNF XJOEPX BOE kjC JT UIF NFTTBHF GSPN UIF OFYU UJNF XJOEPX "CPWF JT UIF TPMVUJPO XIFO JOnVFODF TDPSFT JO BMM UJNF XJOEPXT BSF DBMDVMBUFE +t UPHFUIFS (JWFO UIBU UIF JOnVFODF JT FWPMWJOH GPSXBSE XJUI UJNF XIJDI NFBOT ij TIPVME CF t 1 f g + C HFOFSBUFE XJUIPVU JOGPSNBUJPO BCPVU f ij g XF DBO DPOTUSBJOU UIF NFTTBHF QBTTJOH QSPDFTT CZ POMZ BMMPXJOH GPSXBSE NFTTBHF ˛ BOE EJTDBSEJOH ˇ ɩFO JU UVSOT PVU XF DBO DPNQVUF UIF JOnVFODF UJNF CZ UJNF XJUI B GPSXBSE WFSTJPO PG 5"1 #PUI UIF GPSXBSECBDLXBSE BOE GPSXBSE WFSTJPO PG UIF 5"1 BMHPSJUIN JOIFSJU UIF OJDF QSPQFSUZ PG iMPDBMw VQEBUF XIJDI NBLFT UIF BMHPSJUIN FBTZ UP CF QBSBMMFMJ[FE 8F JNQMFNFOU UIF EJTUSJCVUFE MFBSOJOH VOEFS UIF NBQSFEVDF QMBUGPSN %FUBJMT BSF PNJUUFE EVF UP TQBDF MJNJUBUJPO .0%&- "11-*$"5*0/ ɩF TPDJBM JOnVFODF HSBQIT CZ 5"1 DBO IFMQ XJUI NBOZ BQQMJDBUJPOT )FSF XF JMMVTUSBUF UXP BQQMJDBUJPOT FYQFSU mOEJOH BOE JOnVFODF NBYJNJ[BUJPO &YQFSU mOEJOH )FSF XF QSFTFOU UISFF NFUIPET GPS FYQFSU mOEJOH 1BHF3BOL -BOHVBHF .PEFM 13 1BHF3BOL XJUI HMPCBM *OnVFODF 13* BOE 1BHF3BOL XJUI UPQJDCBTFE JOnVFODF 513* #BTFMJOF 13 0OF CBTFMJOF NFUIPE JT UP DPNCJOF UIF MBOHVBHF NPEFM BOE 1BHF3BOL <> -BOHVBHF NPEFM JT UP FTUJNBUF UIF SFMFWBODF PG B DBOEJEBUF XJUI UIF RVFSZ BOE 1BHF3 BOL JT UP FTUJNBUF UIF BVUIPSJUZ PG UIF DBOEJEBUF ɩFSF BSF EJĊFSFOU DPNCJOBUJPO NFUIPET ɩF TJNQMFTU DPNCJOBUJPO NFUIPE JT UP NVMUJQMZ PS TVN UIF 1BHF3BOL SBOLJOH TDPSF BOE UIF MBOHVBHF NPEFM SFMFWBODF TDPSF 1SPQPTFE 13* *O 13* XF SFQMBDF UIF USBOTJUJPO QSPCBCJMJUZ JO 1BHF3BOL XJUI UIF JO nVFODF TDPSF ɩVT XF IBWF 1 rŒv ˇ .1 ˇ/ rŒv0p.v v0/: D V C $ j v v v j j 0WX0! p.v v / *O USBEJUJPOBM 1BHF3BOL BMHPSJUIN j 0 JT TJNQMZ UIF WBMVF PG POF EJWJEFT UIF OVNCFS PG PVUMJOLT PG OPEF v0 )FSF XF DPOTJEFS UIF JOnVFODF TDPSF 4QFDJmDBMMZ XF EFmOF z z +v v p.v v0/ 0 : j D +z vj v vj z v vj W P0! 0 P P 1SPQPTFE 513* *O UIF TFDPOE FYUFOTJPO XF JOUSPEVDF GPS FBDI OPEF v B WFDUPS PG SBOLJOH TDPSFT rŒv; z FBDI PG XIJDI JT TQFDJmD UP UPQJD z 3BOEPN XBML JT QFSGPSNFE BMPOH XJUI UIF DPBVUIPS SFMBUJPOTIJQ CFUXFFO BVUIPST XJUIJO UIF TBNF UPQJD ɩVT UIF UPQJDCBTFE SBOLJOH TDPSF JT EFmOFE BT 1 rŒv; z ˇ p.zk v/ .1 ˇ/ rŒv0;zp.v v0; z/; D V j C $ j v v v j j 0WX0! 40$*"- */'-6&/$& "/"-:4*4 p.z v/ z v XIFSF j JT UIF QSPCBCJMJUZ PG UPQJD HFOFSBUFE CZ OPEF BOE JU JT PCUBJOFE GSPN UIF UPQJD p.v v ;z/ v v z NPEFM j 0 SFQSFTFOUT UIF QSPCBCJMJUZ PG OPEF 0 JOnVFODJOH OPEF PO UPQJD XF EFmOF JU BT z +v v p.v v0;z/ 0 : j D +z vj v vj v vj W 0! 0 P *OnVFODF NBYJNJ[BUJPO (JWFO B TPDJBM OFUXPSL XJUI UIF MFBSOFE TPDJBM JOnVFODF PO FBDI TPDJBM G .V;E;-/ SFMBUJPOTIJQ JF 0 D UIF PCKFDUJWF JT UP mOE B TNBMM TVCTFU PG OPEFT TFFE OPEFT GSPN UIF OFUXPSL UIBU DPVME NBYJNJ[F UIF TQSFBE PG JOnVFODF ɩF QSPCMFN PG JOnVFODF NBYJNJ[BUJPO IBT CFFO QSPWFO UP CF B /1IBSE QSPCMFN <> " HSFFEZ BQQSPYJNBUJPO BMHPSJUIN DBO HVBSBOUFFT .1 1=e/ UIBU UIF JOnVFODF TQSFBE JT OP XPSTF UIBO $ PG UIF PQUJNBM JOnVFODF TQSFBE 0OF NBKPS QSPCMFN PG UIF HSFFEZ BMHPSJUIN JT JUT MPX FċDJFODZ $IFO FU BM < > EFWFMPQFE OFX IFVSJTUJDT UP BDDFMFSBUF UIF HSFFEZ BMHPSJUIN ɩF TPDJBM JOnVFODF MFBSOFE CZ UIF QSPQPTFE 5"1 BMHPSJUIN DBO QSPWJEF UIF JOQVU UP UIF HSFFEZ BMHPSJUIN &91&3*.&/5"- 3&46-54 *O UIJT TFDUJPO XF QSFTFOU WBSJPVT FYQFSJNFOUT UP FWBMVBUF UIF FċDJFODZ BOE FĊFDUJWFOFTT PG UIF QSPQPTFE BQQSPBDI "MM EBUB TFUT DPEFT BOE UPPMT UP WJTVBMJ[F UIF HFOFSBUFE JOnVFODF HSBQIT BSF QVCMJDMZ BWBJMBCMF BU ?iiT,ff `M2iKBM2`XQ`;fH #@/ i b2ibfbQBM7f &YQFSJNFOUBM TFUVQ 8F QFSGPSN PVS FYQFSJNFOUT PO UISFF SFBMXPSME EBUB TFUT UXP IPNPHF OFPVT OFUXPSLT BOE POF IFUFSPHFOFPVT OFUXPSL ɩF IPNPHFOFPVT OFUXPSLT BSF BDBEFNJD DP BVUIPS OFUXPSL $PBVUIPS GPS TIPSU BOE QBQFS DJUBUJPO OFUXPSL $JUBUJPO GPS TIPSU #PUI BSF FYUSBDUFE GSPN BDBEFNJD TFBSDI TZTUFN "SOFUNJOFS ɩF DPBVUIPS EBUB TFU DPOTJTUT PG BVUIPST BOE DPBVUIPS SFMBUJPOT XIJMF UIF DJUBUJPO EBUB TFU DPOUBJOT QBQFST BOE DJUBUJPOT CFUXFFO UIFTF QBQFST 5PQJD EJTUSJCVUJPOT PG BVUIPST BOE QBQFST BSF EJTDPWFSFE VTJOH B TUBUJTUJDBM UPQJD NPEFMJOH BQQSPBDI "VUIPS$POGFSFODF5PQJD "$5 NPEFM <> ɩF "$5 BQQSPBDI BVUPNBUJDBMMZ FYUSBDUT UPQJDT BOE BTTJHOT BO BVUIPSTQFDJmD UPQJD EJTUSJCVUJPO UP FBDI BVUIPS BOE B QBQFSTQFDJmD UPQJD EJTUSJCVUJPO UP FBDI QBQFS ɩF PUIFS IFUFSPHFOFPVT OFUXPSL JT B mMNEJSFDUPSBDUPSXSJUFS OFUXPSL TIPSUMZ 'JMN XIJDI JT DSBXMFE GSPN 8JLJQFEJB VOEFS UIF DBUFHPSZ PG i&OHMJTIMBOHVBHF mMNTw¤ *O UPUBM UIFSF BSF mMNT EJSFDUPST BDUPST BOE XSJUFST ɩFSF BSF SFMBUJPOTIJQT CFUXFFO UIF IFUFSPHFOFPVT OPEFT JO UIF EBUBTFU ɩF SFMBUJPOTIJQ UZQFT JODMVEF mMNEJSFDUPS mMNBDUPS mMNXSJUFS BOE PUIFS SFMBUJPOTIJQT CFUXFFO BDUPST EJSFDUPST BOE XSJUFST ɩF mSTU UISFF UZQFT PG SFMBUJPOTIJQT BSF FYUSBDUFE GSPN UIF iJOGPCPYw PO UIF mMNT 8JLJ QBHFT "MM UIF PUIFS UZQFT PG QFPQMF SFMBUJPOTIJQT BSF DSFBUFE BT GPMMPXT JG POF QFPQMF JODMVEJOH BDUPST EJSFD UPST BOE XSJUFST BQQFBST PO BOPUIFS QFPQMFT QBHF UIFO B EJSFDUFE SFMBUJPOTIJQ JT DSFBUFE CFUXFFO ?iiT,ff `M2iKBM2`XQ`; ¤?iiT,ff2MXrBFBT2/B XQ`;frBFBf* i2;Q`v,1M;HBb?@H M;m ;2n7BHKb .*/*/( 501*$-&7&- 40$*"- */'-6&/$& "/"-:4*4 UIFN 5PQJD EJTUSJCVUJPOT PG UIF IFUFSPHFOFPVT OFUXPSL JT JOJUJBMJ[FE VTJOH UIF DBUFHPSZ JOGPSNB UJPO EFmOFE PO UIF 8JLJQFEJB QBHF .PSF TQFDJmDBMMZ XF UBLF UFO DBUFHPSJFT XJUI UIF IJHIFTU PDDVSSJOH UJNFT BT UIF UPQJDT ɩF UFO DBUFHPSJFT BSF i"NFSJDBO mMN BDUPST w i"NFSJDBO UFMFWJ TJPO BDUPST w i#MBDL BOE XIJUF mMNT w i%SBNB mMNT w i$PNFEZ mMNT w i#SJUJTI mMNT w i"NFSJDBO mMN EJSFDUPST w i*OEFQFOEFOU mMNT w i"NFSJDBO TDSFFOXSJUFST w BOE i"NFSJDBO TUBHF BDUPSTw "T GPS UIF UPQJD EJTUSJCVUJPO PG FBDI OPEF JO UIF mMN OFUXPSL 1 XF mSTU DBMDVMBUF IPX MJLFMZ B OPEF vi z p.vi z/ Vz CFMPOH UP B DBUFHPSZ UPQJD JF BDDPSEJOH UP Vz XIFSF JT UIF OVNCFS PG OPEFT j j j j j T z p.vi z/ z 1 JO UIF DBUFHPSZ UPQJD ɩVT GPS FBDI OPEF XF XJMM PCUBJO BT TFU f j g D PG MJLFMJIPPE GPS p.z vi / z 1 FBDI OPEF ɩFO XF DBMDVMBUF UIF UPQJD EJTUSJCVUJPO f j g D BDDPSEJOH UP UIF #BZFTJBO SVMF p.z vi / p.z/p.vi z/ p.z/ j / j XIFSF JT UIF QSPCBCJMJUZ PG UIF DBUFHPSZ UPQJD &WBMVBUJPO NFBTVSFT 'PS RVBOUJUBUJWFMZ FWBMVBUF PVS NFUIPE XF DPOTJEFS UXP QFSGPSNBODF NFUSJDT t $16 UJNF *U JT UIF FYFDVUJPO FMBQTFE UJNF PG UIF DPNQVUBUJPO ɩJT EFUFSNJOFT IPX Fċ DJFOU PVS NFUIPE JT t "QQMJDBUJPO JNQSPWFNFOU 8F BQQMZ UIF JEFOUJmFE UPQJDCBTFE TPDJBM JOnVFODF UP IFMQ FYQFSU mOEJOH BO JNQPSUBOU BQQMJDBUJPO JO TPDJBM OFUXPSL ɩJT XJMM EFNPOTUSBUF IPX UIF RVBOUJUBUJWF NFBTVSFNFOU PG UIF TPDJBM JOnVFODF DBO CFOFmU UIF PUIFS TPDJBM OFUXPSLJOH BQQMJDBUJPO ɩF CBTJD MFBSOJOH BMHPSJUIN JT JNQMFNFOUFE VTJOH ."5-"# C BOE BMM FYQFSJNFOUT XJUI JU BSF QFSGPSNFE PO B 4FSWFS SVOOJOH 8JOEPXT XJUI UXP %VBM$PSF *OUFM 9FPO QSP DFTTPST ()[ BOE (# NFNPSZ ɩF EJTUSJCVUFE MFBSOJOH BMHPSJUIN JT JNQMFNFOUFE VOEFS UIF .BQ3FEVDF QSPHSBNNJOH NPEFM VTJOH UIF )BEPPQ QMBUGPSN© 8F QFSGPSN UIF EJTUSJCVUFE USBJO PO DPNQVUFS OPEFT $16 DPSFT XJUI ".% QSPDFTTPST ()[ BOE (# NFNPSZ JO UPUBM 8F TFU UIF NBYJNVN OVNCFS PG JUFSBUJPOT BT BOE UIF UISFTIPME GPS UIF DIBOHF PG r a 1e 3 BOE UP $ ɩF BMHPSJUIN DBO RVJDLMZ DPOWFSHF BGUFS o JUFSBUJPOT JO NPTU PG UIF UJNFT *O BMM FYQFSJNFOUT GPS HFOFSBUJOH FBDI PG UIF UPQJDCBTFE TPDJBM JOnVFODF HSBQIT XF POMZ LFFQ p.v z/ OPEFT UIBU IBWF UIF IJHIFTU QSPCBCJMJUJFT j 4DBMBCJMJUZ QFSGPSNBODF 8F FWBMVBUF UIF FċDJFODZ PG PVS BQQSPBDI PO UIF UISFF EBUB TFUT 8F BMTP DPNQBSF PVS BQQSPBDI XJUI UIF TVNQSPEVDU BMHPSJUIN 5BCMF MJTUT UIF $16 UJNF SFRVJSFE PO UIF UISFF EBUB TFUT XJUI UIF GPMMPXJOH PCTFSWBUJPOT 4VN1SPEVDU WT 5"1 ɩF OFX 5"1 BQQSPBDI JT NVDI GBTUFS UIBO UIF USBEJUJPOBM TVN QSPEVDU BMHPSJUIN XIJDI FWFO DBOOPU DPNQMFUF PO UIF DJUBUJPO EBUB TFU #BTJD WT %JTUSJCVUFE 5"1 ɩF EJTUSJCVUFE 5"1 DBO UZQJDBMMZ BDIJFWF B TJHOJmDBOU SF EVDUJPO PG UIF $16 UJNF PO UIF MBSHFTDBMF OFUXPSL 'PS FYBNQMF PO UIF DJUBUJPO EBUB TFU XF PCUBJO B TQFFEVQ 9 8IJMF PO B NPEFSBUF TDBMFE OFUXPSL UIF DPBVUIPS EBUB TFU UIF TQFFEVQ PG UIF EJTUSJCVUFE 5"1 JT MJNJUFE POMZ 0O B SFMBUJWF TNBMMFS OFUXPSL UIF mMN EBUB TFU ©?iiT,ff? /QQTX T +?2XQ`;f 40$*"- */'-6&/$& "/"-:4*4 UIF EJTUSJCVUFE MFBSOJOH VOEFSQFSGPSNT UIF CBTJD 5"1 MFBSOJOH BMHPSJUIN XIJDI JT EVF UP UIF DPNNVOJDBUJPO PWFSIFBE PG UIF .BQ3FEVDF GSBNFXPSL %JTUSJCVUFE 4DBMBCJMJUZ 8F GVSUIFS DPOEVDU B TDBMBCJMJUZ FYQFSJNFOU XJUI PVS EJTUSJCVUFE 5"1 8F FWBMVBUF UIF TQFFEVQ PG UIF EJTUSJCVUFE MFBSOJOH BMHPSJUIN PO UIF TJY DPNQVUFS OPEFT VTJOH UIF DJUBUJPO EBUB TFU XJUI EJĊFSFOU TJ[FT *U DBO CF TFFO GSPN 'JHVSF B UIBU XIFO UIF TJ[F PG UIF EBUB TFU JODSFBTF UP OFBSMZ POF NJMMJPO FEHFT UIF EJTUSJCVUFE MFBSOJOH TUBSUT UP TIPX B HPPE QBSBMMFM FċDJFODZ TQFFEVQ9 ɩJT DPOmSNT UIBU EJTUSJCVUFE 5"1 MJLF NBOZ EJTUSJCVUFE MFBSOJOH BMHPSJUINT JT HPPE PO MBSHFTDBMF EBUB TFUT 5BCMF 4DBMBCJMJUZ QFSGPSNBODF PG EJĊFSFOU NFUIPET PO SFBM EBUB TFUT > IS NFBOT UIBU UIF BMHPSJUIN EJE OPU UFSNJOBUF XIFO UIF BMHPSJUIN SVOT NPSF UIBO IPVST Methods Citation Coauthor Film Sum-Product N/A > 10hr 1.8 hr Basic TAP Learning > 10hr 369s 57s Distributed TAP Learning 39.33m 104s 148s B %BUBTFU TJ[F WT TQFFEVQ C $PNQVUFS OPEFT WT TQFFEVQ 'JHVSF 4QFFEVQ SFTVMUT 6TJOH PVS MBSHF DJUBUJPO EBUB TFU XF BMTP QFSGPSN TQFFEVQ FYQFSJNFOUT PO B )BEPPQ QMBU GPSN VTJOH DPNQVUFS OPEFT TJODF XF EJE OPU IBWF BDDFTT UP B MBSHF OVNCFS PG DPNQVUFS >4 OPEFT ɩF TQFFEVQ TIPXO JO 'JHVSF C TIPX SFBTPOBCMF QBSBMMFM FċDJFODZ XJUI B " TQFFEVQ VTJOH DPNQVUFS OPEFT 2VBOUJUBUJWF DBTF TUVEZ /PX XF DPOEVDU RVBOUJUBUJWFMZ FWBMVBUJPO PG UIF FĊFDUJWFOFTT PG UIF UPQJDCBTFE TPDJBM JOnVFODF BOBMZTJT UISPVHI DBTF TUVEZ 3FDBMM UIF HPBM PG FYQFSU mOEJOH JT UP JEFOUJGZ QFSTPOT XJUI TPNF FYQFSUJTF PS FYQFSJFODF PO B TQFDJmD UPQJD RVFSZ q 8F EFmOF UIF P.q v/ rŒv CBTFMJOF NFUIPE BT UIF DPNCJOBUJPO <> PG UIF MBOHVBHF NPEFM j BOE 1BHF3BOL .*/*/( 501*$-&7&- 40$*"- */'-6&/$& "/"-:4*4 PR PRI TPRI (%) 020406080100 P@5 P@10 P@20 R−Pre MAP 'JHVSF 1FSGPSNBODF PG FYQFSU mOEJOH XJUI EJĊFSFOU BQQSPBDIFT 8F VTF BO BDBEFNJD EBUB TFU VTFE JO 5BOH FU BM < > GPS UIF FYQFSJNFOUT 4QFDJmDBMMZ UIF EBUB TFU DPOUBJOT 14; 134 BVUIPST 10; 716 QBQFST BOE 1; 434 DPOGFSFODFT 'PVSHSBEF TDPSFT BOE BSF NBOVBMMZ MBCFMFE UP SFQSFTFOU EFmOJUF FYQFSUJTF FYQFSUJTF NBSHJOBM FYQFSUJTF BOE OP FYQFSUJTF 6TJOH UIJT EBUB XF DSFBUF B DPBVUIPS OFUXPSL ɩF UPQJD NPEFM GPS FBDI BVUIPS JT TUJMM PCUBJOFE VTJOH UIF TUBUJTUJDBM UPQJD NPEFMJOH BQQSPBDI <> 8JUI UIF UPQJD NPEFMT XF BQQMZ UIF QSPQPTFE 5"1 BQQSPBDI UP UIF DPBVUIPS OFUXPSL UP JEFOUJGZ UIF UPQJDCBTFE JOnVFODFT 8JUI UIF MFBSOFE UPQJDCBTFE JOnVFODF TDPSFT XF EFmOF UXP FYUFOTJPOT UP UIF 1BHF3BOL NFUIPE 1BHF3BOL XJUI *OnVFODF 13* BOE 1BHF3BOL XJUI UPQJDCBTFE JOnVFODF 513* %F UBJMT PG UIF FYUFOTJPO JT EFTDSJCFE JO 4FDUJPO 'PS FYQFSU mOEJOH XF DBO GVSUIFS DPNCJOF UIF FYUFOEFE 1BHF3BOL NPEFM XJUI UIF SFMFWBODF NPEFM GPS FYBNQMF UIF MBOHVBHF NPEFM CZ P.q v/rŒv p.q z/p.z v/rŒv; z rŒv rŒv; z j PS B UPQJDCBTFE SFMFWBODF NPEFM CZ z j j XIFSF BOE p.q z/ p.z v/ BSF PCUBJOFE SFTQFDUJWFMZ GSPN 13* BOE 513* P j j DBO CF PCUBJOFE GSPN UIF TUBUJT UJDBM UPQJD NPEFM <> 8F FWBMVBUF UIF QFSGPSNBODF PG EJĊFSFOU NFUIPET JO UFSNT PG 1SFDJTJPO! 1! 1! 1! 3QSFDJTJPO 31SF BOE NFBO BWFSBHF QSFDJTJPO ."1 < > 'JHVSF TIPXT UIF SFTVMU PG FYQFSU mOEJOH XJUI EJĊFSFOU BQQSPBDIFT 8F TFF UIBU UIF UPQJDCBTFE TPDJBM JOnVFODFT EJTDPWFSFE CZ UIF 5"1 BQQSPBDI DBO JOEFFE JNQSPWF UIF BDDVSBDZ PG FYQFSU mOEJOH XIJDI DPO mSNT UIF FĊFDUJWFOFTT PG UIF QSPQPTFE BQQSPBDI GPS UPQJDCBTFE TPDJBM JOnVFODF BOBMZTJT 3FTVMUT PG %ZOBNJD *OnVFODFT "OBMZTJT ɩF EZOBNJD TPDJBM JOnVFODF BOBMZTJT DBO CFOFmU NBOZ BQQMJDBUJPOT 8F VTF UIF JOnVFODF NBYJNJ[BUJPO QSPCMFN BT UXP FYBNQMFT UP EFNPOTUSBUF ɩF JOnVFODF NBYJNJ[BUJPO QSPCMFN JT UP mOE B TNBMM TVCTFU PG OPEFT TFFE OPEFT JO B TPDJBM OFU XPSL UIBU DPVME NBYJNJ[F UIF TQSFBE PG JOnVFODF < > *O NPTU QSFWJPVT XPSL EJĊFSFOU BMHPSJUINT XFSF FWBMVBUFE VOEFS TJNQMF BTTVNQUJPOT BCPVU QBJSXJTF JOnVFODF /PX UIF PVUQVU PG PVS TPDJBM JOnVFODF BOBMZTJT DBO CF VTFE BT UIF JOQVU PG UIF JOnVFODF NBYJNJ[BUJPO QSPCMFN 40$*"- */'-6&/$& "/"-:4*4 (a) weight ← WC (b) weight ← PFG 'JHVSF *OnVFODF TQSFBE CZ EJĊFSFOU BMHPSJUINT 1%' SFGFST UP UIF QSPQPTFE EZOBNJD JOnVFODF BOBMZTJT BQQSPBDI 5BCMF %JTDPWFSFE TFFE OPEFT JO JOnVFODF NBYJNJ[BUJPO CZ UIF HSFFEZ BMHPSJUIN XJUI EJĊFS FOU JOnVFODF TDIFNFT 6OJRVF JOnVFODF VOJRVF QSPCBCJMJUZ 8$ JOnVFODF JOWFSTF PG JOEFHSFF 1'( JOnVFODF SFTVMU PG PVS EZOBNJD JOnVFODF BOBMZTJT No. Unique WC PFG 1 Philip S. Yu Philip S. Yu Jiawei Han 2 Jiawei Han Jiawei Han Qiang Yang 3 Christos Faloutsos Wei Wang Christos Faloutsos 4 Qiang Yang Christos Faloutsos Heikki Mannila 5 Heikki Mannila Heikki Mannila Vipin Kumar 6 Wei Wang C. Lee Giles C. Lee Giles 7 Jian Pei Shusaku Tsumoto Saso Dzeroski 8 Vipin Kumar Jian Pei Graham J. Williams 9 Bing Liu Bing Liu Myra Spiliopoulou 10 C. Lee Giles Joost N. Kok Eamonn J. Keogh Overlap 0.4222 0.2444 0.1778 BOE XF DBO UFTU XIFUIFS FYJTUJOH PQUJNJ[BUJPO BMHPSJUINT QFSGPSN BT XFMM BT UIFZ EP VOEFS UIF OBJWF BTTVNQUJPOT 'JHVSF TIPXT UIF TPMVUJPO GPVOE1 CZ TFWFSBM TUBUFPGUIFBSU BMHPSJUINT EFmOJOH UIF vi vj dj TQSFBE QSPCBCJMJUZ GSPN UP TJNQMZ BT dj SFGFSSFE BT 8$ NPEFM XIFSF JT UIF JOEFHSFF PG vj #FZPOE (SFFEZ BMHPSJUIN XF BMTP UFTU 41. <> VTJOH B TJNQMJmFE *$. NPEFM BOE .*" <> B IFVSJTUJD BMHPSJUIN GPS HFOFSBM *$. NPEFM #BTFMJOF BMHPSJUINT JODMVEF SBOEPN SBOEPNMZ QJDLJOH TFFET 1BHF3BOL TFMFDUJOH OPEFT XJUI UPQ 1BHF3BOL TDPSF BOE %F HSFF%JTDPVOU*$ B IFVSJTUJD BMHPSJUIN XJUI HPPE QFSGPSNBODF JO 6*$. <> (SFFEZ BMHPSJUIN .*/*/( 501*$-&7&- */'-6&/$& '30. )&5&30(&/&064 /&5803,4 QSPWJEFT CFTU SFTVMUT BT LOPXO *O 8$ NPEFM 41. BOE .*" QFSGFDUMZ NBUDI (SFFEZ %F HSFF%JTDPVOU*$ IBT OFBSMZ NBUDIJOH QFSGPSNBODF ɩFZ BMM CFBU UIF PUIFS CBTFMJOFT 8$ NPEFM QSFTVNFT TZNNFUSJD JOnVFODF JO DPNNPO XJUI 6*$. XIJMF 1'( EPFT OPU 8IFO 1'( JOnV FODF TDPSF SFQMBDFT UIF XFJHIUT PG 8$ BT TIPXO JO 'JHVSF 41. BOE .*" TUJMM BQQSPYJNBUF PQUJNVN XIJMF %FHSFF%JTDPVOU*$ EFHSBEFT UP %FHSFF ɩFSFGPSF CZ BQQMZJOH PVS JOnVFODF SFTVMUT XF mOE UIBU 41. BOE .*" BSF CFUUFS BQQSPYJNBUJPO UIBO %FHSFF%JTDPVOU*$ JG UIF TZNNFUSJD BTTVNQUJPO PG JOnVFODF EPFT OPU IPME 5BCMF QSFTFOUT UIF EJTDPWFSFE TFFE OPEFT CZ UISFF EJĊFSFOU TDIFNFT UP TFU UIF DBTDBEF JOnVFODF TDPSFT 'PS FBDI TFU PG TFFE OPEFT XF DBMDVMBUF UIF EFOTJUZ NFBTVSF JO OFUXPSL TDJ FODF EJWJEJOH UIF TVN PG DPBVUIPS QBQFST CZ UIF OVNCFS PG EJĊFSFOU QBJST CFUXFFO TFFET JF 10 9 45 2$ D JO PVS DBTF ɩF MBSHFS JT UIF PWFSMBQ UIF NPSF DPODFOUSBUFE BSF UIF TFFE OPEFT JO UIF OFUXPSL 5P NBYJNJ[F UIF JOnVFODF TQSFBE JU JT EFTJSBCMF UP NJOJNJ[F UIF PWFSMBQ 8F TFF UIBU PVS BQQSPBDI DMFBSMZ PVUQFSGPSNT UIF UIF PUIFS NFUIPET *U DBO CF PCTFSWFE UIBU 1IJMJQ 4 :V EPFT OPU BQQFBS BT B UPQ TFFE JO 1'( NPEFM EVF UP UIF MBSHF QSPCBCJMJUZ PG IJN JOnVFODFE CZ PUIFS TFFET *O 6*$. BOE 8$ NPEFM JOnVFODF GSPN OFJHICPST UP UIF OPEF BSF JOEFQFOEFOU XIJMF JO 1'( UIF DPSSFMBUJPO PG JOnVFODF CFUXFFO OFJHICPST JT DBQUVSFE 46.."3: *O UIJT TFDUJPO XF JOUSPEVDF B OPWFM QSPCMFN PG UPQJDCBTFE TPDJBM JOnVFODF BOBMZTJT 8F QSP QPTF B 5PQJDBM "ċOJUZ 1SPQBHBUJPO 5"1 BQQSPBDI UP EFTDSJCF UIF QSPCMFN VTJOH B HSBQIJDBM QSPCBCJMJTUJD NPEFM 5P EFBM XJUI UIF FċDJFOU QSPCMFN XF QSFTFOU B OFX BMHPSJUIN GPS USBJOJOH UIF 5'( NPEFM " EJTUSJCVUFE MFBSOJOH BMHPSJUIN IBT CFFO JNQMFNFOUFE VOEFS UIF .BQSFEVDF QSPHSBNNJOH NPEFM &YQFSJNFOUBM SFTVMUT PO UISFF EJĊFSFOU UZQFT PG EBUB TFUT EFNPOTUSBUF UIBU UIF QSPQPTFE BQQSPBDI DBO FĊFDUJWFMZ EJTDPWFS UIF UPQJDCBTFE TPDJBM JOnVFODFT ɩF EJTUSJCVUFE MFBSOJOH BMHPSJUIN BMTP IBT B HPPE TDBMBCJMJUZ QFSGPSNBODF 8F BQQMZ UIF QSPQPTFE BQQSPBDI UP FYQFSU mOEJOH &YQFSJNFOUT TIPX UIBU UIF EJTDPWFSFE UPQJDCBTFE JOnVFODFT CZ UIF QSPQPTFE BQQSPBDI DBO JNQSPWF UIF QFSGPSNBODF PG FYQFSU mOEJOH .*/*/( 501*$-&7&- */'-6&/$& '30. )&5&30(&/&064 /&5803,4 ɩF QSPQPTFE 5"1 NFUIPE JO 4FDUJPO POMZ DPOTJEFST IPNPHFOFPVT OFUXPSL XJUI TJOHMF UZQF PG PCKFDUT XIJMF NBOZ SFBMXPSME OFUXPSLT VTVBMMZ DPOTJTU PG NVMUJQMF IFUFSPHFOFPVT PCKFDUT *O BEEJUJPO UIF 5"1 NFUIPE BTTVNFT UIBU B UPQJD EJTUSJCVUJPO JT BTTPDJBUFE XJUI FBDI VTFS XIJDI JT BMTP OPU UIF DBTF JO SFBM BQQMJDBUJPOT 8F QSPQPTF UIF QSPCMFN PG UPQJDMFWFM JOnVFODF NJOJOH GSPN IFUFSPHFOFPVT TPDJBM OFU XPSLT ɩF QSPCMFN DBO CF FYQMBJOFE CZ VTJOH UIF FYBNQMF JO 'JHVSF ɩF JOQVU MFGU mHVSF JT B IFUFSPHFOFPVT OFUXPSL DPOTJTUJOH PG XFC EPDVNFOUT VTFST BOE MJOLT CFUXFFO UIFN 5P MFWFSBHF CPUI DPOUFOU JOGPSNBUJPO PG XFC EPDVNFOUT BOE TPDJBM OFUXPSL TUSVDUVSF XF QSPQPTF B QSPCB 40$*"- */'-6&/$& "/"-:4*4 Input: Output: Topics-level influence strength Application: Heterogeneous network and influence propagation User behavior prediction Will she re-tweet iphone ? Bob Topic 1: Avatar Adaa BBobo 0.2 Will he re-tweet Avatar ? Topic 2: iphone indirect 0.8 influence AdaA Bob Ada direct Jerryy 0.7 Ying SmithSmit influence Smith 0.3 YYinging Jerryy click a blog JJerrye write a blog re-tweet a blog write a blog 0.6 0.4 d2 d4 0.4 Yingng d5 0.6 Smith 0.4 d1 d3 0.6 iphone Avatar 'JHVSF 1SPCMFN JMMVTUSBUJPO PG NJOJOH UPQJDMFWFM JOnVFODF JO IFUFSPHFOFPVT OFUXPSLT BOE QSF EJDUJOH VTFS CFIBWJPST CJMJTUJD HFOFSBUJWF NPEFM UP KPJOUMZ MFBSO UPQJDT BOE UP BTTPDJBUF B UPQJD EJTUSJCVUJPO XJUI FBDI VTFS XIJDI JOEJDBUFT IJTIFS JOUFSFTUT #BTFE PO UIF NPEFMJOH SFTVMUT XF DBO FTUJNBUF UIF JOnVFODF TUSFOHUI CFUXFFO GSJFOET 8F GVSUIFS JOWFTUJHBUF UXP LJOET PG EJĊVTJPO NPEFMT GPS DPOTFSWBUJWF BOE OPODPOTFSWBUJWF JOnVFODF QSPQBHBUJPOT JO TPDJBM OFUXPSLT XIJDI VODPWFS UIF JOEJSFDU JOnV FODF CFUXFFO OPODPOOFDUFE VTFST ɩF NJEEMF mHVSF PG 'JHVSF JMMVTUSBUFT UIF PVUQVU PG UPQJD EJTDPWFSZ BOE JOnVFODF QSPQBHBUJPO ɩF TPMJE BSSPX JOEJDBUFT EJSFDU JOnVFODF BOE UIF EBTIFE BSSPX JOEJDBUFT JOEJSFDU JOnVFODF ɩF SJHIU mHVSF JMMVTUSBUFT B QPUFOUJBM BQQMJDBUJPO VTFS CFIBWJPS QSFEJDUJPO CBTFE PO UIF MFBSOFE JOnVFODF *O UIJT TFDUJPO XF QSFTFOU B HFOFSBUJWF QSPCBCJMJTUJD NPEFM UP RVBOUJGZ JOnVFODF CFUXFFO VTFST JO IFUFSPHFOFPVT TPDJBM OFUXPSLT CZ VUJMJ[JOH CPUI DPOUFOU BOE MJOL JOGPSNBUJPO UP NJOF EJSFDU JOnVFODF TUSFOHUI JO IFUFSPHFOFPVT OFUXPSLT 8F TUVEZ UXP LJOET PG EJĊVTJPO NPEFMT GPS DPOTFSWBUJWF BOE OPODPOTFSWBUJWF JOnVFODF QSPQBHBUJPOT UP MFBSO JOEJSFDU JOnVFODF JO TPDJBM OFUXPSLT 8F BQQMZ UIF EJTDPWFSFE JOnVFODF TUSFOHUI UP VTFS CFIBWJPS QSFEJDUJPO BOE WBMJEBUF IPX JU DBO IFMQ TPNF TPDJBM BQQMJDBUJPOT 8F DPOEVDU FYUFOTJWF FYQFSJNFOUT JO GPVS EJĊFSFOU UZQFT PG EBUB TFUT 5XJUUFS ņ %JHH Ň 3FOSFO ň BOE $PSB ʼn BOE UFTU UIF NPEFM QFSGPSNBODF JO CPUI RVBMJUBUJWF BOE RVBOUJUBUJWF XBZT 1SPCMFN 'PSNVMBUJPO -FU VT SFEFmOF UIF JOQVU PG PVS QSPCMFN G .V; D; E/ %FmOJUJPO <)FUFSPHFOFPVT 4PDJBM /FUXPSL> %FmOF B OFUXPSL BT D XIFSF V JT B TFU PG VTFS OPEFT D JT B TFU PG EPDVNFOU OPEFT BOE E EFOPUFT B TFU PG FEHFT UIBU JODMVEFT TPDJBM SFMBUJPOTIJQT DPOOFDUJOH VTFST BOE MJOLT DPOOFDUJOH VTFST BOE EPDVNFOUT 'PS FBDI FEHF ņ?iiT,ffrrrXirBii2`X+QK B NJDSPCMPHHJOH TZTUFN Ň?iiT,ffrrrX/B;;X+QK B TPDJBM OFXT TIBSJOH BOE WPUJOH XFCTJUF ň?iiT,ffrrrX`2M`2MX+QK POF PG UIF MBSHFTU 'BDFCPPLMJLF TPDJBM OFUXPSLT JO $IJOB ʼn?iiT,ffrrrX+bXmK bbX2/mfK++ HHmKf+Q/2@/ i X?iKH B CJCMJPHSBQIJD DJUBUJPO OFUXPSL .*/*/( 501*$-&7&- */'-6&/$& '30. )&5&30(&/&064 /&5803,4 euv .u; v/ E u v euv 1 euv 0 D 2 JG UIFSF FYJTUT BO FEHF CFUXFFO BOE D PUIFSXJTF D ɩF FEHFT DBO CF EJSFDUFE PS VOEJSFDUFE .BOZ POMJOF TPDJBM OFUXPSLT BSF IFUFSPHFOFPVT DPOTJTUJOH PG EJĊFSFOU UZQFT PG PCKFDU OPEFT 'PS FYBNQMF 5XJUUFS JT DPNQSJTFE PG VTFST BOE NJDSPCMPHT %JHH DPOTJTUT PG VTFST BOE XFCTJUF 63- BEESFTTFT $JUBUJPO OFUXPSL DPOTJTUT PG BVUIPST BOE QVCMJDBUJPO QBQFST )FSF XF VTF iEPD VNFOUw UP SFQSFTFOU EJĊFSFOU UZQFT PG BTTPDJBUFE DPOUFOU FH NJDSPCMPH XFCTJUF BOE QBQFS UP FBDI VTFS ɩVT MJOLT JO IFUFSPHFOFPVT OFUXPSLT XPVME DPOUBJO GSJFOETIJQT CFUXFFO VTFST BOE BVUIPSJOH SFMBUJPOTIJQT CFUXFFO VTFST BOE EPDVNFOUT MJOLT CFUXFFO EPDVNFOUT BSF OPU DPOTJE FSFE JO UIJT DIBQUFS ɩF MJOLT DBO CF EJSFDUFE PS VOEJSFDUFE 'PS FYBNQMF JO 5XJUUFS BOE DJUBUJPO OFUXPSLT UIF MJOLT CFUXFFO VTFST BSF EJSFDUFE GSPN OPSNBM VTFST UP UIFJS GPMMPXFST *O %JHH TP DJBM OFUXPSL UIF MJOLT CFUXFFO VTFST BSF VOEJSFDUFE 'VSUIFSNPSF XF BTTVNF UIBU JOnVFODF DBO QSPQBHBUF BMPOH TPDJBM MJOLT UIVT XF IBWF UIF GPMMPXJOH EFmOJUJPO %FmOJUJPO <%JSFDU BOE *OEJSFDU *OnVFODF> (JWFO UXP VTFS OPEFT u; v JO B IFUFSPHFOFPVT G ıv.u/ R 0 u v OFUXPSL XF EFOPUF 2f C [ g BT UIF JOnVFOUJBM TUSFOHUI PG VTFS PO VTFS 'VSUIFS euv 1 ıv.u/ u v euv 0 ıv.u/ NPSF JG D XF DBMM UIF EJSFDU JOnVFODF PG VTFS PO JG D XF DBMM UIF JOEJSFDU JOnVFODF PG VTFS u PO v %JSFDU JOnVFODF JOEJDBUFT UIF JOnVFODF CFUXFFO UXP VTFST XIJDI BSF DPOOFDUFE XIJMF JO EJSFDU JOnVFODF JOEJDBUFT UIF JOnVFODF PG UXP VTFST XIJDI BSF OPU DPOOFDUFE 1MFBTF OPUF UIBU ıv.u/ ıu.v/ JOnVFODF JT BTZNNFUSJD JF ¤ #BTFE PO UIF JOnVFODF CFUXFFO OPEF QBJST XF DBO GVSUIFS EFmOF UIF DPODFQU PG HMPCBM JOnVFODF ƒ.v/ R 0 %FmOJUJPO <(MPCBM *OnVFODF> (JWFO B IFUFSPHFOFPVT OFUXPSL 2f C [ g JT EFmOFE BT UIF HMPCBM JOnVFODF PG v XIJDI SFQSFTFOUT UIF HMPCBM JOnVFOUJBM TUSFOHUI PG VTFS v JO UIF OFUXPSL ɩF HMPCBM JOnVFODF TUSFOHUI IBT B DMPTF SFMBUJPOTIJQ XJUI UIF MPDBM EJSFDUJOEJSFDU JOnV FODF 'PS FYBNQMF JG B VTFS IBT B TUSPOH JOnVFODF PO IFSIJT GSJFOET JU JT WFSZ MJLFMZ UIBU TIFIF IBT B TUSPOH HMPCBM JOnVFODF 5)& "1130"$) '3".&803, 5P TVNNBSJ[F XF IBWF UXP JNQPSUBOU JOUVJUJPOT GPS MFBSOJOH JOnVFODF GSPN IFUFSPHFOFPVT TP DJBM OFUXPSLT JOnVFODF CFUXFFO VTFST WBSJFT PWFS EJĊFSFOU UPQJDT BOE VTFS CFIBWJPST BSF OPU POMZ JOnVFODFE CZ UIFJS GSJFOET CVU BMTP UIFJS nEFHSFF GSJFOET FH GSJFOET GSJFOET *O EFFE JO SFBM OFUXPSLT VTFST NBZ CF JOUFSFTUFE JO EJĊFSFOU UPQJDT FH JO UIF SFTFBSDI OFUXPSL BO BVUIPS NBZ CF JOUFSFTUFE JO UPQJDT iEBUBCBTFw BOE iEBUB NJOJOHw ɩF JOnVFOUJBM TUSFOHUI GSPN POFT DPBVUIPST PO IFSIJN XSU UIF UXP UPQJDT NJHIU CF WFSZ EJĊFSFOU "DUVBMMZ UIJT IBT CFFO RVBMJUBUJWFMZ WFSJmFE JO TPDJPMPHZ < > BOE RVBOUJUBUJWFMZ TUVEJFE JO 5BOH FU BM <> .PSF QSFDJTFMZ XF DBO HJWF UIF GPMMPXJOH EFTDSJQUJPOT GPS UIF JOUVJUJPOT 40$*"- */'-6&/$& "/"-:4*4 T v v R T &BDI OPEF JT BTTPDJBUFE XJUI B WFDUPS 2 PG EJNFOTJPOBM UPQJD EJTUSJCVUJPO v.z/ 1 v.z/ z D XIFSF JOEJDBUFT UIF JOUFSFTU QSPCBCJMJUZ PG UIF OPEF VTFS PO UPQJD z P *OnVFODF DBO QSPQBHBUF PWFS TPDJBM OFUXPSLT UIVT UIF JOnVFODF ıv.u/ PG VTFS u PO v DBO euv 1 euv 0 CF EJSFDU D PS JOEJSFDU D ɩF CFIBWJPS PG B VTFS JT FJUIFS JOnVFODFE CZ IJTIFS GSJFOET XIP IBWF UIF TBNF CFIBWJPS PS HFOFSBUFE EFQFOEJOH PO IJTIFS JOUFSFTUT ɩF MBTU JOUVJUJPO DBO CF CFUUFS FYQMBJOFE CZ BO FYBNQMF PO %JHH " VTFS NBZ EJH B TUPSZ CFDBVTF IJT GSJFOET IBWF EJHHFE UIJT TUPSZ PS TJNQMZ CFDBVTF IF JT JOUFSFTUFE JO UIJT UPQJD 'SPN UIF UFDIOJRVF QFSTQFDUJWF PVS PCKFDUJWF JT UP EFTJHO B NFUIPE UP MFBSO VTFS JOUFSFTUT UIF BTTPDJBUFE UPQJD EJTUSJCVUJPO BOE UP FTUJNBUF VTFS JOnVFODF TJNVMUBOFPVTMZ *O UIJT CPPL XF QSPQPTF B UPQJDMFWFM JOnVFODF NPEFMJOH GSBNFXPSL 'JSTU CZ DPNCJOJOH CPUI UFYUVBM JOGPSNB UJPO BOE MJOL JOGPSNBUJPO JO IFUFSPHFOFPVT OFUXPSLT XF QSFTFOU B QSPCBCJMJTUJD HFOFSBUJWF NPEFM UP MFBSO VTFS JOUFSFTUT XIJDI BSF SFQSFTFOUFE BT NJYUVSFT PG UPQJDT BOE EJSFDU JOnVFODF CFUXFFO VTFST TJNVMUBOFPVTMZ 4FDPOE CBTFE PO EJSFDU JOnVFODF XF TUVEZ UXP UZQFT PG JOnVFODF QSPQBHB UJPO NFDIBOJTN XIJDI BSF DPOTFSWBUJWF BOE OPODPOTFSWBUJWF JOnVFODF QSPQBHBUJPOT UP EFSJWF JOEJSFDU JOnVFODF CFUXFFO VTFST 'JHVSF 1SPCBCJMJTUJD HFOFSBUJWF NPEFM UP FTUJNBUF EJSFDU JOnVFODF TUSFOHUI *OnVFODF JT JOUFSBDUFE XJUI NBOZ QPUFOUJBM GBDUPST FH TJNJMBSJUZ BOE DPSSFMBUJPO < > )FSF XF IBWF UXP HFOFSBM BTTVNQUJPOT JO PSEFS UP NPEFM UIF JOnVFODF TUSFOHUI RVBOUJUBUJWFMZ "TTVNQUJPO 6TFST XJUI TJNJMBS JOUFSFTUT IBWF B TUSPOHFS JOnVFODF PO FBDI PUIFS ɩJT BTTVNQUJPO BDUVBMMZ DPSSFTQPOET UP UIF JOnVFODF BOE TFMFDUJPO UIFPSZ <> *O SFBM OFU XPSLT UIF TJNJMBSJUZ DBO CF DBMDVMBUFE CBTFE PO UIF DPOUFOU JOGPSNBUJPO BTTPDJBUFE XJUI FBDI .*/*/( 501*$-&7&- */'-6&/$& '30. )&5&30(&/&064 /&5803,4 VTFS ɩVT JOnVFODF DBO CF SFQSFTFOUFE BT UP XIJDI FYUFOU UIF UFYUVBM DPOUFOU JT iDPQJFEw GSPN UIF JOnVFODJOH OPEFT 'PS FYBNQMF JO UIF DJUBUJPO OFUXPSL JG UIF DPOUFOU PG EPDVNFOU d1 JT WFSZ TJNJMBS UP UIBU PG EPDVNFOU d2 XF NBZ EFFN UIBU d1 iDPQJFTw B MPU PG JEFBT GSPN d2 UIVT d1 JT JOnVFODFE CZ d2 B MPU "TTVNQUJPO 6TFST XIPTF BDUJPOT GSFRVFOUMZ DPSSFMBUF IBWF B TUSPOHFS JOnVFODF PO FBDI PUIFS ɩF DPPDDVSSFODF GSFRVFODZ JT PGUFO VTFE UP JOEJDBUF UIF DPSSFMBUJPO TUSFOHUI CFUXFFO UXP OPEFT XIJDI JT EFOPUFE CZ UIF XFJHIUT PG FEHFT JO OFUXPSLT ɩVT UIF JOnVFODF TUSFOHUI CFUXFFO UXP OPEFT XPVME CF FOMBSHFE CZ UIFJS GSFRVFOU DPPDDVSSFODF 'PS FYBNQMF JG BVUIPS a DJUFT B OVNCFS PG QBQFST PG BVUIPS b UIFO a TIPVME CF TUSPOHMZ JOnVFODFE CZ b 'PS BOPUIFS FYBNQMF PO 5XJUUFS JG VTFS a SFQMJFT PS SFUXFFUT NBOZ NJDSPCMPHT QPTUFE CZ VTFS b UIFO JU JT WFSZ MJLFMZ UIBU b IBT B TUSPOH JOnVFODF PO a #BTFE PO UIFTF DPOTJEFSBUJPOT XF QSPQPTF B QSPCBCJMJTUJD HFOFSBUJWF NPEFM UP KPJOUMZ MFBSO VTFS JOUFSFTUT BOE EJSFDU JOnVFODF TUSFOHUI CFUXFFO VTFST RVBOUJUBUJWFMZ 5BCMF 7BSJBCMF EFTDSJQUJPOT Notation Description x, x′ the influenced/influencing user w, w′ words in the associated document z,z′ topic assignment to each word d, d′ document associated with influenced/influencing user Ax the user list who may influence x y the influencing user from Ax s the label denoting either influencing or not W the number of words in the data set T the number of topics to be extracted θ the topic mixture of influencing users ψ innovative topic mixture of users φ word distribution for each topic γ the influence mixture of users λ the parameter to draw the label s α the Dirichlet prior for hidden variables " 1SPCBCJMJTUJD (FOFSBUJWF .PEFM 8F QSPQPTF B QSPCBCJMJTUJD NPEFM UP NJOF UPQJDT BOE JOnV FODF TUSFOHUI TJNVMUBOFPVTMZ ɩF NPEFM DPNCJOFT UIF DPOUFOU JOGPSNBUJPO BOE OFUXPSL TUSVDUVSF JO IFUFSPHFOFPVT OFUXPSLT BT TIPXO JO 'JHVSF 8F BTTVNF UIBU UIF CFIBWJPS PG FBDI JOnV FODFE VTFS DBO CF HFOFSBUFE JO UXP XBZT FJUIFS EFQFOEJOH PO IJTIFS PXO JOUFSFTUT PS JOnVFODFE CZ POF PG IJTIFS GSJFOET 'PS FYBNQMF XIFO B VTFS TIBSFT B CMPH PO 3FOSFO IFTIF NBZ MJLF JUT 40$*"- */'-6&/$& "/"-:4*4 GPSFBDI JOnVFODJOH VTFS x0 EP GPSFBDI BTTPDJBUFE EPDVNFOU d 0 EP i d GPSFBDI XPSE 2 0 EP zd0 ;i multi. x/ xd0 ;i %SBX B UPQJD 0 & GSPN UIF UPQJD NJYUVSF PG VTFS 0 wd0 ;i multi..zd;i / zd0 ;i %SBX B XPSE 0 & GSPN 0 TQFDJmD XPSE EJTUSJCVUJPO FOE FOE FOE GPSFBDI JOnVFODFE VTFS x EP GPSFBDI BTTPDJBUFE EPDVNFOUT d EP i d GPSFBDI XPSE 2 EP s bernoul li.&x / 5PTT B DPJO d;i & d;i XIFSF &x p.s 0 xd;i / beta.˛" ;˛" / d;i D D j & s0 s1 XIJDI JOEJDBUFT UIF QSPQPSUJPO CFUXFFO UIF JOOPWBUJPO BOE JOnVFODFE QSPCBCJMJUZ PG xd;i s 0 JG d;i D UIFO y multi.$x/ Ax %SBX B JOnVFODJOH VTFS d;i & GSPN UIF VTFS MJTU z multi.'y / y %SBX B UPQJD d;i & GSPN UIF UPQJD NJYUVSF PG d;i FOE s 1 JG d;i D UIFO z multi. x/ x %SBX B UPQJD d;i & GSPN UIF UPQJD NJYUVSF PG d;i FOE w multi..z / z %SBX B XPSE d;i & d;i GSPN d;i TQFDJmD XPSE EJTUSJCVUJPO FOE FOE FOE "MHPSJUIN 1SPCBCJMJTUJD HFOFSBUJWF QSPDFTT DPOUFOU PS GPMMPX UIF BDUJPO PG POF PG IJTIFS GSJFOET XIP BMTP TIBSF JU ɩVT UIF QSPQPTFE NPEFM DPOTJTUT PG UIF GPMMPXJOH UXP QBSUT BOE UIF XIPMF HFOFSBUJWF QSPDFTT BSF JMMVTUSBUFE JO "MHPSJUIN 5BCMF MJTUT UIF EFTDSJQUJPOT PG WBSJBCMFT t 6TFS JOUFSFTU NPEFMJOH "T TIPXO JO UIF NJEEMF QBSU PG 'JHVSF FBDI VTFS x JT SFQSFTFOUFE BT B NVMUJOPNJBM EJTUSJCVUJPO PWFS UPQJDT XIJDI JOEJDBUFT VTFS JOUFSFTUT 8F BTTVNF UIBU UPQJDT PG EPDVNFOUT BSF HFOFSBUFE CBTFE PO VTFS JOUFSFTUT ɩFO FBDI XPSE w JO EPDVNFOUT JT HFOFSBUFE GSPN POF UPQJD z TFMFDUFE GSPN UIF EJTUSJCVUJPO ɩF EFUBJMT PG UIF HFOFSBUJWF QSPDFTT BSF JMMVTUSBUFE JO UIF mSTU JUFSBUJPO PG "MHPSJUIN t *OnVFODF TUSFOHUI NJOJOH ɩF SJHIU QBSU PG 'JHVSF JMMVTUSBUFT JOnVFODF TUSFOHUI NPE FMJOH ɩF QBSBNFUFS s XIJDI JT HFOFSBUFE GSPN B #FSOPVMMJ EJTUSJCVUJPO XJUI QBSBNFUFS & s 1 JT VTFE UP DPOUSPM UIF JOnVFODF TJUVBUJPO 8F BTTVNF UIBU XIFO D UIF CFIBWJPS JT s 0 HFOFSBUFE CBTFE PO IJTIFS PXO JOUFSFTUT XIJMF XIFO D UIF CFIBWJPS PG UIF VTFS JT JOnVFODFE CZ POF PG IJTIFS GSJFOET ɩFO BOPUIFS QBSBNFUFS $ JT VTFE UP JOEJDBUF UIF JO nVFODF TUSFOHUI GSPN DBOEJEBUF VTFS TFU Ax UP VTFS x CBTFE PO XIJDI POF JOnVFODJOH VTFS .*/*/( 501*$-&7&- */'-6&/$& '30. )&5&30(&/&064 /&5803,4 y JT TFMFDUFE GSPN Ax "U MBTU B UPQJD JT HFOFSBUFE GSPN UIF NJYUVSF PG UPQJDT PG B VTFSUIF VTFS IJNTFMGIFSTFMG x PS POF PG IJTIFS GSJFOET y CBTFE PO XIJDI UIF XPSE w JT HFOFSBUFE ɩJT QBSU DPSSFTQPOET UP UIF TFDPOE JUFSBUJPO PG "MHPSJUIN *O UIF BCPWF HFOFSBUJWF QSPDFTT Ax JT UIF DBOEJEBUF JOnVFODJOH VTFS TFU XSU x UIVT Ax DIBOHFT XJUI x #FTJEFT Ax JT EFUFSNJOFE CZ SFBM BQQMJDBUJPOT XIJDI DPOTJEFST CPUI EJSFDUFE BOE VOEJSFDUFE MJOLT CFUXFFO VTFST 'PS FYBNQMF JO 5XJUUFS OFUXPSL Ax EFOPUFT UIF VTFST XIPN B CMPH JT SFUXFFUFE GSPN XIJMF JO DJUBUJPO OFUXPSLT JU EFOPUFT UIF BVUIPST PG DJUFE QBQFST *O UIFTF OFUXPSLT UIF MJOLT CFUXFFO VTFST BSF EJSFDUFE *O TPNF PUIFS OFUXPSLT TVDI BT 3FOSFO BOE %JHH Ax EFOPUFT UIF GSJFOET PG VTFS x XIP BMTP TIBSF PS EJH UIF TBNF TUPSZ BOE UIF MJOLT BSF VOEJSFDUFE ɩVT UIF QSPQPTFE NPEFM JT BCMF UP IBOEMF CPUI UZQFT PG DBTFT .PEFM -FBSOJOH WJB (JCCT 4BNQMJOH 8F FNQMPZ (JCCT TBNQMJOH UP FTUJNBUF UIF NPEFM (JCCT TBNQMJOH JT BO BMHPSJUIN UP BQQSPYJNBUF UIF KPJOU EJTUSJCVUJPO PG NVMUJQMF WBSJBCMFT CZ ESBXJOH B TFRVFODF PG TBNQMFT XIJDI JUFSBUJWFMZ VQEBUFT FBDI MBUFOU WBSJBCMF VOEFS UIF DPOEJUJPO PG mYJOH SFNBJOJOH WBSJBCMFT 8F MJTU UIF VQEBUF FRVBUJPOT GPS FBDI WBSJBCMF BT CFMPX BOE UIF EFUBJMT PG N. / EFSJWBUJPO DBO SFGFS UP UIF BQQFOEJY *O BMM UIF VQEBUF FRVBUJPOT * JT UIF GVODUJPO XIJDI TUPSFT UIF OVNCFS PG TBNQMFT EVSJOH (JCCT TBNQMJOH 'PS FYBNQMF Nx;z;s.x; z; 1/ SFQSFTFOUT UIF z x s 1 OVNCFS PG TBNQMFT PG UPQJDT XIJDI BSF TVQQPTFE UP CF HFOFSBUFE GSPN VTFS XIFO D p.si 0 s i ;xi ;zi ; :/ D jE! / N .x ;0/ ˛ Nx ;z .yi ;zi / Ny;z;s .yi ;zi ;0/ ˛" x;s i $s 0 0 C C C 0 Nx .yi / Ny;s .yi ;0/ T ˛" Nx .xi / ˛$s ˛$s 0 C C " # C 0 C 1 p.si 1 s i ;xi ;zi ; :/ D jE! / Nx;s .x ;1/ ˛ Nx;z;s .xi ;zi ;1/ ˛ i $s1 C C Nx;s .xi ;1/ T ˛ Nx .xi / ˛$s ˛$s C " # C 0 C 1 p.yi y i ;si 0; di ;xi ;zi ;Ax; :/ jE!Nx;y;sD.xi ;yi ;0/ ˛% Nx ;z .y/i ;zi / Ny;z;s .yi ;zi ;0/ ˛" C 0 0 C C Nx;s .xi ;0/ Ax ˛% Nx .yi / Ny;s .yi ;0/ T ˛" Cj j" # 0 C C " p.zi z i ;si 0; wi ; :/ ! NxjE;z .yi ;ziD/ Ny;z;s .yi ;z/i ;0/ ˛" Nw;z .wi ;zi / Nw ;z .w0 ;z0 / ˛& 0 0 C C C 0 0 i i C Nx .yi / Ny;s .yi ;0/ T ˛" Nz .zi / Nz .zi / W ˛& 0 C C " # C 0 C " p.zi z i ;si 1; wi ; :/ jE! D / Nx;z;s .xi ;zi ;1/ ˛ Nw;z .wi ;zi / Nw ;z .wi0 ;zi0 / ˛& C C 0 0 C : Nx;s .xi ;1/ T ˛ Nz .zi / Nz .zi / W ˛& C " # C 0 C " ɩSPVHI UIF (JCCT TBNQMJOH QSPDFTT XF PCUBJO UIF TBNQMFE DPJO si JOnVFODJOH VTFS yi BOE UPQJD zi GPS FBDI XPSE ɩFO UIF JOnVFODF TUSFOHUI DBO CF FTUJNBUFE CZ &RVBUJPO XIJDI BSF BWFSBHFE PWFS UIF TBNQMJOH DIBJO BGUFS DPOWFSHFODF K EFOPUFT UIF MFOHUI PG UIF TBN QMJOH DIBJO K i 1 Nx;y;s.x; y; 0/ ˛& ıx.y/ $x.y/ i C : D D K Nx;s.x; 0/ A ˛& i 1 XD Cj j# 40$*"- */'-6&/$& "/"-:4*4 ɩF FRVBUJPO JT DPOTJTUFOU UP PVS BTTVNQUJPOT JO B TUBUJTUJDBM XBZ 5BLF DJUBUJPO OFUXPSLT GPS FYBNQMF *G BVUIPS x DJUFT NPSF QBQFST PG BVUIPS y BOE iDPQJFTw NPSF DPOUFOU GSPN y Nx;y;s.x; y; 0/ XJMM CF MBSHFS BOE UIVT UIF JOnVFODF GSPN y UP x XJMM CF TUSPOHFS #FTJEFT JU JT Ax yj 1j ıx.y/ 1 x FBTZ UP HFU UIBU D D JF UIF TVN PG JOnVFODF PO VTFS GSPN BMM UIF VTFST PCUBJOFE JO UIF NPEFM FRVBMTP UP "OE UIF NPEFM EPFT OPU DPOTJEFS UIF JOnVFODF CFUXFFO UIF OPEFT XIJDI ıx.y/ 0 x y BSF OPU DPOOFDUFE JF D XIFO BOE BSF OPU DPOOFDUFE 'VSUIFSNPSF XF DBO FTUJNBUF UIF UPQJDMFWFM JOnVFODF TUSFOHUI 4VQQPTF ıx;z.y/ SFQSF y x z ıx.y/ TFOUTT UIF JOnVFODF TUSFOHUI GSPN VTFS UP VTFS PO UIF UPQJD XIJDI TBUJTGZ UIBU D z 1 ıx;z.y/ D ɩVT UIF UPQJDMFWFM JOnVFODF DBO CF FTUJNBUFE CZ &RVBUJPO P K i 1 1 Nx;y;z;s.x; y; z; 0/ ˛& C T # ıx;z.y/ i : D K Nx;s.x; 0/ A ˛& i 1 XD Cj j# */'-6&/$& 1301"("5*0/ "/% "((3&("5*0/ ɩF BCPWF QSPCBCJMJTUJD NPEFM POMZ EJTDPWFST EJSFDU JOnVFODF CVU EPFT OPU DPOTJEFS JOEJSFDU JOnV FODF *O SFBMJUZ MJLF JOGPSNBUJPO PS WJSVT JOnVFODF BMTP QSPQBHBUFT PWFS OFUXPSLT XIJDI QSPEVDFT EJĊFSFOU UZQFT PG JOEJSFDU JOnVFODF 5BLF 'JHVSF B GPS FYBNQMF *G a1 JOnVFODFT a2 BOE a2 JOnVFODFT a3 UIFO a1 XJMM JOnVFODF a3 QPUFOUJBMMZ JF UXPEFHSFF PG JOnVFODF 'JHVSF C EFNPOTUSBUFT UIF JOnVFODF FOIBODFNFOU JG a1 JOnVFODFT a3 BOE a4 XIJMF a3 BOE a4 BMTP IBWF BO JOnVFODF PO a2 UIFO UIF JOnVFODF GSPN a1 UP a2 TIPVME CF FOIBODFE 8F GVSUIFS TUVEZ BUPNJD BOE JUFSBUJWF JOnVFODF QSPQBHBUJPO PWFS TPDJBM OFUXPSLT JO UIJT TFDUJPO WJB XIJDI JOEJSFDU JOnV FODF DBO CF PCUBJOFE GSPN EJSFDU JOnVFODF BOE HMPCBM JOnVFODF TUSFOHUI DBO CF FTUJNBUFE a1 a1 a2 a3 a4 a3 a2 (a) (b) 'JHVSF *OnVFODF QSPQBHBUJPO "UPNJD *OnVFODF 1SPQBHBUJPO "T TIPXO JO 'JHVSF XF PCTFSWF UIFSF BSF UXP CBTJD QSPDFTTFT GPS JOnVFODF QSPQBHBUJPO t $PODBUFOBUJPO ɩF JOEJSFDU JOnVFODF GSPN a1 UP a3 JO 'JHVSF B DBO CF NPEFMFE BT B DPODBUFOBUF SFTVMU PG UIF EJSFDU JOnVFODF GSPN a1 UP a2 BOE UIF EJSFDU JOnVFODF GSPN a2 UP a3 .*/*/( 501*$-&7&- */'-6&/$& '30. )&5&30(&/&064 /&5803,4 t "HHSFHBUJPO ɩF FOIBODFNFOU PG UIF JOnVFODF GSPN a1 UP a2 JO 'JHVSF C DBO CF EFmOFE BT BO BHHSFHBUF SFTVMU PG UIF EJSFDU JOnVFODF BNPOH UIF OFJHICPSIPPE PG a1 BOE a2 ɩFSFGPSF UIF BUPNJD JOnVFODF QSPQBHBUJPO JT EFmOFE BT ıv.u/ . w Nb.v/ ıv.w/ ıw .u//; D}8 2 W ı Nb.v/ v XIFSF JT UIF TFU PG OFJHICPST PG OPEF ı JT UIF DPODBUFOBUJPO GVODUJPO BOE } JT UIF BHHSFHBUJPO GVODUJPO *O SFBM QSPDFTTFT NVMUJQMJDBUJPO PQFSBUJPO PS NJOJNVN WBMVF JT PGUFO VTFE BT DPODBUFOB UJPO GVODUJPO XIJMF BEEJUJPO PQFSBUJPO PS NBYJNVN WBMVF JT VTFE BT UIF BHHSFHBUJPO GVODUJPO *O QBSUJDVMBS JG XF FNQMPZ NVMUJQMJDBUJPO BOE BEEJUJPO PQFSBUJPOT UP SFQMBDF UIF DPODBUFOBUJPO BOE BHHSFHBUJPO GVODUJPO JO &RVBUJPO SFTQFDUJWFMZ UIFO UIF BUPNJD JOnVFODF QSPQBHBUJPO DBO CF JOTUBOUJBUFE BT ıv.u/ ıv.w/ ıw .u/: D # w N b.v/ 2X 4VQQPTF v SFQSFTFOUT UIF WFDUPS PG UIF JOnVFODF TUSFOHUI GSPN BMM UIF OPEFT JO UIF OFU v v .ıv.u1/; ıv.u2/; :::; ıv.un// XPSL PO OPEF JF 0 D "OE XF VTF TVQFSTDSJQU1 UP EFOPUF UIF QSPQBHBUJPO TUFQ JF EFOPUFT UIF JOJUJBM JOnVFODF TUSFOHUI BOE EFOPUFT UIF JOnVFODF TUSFOHUI BGUFS UIF BUPNJD QSPQBHBUJPO ɩFO UIF BUPNJD JOnVFODF QSPQBHBUJPO DBO CF SFQSFTFOUFE BT UIF NBUSJY NVMUJQMJDBUJPO 1 0 M v D v # M M .v v ::: v / XIFSF JT UIF USBOTJUJPO NBUSJY BOE D 1 I 2 I I n JF FBDI FMFNFOU JO UIF USBOTJ M.v; u/ ıv.u/ UJPO NBUSJY D *UFSBUJWF *OnVFODF 1SPQBHBUJPO *O SFBMJUZ UIF JOEJSFDU JOnVFODF BMPOH MPOHFS QBUIT FH UISFF EFHSFF PS GPVSEFHSFF JOnVFODF BMTP IBWF FĊFDU PO UIF OPEFT JO B OFUXPSL *O PUIFS XPSET JO nVFODF DBO QSPQBHBUF JUFSBUJWFMZ UP DPMMFDU UIF DPOUSJCVUF PG JOnVFODF PO MPOHFS QBUIT ɩVT UIF BUPNJD JOnVFODF QSPQBHBUJPO TIPVME CF QFSGPSNFE JUFSBUJWFMZ UP QSPQBHBUF EJSFDU JOnVFODF PWFS UIF FOUJSF OFUXPSL ɩVT UIF JOnVFODF TUSFOHUI PO kMFOHUI QBUIT DBO CF DBMDVMBUFE CZ k TUFQT PG BUPNJD QSPQBHBUJPOT *G UIF BUPNJD QSPQBHBUJPO JT EFmOFE BT &RVBUJPO UIF JOnVFODF TUSFOHUI WFDUPS BGUFS kTUFQ BUPNJD QSPQBHBUJPO DBO CF DBMDVMBUFE CZ UIF NBUSJY QPXFSJOH PQFSBUJPO k k 1 0 k ! M M ; v D v # D v # M k M k 1 M k k XIFSF D ! # EFOPUFT UIF JOnVFODF TUSFOHUI WFDUPS PO MFOHUI QBUIT 'PSNBMMZ XF EFmOF UIF JUFSBUJWF JOnVFODF QSPQBHBUJPO BT GPMMPXT 40$*"- */'-6&/$& "/"-:4*4 t FOVNFSBUF BMM QBUIT CFUXFFO FBDI UXP OPEFT t DBMDVMBUF UIF JOnVFODF QSPQBHBUJPO TUSFOHUI PO FBDI QBUI WJB B DPODBUFOBUJPO GVODUJPO BOE t DPNCJOF UIF JOnVFODF TUSFOHUI PO BMM UIF QBUIT WJB BO BHHSFHBUJPO GVODUJPO 4VQQPTF UIF mOBM JOnVFODF TUSFOHUI CFUXFFO UXP OPEFT BGUFS kTUFQ JUFSBUJWF QSPQBHBUJPO JT fk EFOPUFE BT #BTFE PO UIF BCPWF EFmOJUJPO JU TIPVME DPMMFDU BMM UIF DPOUSJCVUFT PG UIF JOnVFODF TUSFOHUI PO QBUIT XJUI UIF MFOHUI SBOHJOH GSPN UP k JF fk . i 0; 1; 2; : : : ; k i /: D}8 2f gW fk *G BEEJUJPO PQFSBUJPO JT VTFE BT UIF BHHSFHBUJPO GVODUJPO DBO CF JOGFSSFE GSPN UIF TFRVFODFT PG QSPQBHBUJPO WJB B XFJHIUFE MJOFBS DPNCJOBUJPO <> k fk i ˇi ; D i 0 XD i ˇi EFOPUFT UIF XFJHIU GPS UIF JOnVFODF TUSFOHUI PO iMFOHUI QBUIT JF *OUVJUJWFMZ UIF FĊFDU PG UIF JOnVFODF PO TIPSUFS QBUIT TIPVME CF MBSHFS UIBO UIF POF PO MPOHFS QBUIT BT UIF JUFSBUJWF QSPQBHBUJPO QSPDFTT CSJOHT JO NPSF PVUTJEF JOGPSNBUJPO 5FDIOJDBMMZ ˇi TIPVME EFDSFBTF XJUI UIF JODSFBTF PG JUFSBUJPO TUFQ i %JĊFSFOU TUSBUFHJFT DBO CF FNQMPZFE UP BTTJHO UIF XFJHIUT *O UIF OFYU TFDUJPO XF XJMM TUVEZ UXP LJOET PG TUSBUFHJFT XIJDI BSF DPOTFSWBUJWF QSPQBHBUJPO BOE OPODPOTFSWBUJWF QSPQBHBUJPO SFTQFDUJWFMZ (MPCBM *OnVFODF &TUJNBUJPO (MPCBM JOnVFODF JT UP NFBTVSF POFT JOnVFOUJBM BCJMJUZ PWFS UIF XIPMF OFUXPSL 'PS FYBNQMF TPNF BVUIPST BSF WFSZ JOnVFOUJBM PO UIF UPQJD PG iEBUB NJOJOHw *O UIJT TFDUJPO XF QSPQPTF POF XBZ UP FTUJNBUF POF OPEFT HMPCBM JOnVFODF PWFS UIF XIPMF OFUXPSL *OUVJUJWFMZ UIF HMPCBM JOnVFODF PG POF OPEF ƒ.u/ TIPVME CF SFMBUFE UP JUT JOnVFODF PO BMM UIF PUIFS OPEFT JO UIF OFUXPSL *G POF OPEF TUSPOHMZ JOnVFODFT NBOZ PUIFS OPEFT JUT HMPCBM JOnVFODF NJHIU CF BMTP TUSPOH ɩFSFGPSF UIF HMPCBM JOnVFODF PG B OPEF JT EFmOFE BT BO BHHSFHBUJPO PG JUT JOnVFODF PO UIF PUIFS OPEFT TQFDJmDBMMZ ƒ.u/ ıv.u/: D v X ɩF JOnVFODF TDPSFT ıv.u/ JODMVEF CPUI EJSFDU BOE JOEJSFDU JOnVFODFT $0/4&37"5*7& "/% /0/$0/4&37"5*7& 1301"("5*0/ *O UIJT TFDUJPO XF EFTDSJCF UXP UZQFT PG EJĊVTJPO QSPDFTTDPOTFSWBUJWF BOE OPODPOTFSWBUJWF EJĊVTJPO QSPDFTTFTCBTFE PO XIJDI XF QSPQPTF UXP LJOET PG NFUIPET UP QSPQBHBUF JOnVFODF PWFS UIF OFUXPSL BOE UP PCUBJO JOEJSFDU JOnVFODF TUSFOHUI .*/*/( 501*$-&7&- */'-6&/$& '30. )&5&30(&/&064 /&5803,4 'JSTU XF GPSNBMMZ EFmOF B QSPQBHBUJPO QSPDFTT PWFS B OFUXPSL %FmOJUJPO G <1SPQBHBUJPO 1SPDFTT>V " QSPQBHBUJPOV QSPDFTT PWFS B OFUXPSL JT EFmOFE BT Ft .w/ .R 0 / .R 0 / V G w B GVODUJPO f W C [f g j j ! C [f g j jg XIFSF JT UIF TFU PG OPEFT JO JT B V EJNFOTJPOBM WFDUPS XIJDI SFQSFTFOUT B XFJHIU EJTUSJCVUJPO PWFS UIF OPEFT JO UIF OFUXPSL t EFOPUFT QSPQBHBUJPO TUFQ ɩFSFGPSF JO B QSPQBHBUJPO QSPDFTT FBDI OPEF JO B OFUXPSL JT mSTU JOJUJBMJ[FE XJUI TPNF NBTT XIJDI JT EFOPUFE BT UIF XFJHIU PG UIF OPEF ɩFO WJB FBDI TUFQ PG QSPQBHBUJPO TPNF OPEFT USBOTGFS B QBSU PG UIF XFJHIUT UP UIFJS OFJHICPST ɩVT UISPVHI B tTUFQ QSPQBHBUJPO QSPDFTT B V V j jEJNFOTJPOBM OPOOFHBUJWF WFDUPS JT NBQQFE UP BOPUIFS j jEJNFOTJPOBM OPOOFHBUJWF WFDUPS t 1 *O QBSUJDVMBS XIFO D UIF QSPQBHBUJPO JT BUPNJD QSPQBHBUJPO $POTFSWBUJWF 1SPQBHBUJPO %FmOJUJPO F w .RC V <$POTFSWBUJWF 1SPQBHBUJPO> 'PS B QSPQBHBUJPO QSPDFTT JG 8 2 [ 0 / w 1 F .w/ 1 f g j j jj jj D jj jj JF JU QSFTFSWFT UIF TVN PG UIF FOUSJFT XF DBMM UIF QSPQBHBUJPO QSPDFTT DPOTFSWBUJWF QSPQBHBUJPO ɩFSFGPSF DPOTFSWBUJWF QSPQBHBUJPO TJNQMZ SFEJTUSJCVUFT UIF XFJHIUT BNPOH UIF OPEFT JO UIF OFUXPSL BOE LFFQT UIF TVN PG XFJHIUT DPOTUBOU ɩFSF BSF NBOZ DPOTFSWBUJWF QSPQBHBUJPO FY BNQMFT JO UIF SFBM XPSME 5BLF UIF DJSDVMBUJPO PG NPOFZ GPS FYBNQMF "U FBDI TUFQ PG QSPQBHBUJPO TPNF OPEFT USBOTGFS B GSBDUJPO PG UIFJS NPOFZ UP UIFJS OFJHICPST #VU UIF UPUBM NPOFZ JO UIF OFU XPSL EPFT OPU DIBOHF 5SBċD USBOTQPSUBUJPO BOE FOFSHZ DZDMF BSF BMTP DPOTFSWBUJWF QSPQBHBUJPOT BT UIF UPUBM USBċD PS FOFSHZ EPFT OPU DIBOHF XJUI UIF QSPQBHBUJPO QSPDFTT .BUIFNBUJDBMMZ SBOEPN XBML JT B DBOPOJDBM FYBNQMF PG DPOTFSWBUJWF QSPQBHBUJPO *O B SBO EPN XBML B QBSUJDMF TUBSUT UP MPDBUF PO B OPEF ɩFO BU FBDI TUFQ UIF QBSUJDMF TFMFDUT POF PG UIF PVUOFJHICPST BU SBOEPN BOE NPWFT UP UIBU OPEF " XFJHIU WFDUPS JT VTFE UP SFQSFTFOU UIF QSPC BCJMJUZ XJUI XIJDI UIF QBSUJDMF DBO CF GPVOE PO FBDI OPEF ɩVT UIF TVN PG UIF XFJHIUT FRVBMT UP POF "OE BGUFS JUFSBUJWF QSPQBHBUJPOT UIF QSPCBCJMJUJFT PG mOEJOH UIF QBSUJDMF PO UIF OPEFT DIBOHF CVU UIF TVN SFNBJOT UP CF POF BMM UIF UJNF 1BHF3BOL JT B DMBTTJDBM SBOEPN XBML NPEFM XIJDI JT SFQSFTFOUFE BT pr.w/ .1 ˇ/ w0 ˇ pr.w/ M; D $ # C # # M JT B USBOTJUJPO NBUSJY JO XIJDI UIF FMFNFOU M.a; b/ EFOPUFT UIF USBOTGFS QSPCBCJMJUZ GSPN OPEF a UP b ˇ JT B EBNQJOH GBDUPS XIJDI JT VTFE UP FOTVSF UIF TUBUJPOBSZ QSPCBCJMJUZ EJTUSJCVUJPO 1 ˇ PG UIF QSPQBHBUJPO $ JT UIF SFTUBSU QSPCBCJMJUZ XIJDI HJWFT UIF QSPCBCJMJUZ EJTUSJCVUJPO XIFO UIF SBOEPN XBML USBOTJUJPO SFTUBSUT w0 JT UIF JOJUJBM XFJHIU EJTUSJCVUJPO XIJDI JT VTVBMMZ TFU UP CF VOJGPSN WFDUPS 1FSTPOBMJ[FE 1BHF3BOL <> FYUFOET UIF NPEFM CZ TFUUJOH w0 UP CF B OPOVOJGPSN TUBSUJOH WFDUPS 40$*"- */'-6&/$& "/"-:4*4 $POTFSWBUJWF *OnVFODF 1SPQBHBUJPO 8F NPEFM UIF DPOTFSWBUJWF JOnVFODF QSPQBHBUJPO BT B QFS TPOBMJ[FE 1BHF3BOL JO B OFUXPSL BT &RVBUJPO ft .1 ˇ/ 0 ˇ ft 1 M: D $ # C # ! # ɩF QSPQBHBUJPO QSPCBCJMJUZ NBUSJY M DBO CF TFU JO WBSJPVT XBZT *G XF VTF EJSFDU JOnVFODF M.v; u/ ı0.u/ M.v; u/ 1 TUSFOHUI UP EFmOF UIF QSPQBHBUJPO QSPCBCJMJUZ JF D v UIFO u D *U JT FBTZ UP QSPWF UIBU UIF TVN PG JOnVFODF TUSFOHUI GSPN BMM UIF OPEFT PO POF OPEF v SFNBJOT UP CF ft P v 1 1 POF BGUFS JOnVFODF QSPQBHBUJPO JF jj jj D ɩVT &RVBUJPO EFmOFT B DPOTFSWBUJWF JOnVFODF QSPQBHBUJPO ɩJT DPOTFSWBUJWF JOnVFODF QSPQBHBUJPO QSPWJEFT B TUSBUFHZ GPS UIF DPNCJOBUJPO QSPDFTT JO UIF JUFSBUJWF QSPQBHBUJPO 'SPN &RVBUJPO JU JT FBTZ UP HFU UIBU t 1 ! ft .1 ˇ/ 0 .ˇi M i / 0 ˇt M t : D $ # # # C # # i 0 XD t t 0 M t "T UIF JOnVFODF WFDUPS PO MFOHUI QBUI JT D # t 1 ! ft .1 ˇ/ .ˇi i / ˇt t : D $ # # C # i 0 XD ɩVT UIF DPOTFSWBUJWF JOnVFODF QSPQBHBUJPO EFmOFE JO &RVBUJPO BTTJHOT EJĊFSFOU XFJHIUT UP UIF JOnVFODFT PO EJĊFSFOUMFOHUI QBUIT ˇ 0 ˇ 1 t ˇt JT B EBNQJOH GBDUPS JF Ä Ä ɩVT XIFO JODSFBTFT EFDSFBTFT XIJDI NBLFT UIF FĊFDU PG JOnVFODF PO MPOHFS QBUIT TNBMMFS /PODPOTFSWBUJWF 1SPQBHBUJPO %FmOJUJPO F w .RC V 'PS B QSPQBHBUJPO QSPDFTT JG 9 2 [ 0 / w 1 F .w/ 1 f g j j jj jj ¤ jj jj XF DBMM UIF QSPQBHBUJPO QSPDFTT OPODPOTFSWBUJWF QSPQBHBUJPO $PNQBSFE XJUI DPOTFSWBUJWF QSPQBHBUJPO OPODPOTFSWBUJWF QSPQBHBUJPO EPFT OPU LFFQ UIF TVN PG XFJHIUT DPOTUBOU ɩFSF BSF BMTP NBOZ OPODPOTFSWBUJWF QSPQBHBUJPO FYBNQMFT JO UIF SFBM XPSME 5BLF UIF TQSFBE PG B WJSVT GPS FYBNQMF 4VQQPTF B WJSVT JT QSPQBHBUJOH PWFS UIF TPDJBM OFU XPSL 8IFO POF JOGFDUFE OPEF JOGFDUT JUT OFJHICPST JU JT TUJMM JOGFDUFE ɩVT UIF UPUBM OVNCFS PG JOGFDUFE OPEFT JT JODSFBTFE XJUI UJNF ɩFSFGPSF UIF TQSFBE PG WJSVT JT B LJOE PG OPODPOTFSWBUJWF QSPDFTT #FTJEFT JOGPSNBUJPO EJĊVTJPO BOE PSBM BEWFSUJTJOH BSF BMTP OPODPOTFSWBUJWF QSPQBHB UJPOT BT UIF OVNCFS PG OPEFT XIJDI BDDFQU UIF JOGPSNBUJPO PS BEWFSUJTFNFOU JODSFBTFT XJUI QSPQ BHBUJPO TUFQ "MQIB$FOUSBMJUZ XIJDI XBT JOUSPEVDFE CZ #POBDJDI < > DBO CF VTFE UP NPEFM OPO DPOTFSWBUJWF QSPQBHBUJPO ɩF "MQIB$FOUSBMJUZ WFDUPS c.w/ JT EFmOFE BT UIF TPMVUJPO PG UIF GPM MPXJOH FRVBUJPO .*/*/( 501*$-&7&- */'-6&/$& '30. )&5&30(&/&064 /&5803,4 t t 1 c .w/ w0 ˇ c ! .w/ M; D C # # ˇ JT B EBNQJOH GBDUPS ɩF TUBSUJOH WFDUPS w0 JT VTVBMMZ TFU UP CF JOEFHSFF DFOUSBMJUZ BOE M VTFT UIF BEKBDFODZ NBUSJY1 ˇ< &1 M c.w/ w0 8IFO "1 XIFSF JT UIF MBSHFTU FJHFOWBMVF PG XF DBO HFU UIBU D # .I ˇM / 1 j Ij n $ ! XIFSF JT UIF JEFOUJUZ NBUSJY PG TJ[F 6TJOH UIF JEFOUJUZ 1 t t 1 .ˇ M / .I ˇ M/! I # D $ # $ t 1 XD XF DBO HFU 1 1 t t c.w/ w0 .I ˇ M/! w0 .ˇ M /: D # $ # D # # t 0 XD #FTJEFT "MQIB$FOUSBMJUZ ,BU[ TDPSF <> 4FOEFS3BOL <> BOE FJHFOWFDUPS DFOUSBMJUZ <> BSF PUIFS FYBNQMFT PG OPODPOTFSWBUJWF NBUIFNBUJDBM NFUSJDT 8F NPEFM UIF OPODPOTFSWBUJWF JOnVFODF QSPQBHBUJPO QSPDFTT JO UIF GPSN PG "MQIB $FOUSBMJUZ BT &RVBUJPO ft 0 ˇ ft 1 M: D C # ! # 'PS "MQIB$FOUSBMJUZ M JT VTVBMMZ TFU UP CF BEKBDFODZ NBUSJY )FSF XF BMTP VTF EJSFDU JOnVFODF M M.v; u/ ıv.u/ TUSFOHUI UP EFmOF UIF USBOTJUJPO NBUSJY JF D *U JT FBTZ UP QSPWF UIBU UIF TVN PG JOnVFODF TUSFOHUI GSPN BMM UIF OPEFT PO OPEF v JODSFBTFT XJUI OPODPOTFSWBUJWF QSPQBHBUJPO ft v 1 >1 TUFQ JF jj jj ɩVT &RVBUJPO EFmOFT B OPODPOTFSWBUJWF QSPQBHBUJPO GPS MPDBM JOnVFODF ɩJT OPODPOTFSWBUJWF JOnVFODF QSPQBHBUJPO QSPWJEFT BOPUIFS TUSBUFHZ GPS UIF DPNCJOBUJPO QSPDFTT JO UIF JUFSBUJWF QSPQBHBUJPO 'SPN &RVBUJPO XF DBO HFU t t ft 0 .ˇi M i / ˇi i : D # # D # i 0 i 0 XD XD ɩVT JU BTTJHOT EJĊFSFOU XFJHIUT UP UIF JOnVFODF TUSFOHUI PO EJĊFSFOUMFOHUI QBUIT )PX FWFS UIF XFJHIU BTTJHONFOU TUSBUFHZ JT EJĊFSFOU GSPN DPOTFSWBUJWF QSPQBHBUJPO SFGFSSJOH UP &RVB UJPO #PUI DPOTFSWBUJWF BOE OPODPOTFSWBUJWF JOnVFODF QSPQBHBUJPOT DPMMFDU BMM UIF DPOUSJCVUFT PG EJSFDU BOE JOEJSFDU JOnVFODF PO UIF QSPQBHBUJOH QBUIT "OE CPUI PG UIFN EFmOF B XFJHIU BTTJHONFOU TUSBUFHZ UP EJTUJOHVJTI UIF FĊFDU PG JOnVFODF PO EJĊFSFOUMFOHUI QBUIT ɩF NBKPS EJĊFSFODF CFUXFFO UIFTF UXP UZQFT PG NPEFMT JT UIBU DPOTFSWBUJWF QSPQBHBUJPO LFFQT UIF TVN PG JOnVFODF JO UIF XIPMF OFUXPSL DPOTUBOU XIJMF OPODPOTFSWBUJWF QSPQBHBUJPO EPFT OPU 40$*"- */'-6&/$& "/"-:4*4 *OUVJUJWFMZ JOEJSFDU JOnVFODF TUSFOHUI PO TIPSUFSQBUIT TIPVME CF NPSF SFMJBCMF TJODF UIFSF IBWF CFFO GFXFS QSPQBHBUJPO TUFQT ɩF NPSF JUFSBUJPO TUFQT UIF NPSF PVUTJEF JOGPSNBUJPO XJMM CF CSPVHIU ɩVT CPUI DPOTFSWBUJWF BOE OPODPOTFSWBUJWF QSPQBHBUJPOT VUJMJ[F B EBNQJOH GBDUPS ˇ t 0 ˇ 1 t ˇt UP QFOBMJ[F MBSHFS TUFQ QSPQBHBUJPOT "T Ä Ä XIFO JODSFBTFT EFDSFBTFT HSFBUMZ .t 1/ XIJDI NBLFT UIF FĊFDU PG JOnVFODF PO C MFOHUI QBUIT WFSZ TNBMM *O BOPUIFS XPSE XF EP OPU OFFE UP JUFSBUF JOnVFODF QSPQBHBUJPO GPS NBOZ UJNFT UP PCUBJO UIF mOBM JOEJSFDU JOnVFODF t ˇ 0 JF DBO CF TFU BT B TNBMM OVNCFS #FTJEFT XIFO D CPUI DPOTFSWBUJWF BOE OPODPOTFSWBUJWF QSPQBHBUJPOT POMZ VUJMJ[F EJSFDU JOnVFODF BOE JHOPSF UIF FĊFDU PG JOEJSFDU JOnVFODF 64&3 #&)"7*03 13&%*$5*0/ ɩF MFBSOFE JOnVFODF TUSFOHUI DBO CF VTFE UP IFMQ XJUI NBOZ BQQMJDBUJPOT )FSF XF JMMVTUSBUF POF BQQMJDBUJPO PO VTFS CFIBWJPS QSFEJDUJPO JF IPX UIF MFBSOFE JOnVFODF DBO IFMQ JNQSPWF UIF QFSGPSNBODF PG VTFS CFIBWJPS QSFEJDUJPO 8F FWBMVBUF PVS BQQSPBDI GPS VTFS CFIBWJPS QSFEJDUJPO PO 3FOSFO 5XJUUFS BOE %JHH ɩF VTFS CFIBWJPS JT EFmOFE BT POF UJNF DPOOFDUJPO CFUXFFO B VTFS BOE B EPDVNFOU 8F IFSF UBLF %JHH BT UIF FYBNQMF GPS FYQMBOBUJPO *OUVJUJWFMZ JG NPSF GSJFOET PG B VTFS EJH B TUPSZ UIFSF JT B MBSHFS QSPCBCJMJUZ UIBU UIF VTFS XJMM BMTP EJH JU ɩVT B WPUFCBTFE SFMBUJPOBM OFJHICPS DMBTTJmFS <> DBO CF VTFE BT B CBTFMJOF ɩFO XF VTF UIF JOnVFODF TUSFOHUI PCUBJOFE GSPN PVS BQQSPBDI UP EJTUJOHVJTI EJĊFSFOU GSJFOET XFJHIUT BOE FTUJNBUF UIF QSPCBCJMJUZ PG VTFST EJHHJOH TUPSJFT BT GPMMPXT 1 p.d u/ ıu.v/p.d v/ j D ıu.v/ j v v Nb.u/ 2X P XIFSF Nb.u/ EFOPUFT UIF GSJFOET PG u #FTJEFT UIF TJNJMBSJUZ CFUXFFO VTFST DBO BMTP CF VTFE UP EJTUJOHVJTI EJĊFSFOU GSJFOET XFJHIUT JO UIF BCPWF JOUVJUJWF NFUIPE GPS QSFEJDUJPO ɩVT UIF QSFEJDUJPO QSPCBCJMJUZ JT FTUJNBUFE BT &RVBUJPO GPS DPNQBSJTPO XIFSF UIF TJNJMBSJUZ CFUXFFO VTFST s.v; u/ JT DBMDVMBUFE BT UIF &VDMJEFBO EJTUBODF PG VTFS EJTUSJCVUJPOT PWFS UPQJDT 1 p.d u/ s.v; u/p.d v/: j D s.v; u/ j v v Nb.u/ 2X P 8F XJMM UFTU UIF VTFS CFIBWJPS QSFEJDUJPO QFSGPSNBODF CBTFE PO UIF BCPWF UISFF NFUIPET JO UIF GPMMPXJOH FYQFSJNFOUT BOE EFNPOTUSBUF UIF FĊFDU PG JOnVFODF TUSFOHUI PCUBJOFE GSPN CPUI DPOTFSWBUJWF BOE OPODPOTFSWBUJWF JOnVFODF QSPQBHBUJPOT GPS TPDJBM OFUXPSL BQQMJDBUJPOT .*/*/( 501*$-&7&- */'-6&/$& '30. )&5&30(&/&064 /&5803,4 &7"-6"5*0/ *O UIJT TFDUJPO XF QSFTFOU WBSJPVT FYQFSJNFOUT UP FWBMVBUF UIF FċDJFODZ BOE FĊFDUJWFOFTT PG UIF QSPQPTFE BQQSPBDI ɩF EBUB TFUT BOE DPEFT BSF QVCMJDMZ BWBJMBCMFŊ &YQFSJNFOUBM 4FUVQ %BUB 4FUT 8F QSFQBSF GPVS EJĊFSFOU UZQFT PG IFUFSPHFOFPVT OFUXPSLT GPS PVS FYQFSJNFOUT JO DMVEJOH 3FOSFO 5XJUUFS %JHH BOE $JUBUJPO OFUXPSLT 3FOSFO JT B WFSZ QPQVMBS 'BDF#PPLTUZMF TPDJBM XFCTJUF JO $IJOB PO XIJDI VTFST FTQFDJBMMZ UIF VOEFSHSBEVBUF BOE HSBEVBUF TUVEFOUT DPO OFDU XJUI UIFJS DMBTTNBUFT PS GSJFOET BOE TIBSF JOUFSFTUJOH XFC DPOUFOU 5XJUUFS JT B NJDSPCMPH XFCTJUF PO XIJDI VTFST DBO QVCMJTI CMPHT BOE SFUXFFU GSJFOET CMPHT %JHH JT B EJĊFSFOU UZQF PG TPDJBM XFCTJUF PO XIJDI VTFST DBO TVCNJU EJH BOE DPNNFOU PO TUPSJFT 6TFST BMTP IBWF MJOLT UP UIFJS GSJFOET XIJDI JOEJDBUF UIFJS SFMBUJPOTIJQ 8F DPMMFDU VTFS SFMBUJPOTIJQ BOE EPDVNFOU DPOUFOU GSPN UIFTF XFCTJUFT t 3FOSFO TPDJBM OFUXPSL ɩF EBUB DPOUBJOT VTFST BOE UIF XFC DPOUFOU TIBSFE CZ UIFTF VTFST JO POF NPOUI XIJDI JODMVEFT BCPVU EPDVNFOUT BOE XPSET t 5XJUUFS TPDJBM OFUXPSL ɩF EBUBTFU JODMVEFT BCPVU NJMMJPOT PG NJDSPCMPHT SFMBUFE UP BCPVU VTFST BOE LFZXPSET SFNPWJOH UIF TUPQ XPSET BOE UIF JOGSFRVFOU XPSET t %JHH TPDJBM OFUXPSL ɩF EBUB DPOUBJOT BCPVU NJMMJPO TUPSJFT SFMBUFE UP VTFST BOE LFZXPSET JO XIJDI XF BJN UP NJOF VTFS JOnVFODF BT XFMM t $JUBUJPO OFUXPSL 8F DSBXMFE UIF DJUBUJPO EBUB PG BCPVU EPDVNFOUT GSPN UIF *O UFSOFU PO TFWFSBM TQFDJmD UPQJDT FH iUPQJD NPEFMT w iTFOUJNFOU BOBMZTJT w iBTTPDJBUJPO SVMF NJOJOH w iQSJWBDZ TFDVSJUZ w FUD #FTJEFT UIF QVCMJD DJUBUJPO EBUB TFU $PSB JT BMTP VTFE JO PVS FYQFSJNFOUT 8F BQQMZ PVS NPEFM UP UIF BCPWF GPVS EBUB TFUT ɩF BMHPSJUINT BSF JNQMFNFOUFE JO $ BOE SVO PO BO *OUFM $PSF 5 BOE B QSPDFTTPS XJUI (# %%3 3". ɩF QBSBNFUFST PG UIF NPEFM XJMM CF EJTDVTTFE JO UIF GPMMPXJOH TVCTFDUJPOT &WBMVBUJPO "TQFDUT 8F FWBMVBUF PVS NFUIPE PO UIF GPMMPXJOH UISFF BTQFDUT t *OnVFODF TUSFOHUI QSFEJDUJPO "T JU JT NPSF JOUVJUJWF BOE FBTJFS GPS QFPQMF UP EJTUJOHVJTI UIF JOnVFODF TUSFOHUI JO DJUBUJPO OFUXPSLT XF NBOVBMMZ MBCFM UIF DJUBUJPO EBUB BOE UIFO UFTU UIF JOnVFODF QSFEJDUJPO QFSGPSNBODF JO JU 8F DPNQBSF UIF SFTVMUT PG PVS BQQSPBDI XJUI QSFWJPVT XPSL <> UP EFNPOTUSBUF PVS NPEFMT CFUUFS QFSGPSNBODF JO UFSNT PG JOnVFODF QSFEJDUJPO t 6TFS CFIBWJPS QSFEJDUJPO 8F VTF UIF EFSJWFE JOnVFODF TUSFOHUI UP IFMQ QSFEJDU VTFS CFIBW JPST BOE DPNQBSF UIF QSFEJDUJPO QFSGPSNBODF XJUI UIBU PG CBTFMJOF BT XFMM BT UIF NFUIPE Ŋ?iiT,ff `M2iKBM2`XQ`;f?2i2`BM7 40$*"- */'-6&/$& "/"-:4*4 CBTFE PO VTFS TJNJMBSJUZ BT EFTDSJCFE JO 4FDUJPO ɩF SFTVMUT EFNPOTUSBUF IPX UIF RVBOUJUBUJWF NFBTVSFNFOU PG UIF JOnVFODF DBO CFOFmU TPDJBM OFUXPSL BQQMJDBUJPOT t 5PQJDMFWFM JOnVFODF DBTF TUVEZ 8F TIPX TFWFSBM DBTF TUVEJFT UP EFNPOTUSBUF DPODSFUF JOnVFODF XFJHIUT CFUXFFO VTFST BOE TIPX IPX FĊFDUJWFMZ PVS NFUIPE DBO JEFOUJGZ UPQJD MFWFM JOnVFODF *O QBSUJDVMBS XF TUVEZ UIF HMPCBM JOnVFODF PG BVUIPST JO DJUBUJPO OFUXPSLT UP EFNPOTUSBUF TFNBOUJD NFBOJOH PG UPQJDMFWFM JOnVFODF "OE XF DPNQBSF UIF SFTVMUT XJUI UIBU PG QSFWJPVT XPSL <> XIJDI DBO BMTP CF VTFE UP NJOF UPQJDMFWFM JOnVFODF UP EFNPO TUSBUF UIF CFUUFS QFSGPSNBODF PG PVS BQQSPBDI 3FTVMUT *OnVFODF 4USFOHUI 1SFEJDUJPO *O %JFU[ FU BM <> SFTFBSDIFST FWBMVBUFE UIF EPDVNFOU JOnVFODF QSFEJDUJPO QFSGPSNBODF JO B NBOVBMMZ MBCFMFE EBUB TFU 8F VTF UIF TBNF EBUB GSPN UIF BVUIPST BOE BMTP UFTU UIF JOnVFODF QSFEJDUJPO QFSGPSNBODF PG PVS NPEFM JO JU )PXFWFS UIF EBUB TFU XIJDI POMZ DPOUBJOT DJUJOH EPDVNFOUT BOE EPDVNFOUT JO BMM JT TP TNBMM UIBU UIF SFTVMUT DPVME CF BEIPD TPNFUJNFT ɩFSFGPSF CFTJEFT VTJOH UIJT EBUB XF BMTP NBOVBMMZ MBCFM EPDVNFOU JOnVFODF TUSFOHUI JO B MBSHFS EBUB TFU XJUI BCPVU EPDVNFOUT 8F DMBTTJGZ UIF JOnVFODF TUSFOHUI JOUP UISFF MFWFMT 4JNJMBS UP %JFU[ FU BM <> XF VTF UIF RVBMJUZ NFBTVSF BWFSBHFE "6$ "SFB 6OEFS UIF 30$ $VSWF WBMVFT GPS UIF EFDJTJPO CPVOEBSJFT i WT w BOE i WT w GPS FBDI DJUJOH EPDVNFOU UP FWBMVBUF UIF QSFEJDUJPO QFSGPSNBODF 'JHVSF TIPXT UIF DPNQBSBUJWF SFTVMUT JO UIFTF UXP EBUB TFUT XIFSF %BUB JT UIF TNBMM EBUB TFU PCUBJOFE GSPN %JFU[ FU BM <> XIJMF %BUB JT PVS MBSHFS MBCFMFE EBUB TFU M1 BOE M2 BSF VTFE UP EFOPUF PVS NPEFM BOE UIF NPEFM PG %JFU[ FU BM <> SFTQFDUJWFMZ "OE XF VTF UIF SFBM BOE EBTI MJOFT UP EJTUJOHVJTI UIF SFTVMUT PG UIFTF UXP NPEFMT JO UIF mHVSF 8F DBMDVMBUF BMM UIF "6$ WBMVFT XJUI UIF OVNCFS PG UPQJDT DIBOHJOH GSPN UP ɩVT UIJT mHVSF EFNPOTUSBUFT UIBU JO UIF TNBMM EBUB TFU PVS NPEFM DBO BDIJFWF BT HPPE QSFEJDUJPO QFSGPSNBODF BT UIF XPSL PG %JFU[ FU BM <> XIJMF JO UIF MBSHFS EBUB TFU PVS QSFEJDUJPO QFSGPSNBODF JT CFUUFS UIBO UIFJST 'VSUIFSNPSF XF DPNQBSF UIF JOnVFODF QSFEJDUJPO QFSGPSNBODF CFGPSF BOE BGUFS JOnVFODF QSPQBHBUJPO JO PVS MBCFMFE EBUB TFU ɩF SFTVMUT QSPWF UIBU UIF JOnVFODF QSFEJDUJPO QFSGPSNBODF JT FOIBODFE BGUFS JOnVFODF QSPQBHBUJPO "6$ WBMVFT BSF FOIBODFE GSPN UP P .PSFPWFS UIF JOnVFODF QSFEJDUJPO QFSGPSNBODF JT SPCVTU UP UIF QBSBNFUFST t BOE ˇ *O QBSUJDVMBS XIFO t DIBOHFT UIF QFSGPSNBODF DIBOHFT MJUUMF XIJDI JT DPOTJTUFOU UP UIF PCTFSWBUJPO JO 'JHVSF *U NFBOT UIBU JOnVFODF EPFT QSPQBHBUF PWFS UIF OFUXPSL CVU UIF FĊFDU PG QSPQBHBUJPO JT SFEVDFE XJUI QSPQBHBUJPO TUFQ 6TFS #FIBWJPS 1SFEJDUJPO 8F FNQMPZ PVS NPEFM UP EJTDPWFS UIF DPODSFUF JOnVFODF TUSFOHUI CFUXFFO UIF VTFST JO 3FOSFO TPDJBM OFUXPSLT ɩFO XF BQQMZ UIF MFBSOFE JOnVFODF TUSFOHUI UP VTFS CFIBWJPS QSFEJDUJPO BT EFTDSJCFE JO 4FDUJPO *O QBSUJDVMBS UIF QBSBNFUFST XIJDI BSF UIF EBNQJOH GBDUPS ˇ BOE JUFSBUJPO TUFQ t GPS CPUI DPOTFSWBUJWF BOE OPODPOTFSWBUJWF JOnVFODF QSPQBHBUJPOT BSF WBSJFE UP UFTU UIF FĊFDU PG JOnVFODF QSPQBHBUJPO QSPDFTT "CPVU UVQMFT .*/*/( 501*$-&7&- */'-6&/$& '30. )&5&30(&/&064 /&5803,4 'JHVSF *OnVFODF QSFEJDUJPO QFSGPSNBODF DPNQBSJTPO 5BCMF $POTFSWBUJWF BOE OPODPOTFSWBUJWF JOnVFODF QSPQBHBUJPO FĊFDU PO VTFS CFIBWJPS QSFEJD UJPO method influence propagation baseline D β =0.3 β =0.5 β =0.8 p steps CIP NCIP CIP NCIP CIP NCIP t =1 0.168 0.168 0.168 0.168 0.172 0.168 average t =5 0.168 0.168 0.170 0.170 0.180 0.175 0.101 0.160 t =10 0.168 0.168 0.170 0.170 0.180 0.178 t =1 0.044 0.045 0.041 0.044 0.039 0.042 variance t =5 0.044 0.045 0.042 0.043 0.041 0.041 0.011 0.048 t =10 0.044 0.045 0.043 0.042 0.041 0.041 JO 3FOSFO EBUB TFU BSF VTFE BT UFTUJOH TBNQMFT &BDI UVQMF SFQSFTFOUT UIBU B VTFS TIBSFT B XFC EPDVNFOU XIPTF QSPCBCJMJUZ JT FTUJNBUFE BT &RVBUJPO ɩF BWFSBHF BOE WBSJBODF WBMVFT PG UIF QSFEJDUFE QSPCBCJMJUJFT GPS BMM UIF TBNQMFT BSF DBMDV MBUFE BOE TIPXO JO 5BCMF XIFSF %* EFOPUFT EJSFDU JOnVFODF $*1 BOE /$*1 EFOPUF DPOTFSWB UJWF BOE OPODPOTFSWBUJWF JOnVFODF QSPQBHBUJPOT SFTQFDUJWFMZ ɩF SFTVMUT EFNPOTUSBUF UIBU VTJOH JOnVFODF FTQFDJBMMZ UIF QSPQBHBUFE JOnVFODF DBO HSFBUMZ JNQSPWF UIF QSFEJDUFE QSPCBCJMJUJFT #VU UIF QBSBNFUFST t BOE ˇ BT XFMM BT UIF QSPQBHBUJPO NFDIBOJTN EP OPU BĊFDU UIF QSPCBCJMJUJFT B MPU ɩFO HJWFO B UISFTIPME XF DBMDVMBUF UIF QSFEJDUJPO QSFDJTJPO XIJDI NFBOT IPX NBOZ UFTU JOH TBNQMFT QSPCBCJMJUJFT BSF MBSHFS UIBO UIF UISFTIPME 'JHVSF TIPXT GPVS DVSWFT PG QSFEJD UJPO QSFDJTJPO DIBOHJOH XJUI UIF UISFTIPME JO 3FOSFO EBUB TFU XIJDI JOEJDBUF UIF QFSGPSNBODF PG CBTFMJOF VTJOH EJSFDU JOnVFODF XJUIPVU JOnVFODF QSPQBHBUJPO DPOTFSWBUJWF BOE OPODPOTFSWBUJWF ˇ 0:8; t 5 JOnVFODF QSPQBHBUJPOT XJUI QBSBNFUFS D D SFTQFDUJWFMZ ɩF SFTVMUT EFNPOTUSBUF UIBU JOnVFODFCBTFE CFIBWJPS QSFEJDUJPO BQQSPBDI PVUQFSGPSNT UIF CBTFMJOF ɩVT JU QSPWFT UIBU UIF 40$*"- */'-6&/$& "/"-:4*4 0.6 baseline 0.5 no propagation conservative propagation 0.4 non−conservative propagation 0.3 Precision 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 threshold 'JHVSF 6TFS CFIBWJPS QSFEJDUJPO QSFDJTJPO PO 3FOSFO OFUXPSL 0.9 0.8 indirect influence similarity 0.7 baseline 0.6 direct influence 0.5 0.4 Precision 0.3 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 threshold 'JHVSF 6TFS CFIBWJPS QSFEJDUJPO QSFDJTJPO PO %JHH OFUXPSL JOnVFODF PCUBJOFE GSPN PVS NPEFM CFOFmUT UIF VTFS CFIBWJPS QSFEJDUJPO HSFBUMZ .PSFPWFS CPUI DPOTFSWBUJWF BOE OPODPOTFSWBUJWF JOnVFODF QSPQBHBUJPOT JNQSPWF UIF QSFEJDUJPO QSFDJTJPO BOE BMNPTU BDIJFWF UIF TBNF QFSGPSNBODF #FTJEFT XF BQQMZ PVS NPEFM UP UIF BQQMJDBUJPO PG VTFS CFIBWJPS QSFEJDBUJPO JO 5XJUUFS BOE %JHH TPDJBM OFUXPSLT *O UIJT FYQFSJNFOU XF FNQMPZ OPODPOTFSWBUJWF JOnVFODF QSPQBHBUJPO t 5; ˇ 0:8 XJUI D D UP PCUBJO JOEJSFDU JOnVFODF 8F SBOEPNMZ TFMFDU BCPVU UVQMFT GSPN %JHH BOE 5XJUUFS EBUB TFUT BT UFTUJOH TBNQMFT BOE FTUJNBUF UIFJS QSPCBCJMJUJFT 5BCMF TIPXT UIF BWFSBHF BOE WBSJBODF WBMVFT PG UIF QSFEJDUFE QSPCBCJMJUJFT GPS BMM UIF TBNQMFT ɩF QSFEJDUJPO QSFDJTJPO DVSWFT GPS UIFTF UXP EBUB TFUT BSF TIPXO JO 'JHVSFT BOE SFTQFDUJWFMZ ɩF SFTVMUT EFNPOTUSBUF UIBU JOnVFODFCBTFE CFIBWJPS QSFEJDUJPO BQQSPBDI PVUQFSGPSNT UIF CBTFMJOF BOE UIF TJNJMBSJUZCBTFE NFUIPE *O QBSUJDVMBS JU TIPXT UIBU JOnVFODF QSPQBHBUJPO QSPDFTT FOIBODFT UIF VTFS CFIBWJPS QSFEJDUJPO QFSGPSNBODF JO %JHH TPDJBM OFUXPSL CVU JU UBLFT MJUUMF FĊFDU JO 5XJUUFS TPDJBM OFUXPSL 'VSUIFSNPSF DPNQBSJOH UIFTF UXP mHVSFT XF DBO HFU UIBU UIF FĊFDU PG JOnVFODF JO %JHH TPDJBM OFUXPSL JT MBSHFS UIBO UIBU JO 5XJUUFS TPDJBM OFUXPSL ɩF DPODMVTJPO JT DPOTJTUFOU UP UIF PCTFSWBUJPO JO 'JHVSF .*/*/( 501*$-&7&- */'-6&/$& '30. )&5&30(&/&064 /&5803,4 0.7 indirect influence 0.6 similarity baseline 0.5 direct influence 0.4 0.3 Precision 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 threshold 'JHVSF 6TFS CFIBWJPS QSFEJDUJPO QSFDJTJPO PO 5XJUUFS OFUXPSL 5BCMF #FIBWJPS QSFEJDUJPO QSPCBCJMJUZ Digg Social Network method baseline similarity DI NCIF p average 0.112 0.121 0.366 0.405 variance 0.006 0.008 0.075 0.048 Twitter Social Network method baseline similarity DI NCIF p average 0.215 0.222 0.319 0.310 variance 0.078 0.089 0.129 0.136 5PQJDMFWFM *OnVFODF $BTF 4UVEJFT $BTF 4UVEZ 5PQJDMFWFM JOnVFODF HSBQI 8F BQQMZ PVS NPEFM UP UIF DJUBUJPO OFUXPSL XIJDI XF DSBXMFE GSPN UIF *OUFSOFU BOE TFU UIF OVNCFS PG UPQJDT UP CF FNQJSJDBMMZ 'JHVSF EFNPOTUSBUFT UIF JOnVFODF SFMBUJPOTIJQ CFUXFFO UIF QBQFST PO UIF UPQJD iTUBUJTUJDBM UPQJD NPE FMTw ɩF DPMPS CBST TIPX UIF UPQJD EJTUSJCVUJPOT PG UIFTF EPDVNFOUT *O PSEFS UP TIPX UIF NBKPS JOnVFODJOH OPEFT DMFBSMZ XF SBOL UIF JOnVFODJOH OPEFT BDDPSEJOH UP FBDI JOnVFODFE OPEF CBTFE PO UIF JOnVFODF TUSFOHUI BOE POMZ EJTQMBZ UIF UPQ NPTU JOnVFODJOH POFT JO UIJT mHVSF ɩVT XF DBO HFU UIBU UIF UPQ NPTU JOnVFODJOH EPDVNFOUT PO EPDVNFOU i-%"w BSF i1-4"w BOE iWBSJ BUJPOBM JOGFSFODFw 'VSUIFSNPSF UIF SFTVMUT EFNPOTUSBUF UIBU UIFSF BSF NBOZ EPDVNFOUT XIJDI BSF NPTU JOnVFODFE CZ i-%" w FH iUIF BVUIPSUPQJD NPEFM w iDPSSFMBUFE UPQJD NPEFM w iEZ OBNJD UPQJD NPEFM w FUD #FTJEFT UIF JOnVFODF GSPN i-%" w TUSPOH JOnVFODFT BMTP FYJTU BNPOH UIFTF EPDVNFOUT FH iBVUIPSUPQJD NPEFMw JOnVFODFT iBVUIPSSFDJQJFOUNPEFMw TUSPOHMZ XIJMF iDPSSFMBUFE UPQJD NPEFMw JOnVFODFT iEZOBNJD UPQJD NPEFMw B MPU 40$*"- */'-6&/$& "/"-:4*4 'JHVSF %PDVNFOU JOnVFODF DBTF TUVEZ .*/*/( 501*$-&7&- */'-6&/$& '30. )&5&30(&/&064 /&5803,4 'JHVSF "VUIPS JOnVFODF DBTF TUVEZ 'JHVSF BMTP TIPXT UIF DPOOFDUJPOT CFUXFFO BVUIPST BOE EPDVNFOUT CZ EBTI MJOFT ɩF JOnVFODFT CFUXFFO UIFTF BVUIPST BSF WJTVBMJ[FE JO 'JHVSF 8F POMZ ESBX UIF MJOFT XIFO UIF QPJOUJOH OPEFT BSF UIF UPQ mWF NPTU JOnVFODJOH BVUIPST PO UIF QPJOUFE OPEFT ɩF UIJDLOFTT PG UIF MJOFT JOEJDBUFT UIF JOnVFODF TUSFOHUI 'SPN UIF SFTVMUT XF DBO HFU TPNF NFBOJOHGVM DPODMVTJPOT 'PS FYBNQMF +PSEBO JT POF PG UIF NPTU JOnVFOUJBM SFTFBSDIFST UP #MFJ "MUIPVHI i1-4"w TUSPOHMZ JOnVFODFT i-%"w BT 'JHVSF TIPXT )PGNBOO EPFT OPU IBWF B HSFBU JOnVFODF PO #MFJ ɩF SFBTPO JT UIBU UIF BSFB PG )PGNBOO WBSJFT GSPN UIF BSFB PG #MFJ UIJT DBO CF PCTFSWFE GSPN UIF UPQJD EJTUSJCVUJPOT SFQSFTFOUFE CZ DPMPSFE CBST BOE GVSUIFSNPSF #MFJ POMZ DJUFE GFX EPDVNFOUT PG )PGNBOO JF DPSSFMBUJPO WBMVF JT TNBMM 0UIFS JOUFSFTUJOH SFTVMUT BSF BMTP PCUBJOFE FH UIF JOnVFODF PG #MFJ PO -BĊFSUZ JT MBSHFS UIBO UIF JOnVFODF PG -BĊFSUZ PO #MFJ #FTJEFT UIF TFMGMPPQ MJOFT XIJDI JOEJDBUF UIF TFMGJOnVFODF TIPX +PSEBO BOE #MFJ JOnVFODF UIFNTFMWFT HSFBUMZ 5BCMF "VUIPS SBOLJOH PO iTUBUJTUJDBM UPQJD NPEFMTw Indirect Influence Direct Influence Pagerank t =1 t =5 TM Cover D Blei D Blei M Jordan A McCallum A McCallum A McCallum D Blei D Blei TM Cover M Jordan J Lafferty M Jordan M Jordan TM Cover A McCallum P Kantor P Kantor P Kantor Z Ghahramani $BTF 4UVEZ 5PQJDMFWFM HMPCBM JOnVFODF JMMVTUSBUJPO 5BCMF TIPXT BO FYBNQMF PG BVUIPS SBOLJOH CZ FTUJNBUFE HMPCBM JOnVFODF PO iTUBUJTUJDBM UPQJD NPEFMTw t EFOPUFT UIF OVNCFS PG QSPQ 40$*"- */'-6&/$& "/"-:4*4 BHBUJPO TUFQT ɩF SFTVMUT BSF WFSZ NFBOJOHGVM *G POF OPEF IBT B IJHI SFQVUBUJPO PWFS UIF XIPMF OFUXPSL JU DBO CF USFBUFE BT B LFZ OPEF XIJDI JT WFSZ JOnVFOUJBM PWFS UIF XIPMF OFUXPSL *O BO PUIFS XPSE BVUIPSJUZ PG POF OPEF DBO BMTP CF VTFE UP SFQSFTFOU JUT HMPCBM JOnVFODF GSPN TPNF QPJOU PG WJFX ɩFSFGPSF XF DBO FNQMPZ 1BHF3BOL < > PWFS UPQJDMFWFM OFUXPSLT UP FTUJ NBUF UIF OPEFT HMPCBM JOnVFODF PO POF UPQJD ɩF BVUIPS SBOLJOH CBTFE PO UIF BVUIPSJUZ GSPN 1BHF3BOL JT BMTP JMMVTUSBUFE 8F DBMDVMBUF UIF DPSSFMBUJPO DPFċDJFOUT CFUXFFO UIF HMPCBM JOnV FODF WBMVFT FTUJNBUFE JO UIF UXP XBZT XIJDI SBOHFT GSPN o XIFO UIF OVNCFS PG UPQJDT BOE JUFSBUJPO DIBOHF *U QSPWFT UIBU FTUJNBUJOH HMPCBM JOnVFODF CBTFE PO PVS GSBNFXPSL DBO HFU IJHIMZDPSSFMBUFE SFTVMUT XJUI 1BHF3BOL BVUIPSJUZ ɩVT UP TPNF FYUFOU JU EFNPOTUSBUFT UIBU UIF JOnVFODF EJTDPWFSFE CZ PVS NPEFM JT DPOTJTUFOU UP UIF HMPCBM DIBSBDUFSJTUJDT PG UIF XIPMF OFUXPSL TUSVDUVSF 5BCMF *OnVFODF BHHSFHBUJPO WBMVFT PO UPQJDT Topic OODB IR DM DBP Maximal value 2.525 2.333 3.877 3.607 Minimal value 0.0005 0.001 0.0006 0.0009 Average value 0.078 0.091 0.095 0.087 D DeWitt 1.487 0.181 1.087 3.607 M Stonebraker 2.525 0.632 0.481 2.851 C Faloutsos 0.357 0.242 1.571 1.187 W Bruce 0.538 2.333 0.172 0.483 R Agrawal 0.518 0.189 3.877 0.600 J Han 0.666 0.138 2.029 0.240 *O PSEFS UP TIPX UIF JOnVFODF SFTVMUT JO NPSF HFOFSBM BSFBT XF TFMFDU mWF DBUFHPSJFT PG EPDVNFOUT JO $PSB EBUB BOE TFU UIF OVNCFS PG UPQJDT UP mWF 'JWF NFBOJOHGVM UPQJDT BDDPSEJOH UP UIF mWF DBUFHPSJFT EBUB NJOJOH i%.w JOGPSNBUJPO SFUSJFWBM i*3w OBUVSBM MBOHVBHF QSPDFTTJOH i/-1w PCKFDUPSJFOUFE EBUBCBTF i00%#w BOE EBUBCBTF QFSGPSNBODF i%#1w BSF PCUBJOFE 'JHVSF TIPXT TFWFSBM GBNPVT BVUIPST FTUJNBUFE HMPCBM JOnVFODF EJTUSJCVUJPOT PO UIF mWF UPQJDT ɩF SFTVMUT BSF WFSZ UFMMJOH 'PS FYBNQMF 8 #SVDF JT NPTU JOnVFOUJBM PO UPQJD i*3 w XIJMF 3 "HSBXBM BOE + )BO BSF NPTU JOnVFOUJBM PO UPQJD i%.w *U JT JOUFSFTUJOH UP mOE UIBU $ 'BMPVTUTPT JT JOnVFOUJBM PO CPUI UPQJD i%.w BOE UPQJD i%#1 w XIJDI JT DPOTJTUFOU UP UIF SFBM TJUVBUJPO #FTJEFT UIF UXP UPQJDT SFMBUFE UP EBUBCBTF % %F8JUU JT BMTP WFSZ JOnVFOUJBM PO UPQJD i%.w ɩF SFBTPO TIPVME CF UIBU UIF BSFB i%.w EFWFMPQT GSPN EBUBCBTF 'VSUIFSNPSF 5BCMF TIPXT UIF NBYJNBM NJOJNBM BOE BWFSBHF WBMVFT PG UIF FTUJNBUFE HMPCBM JOnVFODF JO UIF XIPMF OFUXPSL XSU FBDI UPQJD XIJDI EFNPOTUSBUFT UIBU UIFTF BVUIPST BMNPTU IBWF UIF MBSHFTU WBMVFT JO UIFJS EPNBJOT ɩVT JU QSPWFT UIF WBMJEJUZ PG UIF XBZ PG HMPCBM JOnVFODF FTUJNBUJPO $BTF 4UVEZ 5PQJDMFWFM JOnVFODF DPNQBSJTPO 8PSL <> BMTP QSPQPTFE B NFUIPE UP EJT DPWFS UPQJDMFWFM JOnVFODF 8F DPNQBSF UIF BVUIPS JOnVFODF SFTVMUT PCUBJOFE CZ PVS NPEFM M1 XJUI UIF SFTVMUT CZ UIF NPEFM JO <> M3 "T TPNFUJNFT JU JT IBSE UP MBCFM UIF BVUIPS JOnVFODF .*/*/( 501*$-&7&- */'-6&/$& '30. )&5&30(&/&064 /&5803,4 5BCMF *OnVFODJOH BVUIPS SBOLJOH XSU TFWFSBM BVUIPST D Blei A McCallum T Griffiths M1 M3 M1 M3 M1 M3 H Attias D Blei A McCallum A McCallum T Hofmann T Griffiths D Blei M Stephens D Blei D Kauchak M Steyvers R Kass M Jordan J Pritchard Andrew Ng E Stephen T Griffiths N Chater K Nigam P Donnelly T Griffiths R Madsen T Minka D Lawson T Jaakkola C Meghini M Jordan C Elkan A McCallum H Neville OODB IR DM DBP NLP s o er ruce ts ak B J Han ewitt r D eb W D n to CFalou R Agrawal S M 'JHVSF &TUJNBUFE HMPCBM JOnVFODF EJTUSJCVUJPO PO UPQJDT TUSFOHUI XF POMZ TIPX UIF UPQ mWF NPTU JOnVFODJOH BVUIPST PO TPNF XFMMLOPXO SFTFBSDIFST #MFJ .D$BMMVN BOE (SJċUIT PCUBJOFE CZ UIFTF UXP NPEFMT JO 5BCMF ɩF SFTVMUT EFNPOTUSBUF UIBU PVS NPEFM DBO HFU NFBOJOHGVM SFTVMUT CVU M3DBOOPU 'PS FYBNQMF PVS NPEFM EJTDPWFST UIBU +PSEBO #MFJ BOE )PGNBOO BSF POF PG UIF NPTU JOnVFOUJBM SFTFBSDIFST GPS #MFJ .D$BMMVN BOE (SJċUIT SFTQFDUJWFMZ #VU M3 EPFT OPU HFU UIFTF SFTVMUT "T M3 POMZ VTFT UIF MJOL JOGPSNBUJPO PG BVUIPS DJUBUJPO JU XJMM MPTF UIF JOGPSNBUJPO PG SFMBUJPOTIJQT CFUXFFO BVUIPST BOE EPDVNFOUT .PSFPWFS UIF BTTVNQUJPO VTFE JO 5BOH FU BM <> XIJDI TUBUFT UIBU UIF OPEF XJMM CF NPSF JOnVFOUJBM JG JU IBT B HSFBU TFMGJOnVFODF NBLFT FBDI QFSTPO NPTU JOnVFOUJBM PO IJNTFMG 4JNJMBS UP PVS NPEFM M3 DBO BMTP HFU UIF JOnVFODF EJTUSJCVUJPOT PO UPQJDT CZ JOQVUUJOH UIF OPEFT UPQJD NJYUVSFT #VU UIF EJĊFSFODF JT UIBU UIF UPQJD JOGPSNBUJPO JT VTFE BT BO JOQVU QSJPS JOTUFBE PG BO JOUFHSBUFE QBSBNFUFS JO UIF NFUIPE M3 XIJMF PVS NFUIPE DBO PCUBJO UPQJDT TJNVMUBOFPVTMZ 'JHVSF TIPXT BO FYBNQMF PG UIF JOnVFODF GSPN +PSEBO UP #MFJ BOE DPNQBSFT UIF UPQJD EJTUSJCVUJPOT PG JOnVFODF PCUBJOFE CZ PVS NPEFM BOE M3 SFTQFDUJWFMZ 'JSTU +PSEBO BOE #MFJT EJTUSJCVUJPOT PO UPQJDT BSF JMMVTUSBUFE XIJDI JOEJDBUF UIBU CPUI PG UIFN NBJOMZ XPSL PO 5PQJD ɩFO XF DBO TFF UIBU UIF JOnVFODF PCUBJOFE CZ PVS NPEFM IBT UIF MBSHFTU TUSFOHUI PO 5PQJD CVU UIF JOnVFODF EJTUSJCVUJPO GSPN M3 JT nBU GSPN XIJDI JU JT OPU PCWJPVT UP UFMM UIF 40$*"- */'-6&/$& "/"-:4*4 JOnVFODF TFNBOUJD NFBOJOH ɩVT JU JT QSPWFE UIBU PVS NPEFM DBO PCUBJO NPSF NFBOJOHGVM UPQJD EJTUSJCVUJPOT PG JOnVFODF 'JHVSF 5PQJD EJTUSJCVUJPOT PG BVUIPST BOE JOnVFODF 46.."3: *O UIJT TFDUJPO XF QSFTFOU BO BQQSPBDI GPS NJOJOH UPQJDMFWFM JOnVFODF JO IFUFSPHFOFPVT OFU XPSLT ɩF BQQSPBDI QSJNBSJMZ DPOTJTUT PG UXP TUFQT JF B QSPCBCJMJTUJD NPEFM UP NJOF EJSFDU JOnVFODF CFUXFFO OPEFT BOE EJĊFSFOU UZQFT PG JOnVFODF QSPQBHBUJPO NFUIPET UP NJOF JOEJSFDU BOE HMPCBM JOnVFODF *O UIF QSPCBCJMJTUJD NPEFM XF DPNCJOF UIF UFYUVBM DPOUFOU BOE IFUFSPHF OFPVT MJOL JOGPSNBUJPO JOUP B VOJmFE HFOFSBUJWF QSPDFTT *OnVFODF QSPQBHBUJPO NFUIPET GVSUIFS QSPQBHBUF JOnVFODF BMPOH UIF MJOLT JO UIF FOUJSF OFUXPSL 8F BMTP EFNPOTUSBUF UIBU UIF MFBSOFE JOnVFODF DBO CFOFmU TFWFSBM SFBM QSFEJDUJPO BQQMJDBUJPOT $0/$-64*0/4 *O UIJT DIBQUFS XF JOUSPEVDF UXP NFUIPEPMPHJFT GPS RVBOUJGZJOH UIF UPQJDMFWFM JOnVFOUJBM TUSFOHUI CFUXFFO VTFST GPS MBSHF TPDJBM OFUXPSLT BOE QPUFOUJBM BQQMJDBUJPOT UP VTFS CFIBWJPSBM QSFEJDUJPO $ )"15&3 6TFS #FIBWJPS .PEFMJOH BOE 1SFEJDUJPO 8F OPX UVSO UP EJTDVTT IPX UP MFWFSBHF UIF EJĊFSFOU TPDJBM QIFOPNFOB UP NPEFM BOE QSFEJDU VTFST CFIBWJPST TPDJBM BDUJPOT 'SPN B CSPBE WJFXQPJOU UIF DPODFQU PG VTFS NPEFMJOH JT DPODFSOFE XJUI UIF QSPDFTT PG CVJMEJOH VQ B VTFS NPEFM UP DIBSBDUFSJ[F VTFST TLJMMT EFDMBSBUJWF LOPXMFEHF BOE TQFDJmD OFFET UP B TZTUFN <> 8F USZ UP OBSSPX EPXO UIJT DPODFQU JO UIJT CPPL UP NPEFMJOH IPX VTFST CFIBWJPST BDUJPOT BSF JOnVFODFE CZ WBSJPVT GBDUPST TVDI BT QFSTPOBM JOUFSFTUT TPDJBM JOnV FODF BOE HMPCBM USFOET 2VJUF B GFX SFMBUFE TUVEJFT IBWF CFFO DPOEVDUFE GPS FYBNQMF EZOBNJD TPDJBM OFUXPSL BOBMZTJT < > TPDJBM JOnVFODF BOBMZTJT < > BOE HSPVQ CFIBWJPS BOBMZTJT < > 07&37*&8 *O TPDJPMPHZ UIF OPUJPO PG TPDJBM BDUJPO XBT mSTU QSPQPTFE CZ 8FCFS <> "DDPSEJOH UP 8FCFS iBO "DUJPO JT ATPDJBM JG UIF BDUJOH JOEJWJEVBM UBLFT BDDPVOU PG UIF CFIBWJPS PG PUIFST BOE JT UIFSFCZ PSJFOUFE JO JUT DPVSTFw 8F BJN UP TZTUFNBUJDBMMZ TUVEZ IPX TPDJBM BDUJPOT FWPMWF JO B EZOBNJD TPDJBM OFUXPSL BOE UP XIBU FYUFOU EJĊFSFOU GBDUPST BĊFDU UIF VTFS BDUJPOT 5P DMFBSMZ NPUJWBUF UIJT XPSL XF DPOEVDU UIF GPMMPXJOH BOBMZTJT PO UISFF SFBM TPDJBM OFU XPSLT 5XJUUFS 'MJDLS ¤ BOE "SOFU.JOFS© 0O 5XJUUFS XF EFmOF UIF BDUJPO BT XIFUIFS B VTFS EJTDVTTFT UIF UPQJD i)BJUJ &BSUIRVBLFw PO IJT NJDSPCMPHT UXFFUT 0O 'MJDLS XF EFmOF UIF BD UJPO BT XIFUIFS B VTFS BEET B QIPUP UP IJT GBWPSJUF MJTU 0O "SOFU.JOFS UIF BDUJPO JT EFmOFE BT XIFUIFS B SFTFBSDIFS QVCMJTIFT B QBQFS PO B TQFDJmD DPOGFSFODF PS KPVSOBM ɩF BOBMZTJT JODMVEFT UISFF BTQFDUT TPDJBM JOnVFODF UJNFEFQFOEFODZ PG VTFST BDUJPOT BOE BDUJPO DPSSFMBUJPO CFUXFFO VTFST 'JHVSF TIPXT UIF FĊFDU PG TPDJBM JOnVFODF 8F TFF UIBU XJUI UIF QFSDFOUBHF PG POFT GSJFOET QFSGPSNJOH BO BDUJPO JODSFBTJOH UIF MJLFMJIPPE UIBU UIF VTFS BMTP QFSGPSNT UIF BDUJPO JT JODSFBTFE 'PS FYBNQMF XIFO UIF QFSDFOUBHF PG POFT GSJFOET EJTDVTTJOH i)BJUJ &BSUIRVBLFw PO UIFJS UXFFUT JODSFBTFT UIF MJLFMJIPPE UIBU UIF VTFS QPTUT UXFFUT BCPVU i)BJUJ &BSUIRVBLFw JT BMTP JODSFBTFE TJHOJmDBOUMZ 'JHVSF JMMVTUSBUFT IPX B VTFST BDUJPO JT EFQFOEFOU PO IJT IJTUPSJD CF IBWJPST *U DBO CF TFFO UIBU B TUSPOH UJNFEFQFOEFODZ FYJTUT GPS VTFST BDUJPOT 'PS JOTUBODF PO 5XJUUFS VTFST XIP QPTUFE UXFFUT BCPVU i)BJUJ &BSUIRVBLFw XJMM IBWF B NVDI IJHIFS QSPCBCJMJUZ ?iiT,ffrrrXirBii2`X+QK B NJDSPCMPHHJOH TZTUFN ¤?iiT,ffrrrX7HB+F`X+QK B QIPUP TIBSJOH TZTUFN ©?iiT,ff `M2iKBM2`XQ`; BO BDBEFNJD TFBSDI TZTUFN 64&3 #&)"7*03 .0%&-*/( "/% 13&%*$5*0/ 0.6 0.2 0.6 0.4 0.15 0.4 0.1 0.2 0.2 0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.1 0.3 0.5 0.7 0.9 Twitter Flickr ArnetMiner 'JHVSF 4PDJBM JOnVFODF ɩF YBYJT TUBOET GPS UIF QFSDFOUBHF PG POFT GSJFOET XIP QFSGPSN BO BDUJPO BU t 1 t $ BOE UIF ZBYJT SFQSFTFOUT UIF MJLFMJIPPE UIBU UIF VTFS BMTP QFSGPSNT UIF BDUJPO BU 0.3 dependent dependent dependent average 0.6 average average 0.6 0.2 0.4 0.4 0.1 0.2 0.2 0 0 0 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 Twitter Flickr ArnetMiner 'JHVSF 5JNFEFQFOEFODZ PG VTFST BDUJPOT ɩF YBYJT TUBOET GPS EJĊFSFOU UJNFTUBNQT iEFQFOEFOUw EFOPUFT UIF MJLFMJIPPE UIBU B VTFS QFSGPSNT BO BDUJPO XIJDI XBT QSFWJPVTMZ QFSGPSNFE CZ IFSTFMG iBWFSBHFw SFQ SFTFOUT UIF MJLFMJIPPE UIBU B VTFS QFSGPSNT UIF BDUJPO PO BWFSBHF o UP QPTU UXFFUT PO UIJT UPQJD UIBO UIPTF XIP OFWFS EJTDVTTFE UIJT UPQJD PO UIFJS CMPHT 'JHVSF TIPXT UIF DPSSFMBUJPO CFUXFFO VTFST BDUJPOT BU UIF TBNF UJNFTUBNQ "O JOUFSFTUJOH QIFOPNFOPO JT UIBU GSJFOET NBZ QFSGPSN BO BDUJPO BU UIF TBNF UJNF &H PO 5XJU UFS UXP GSJFOET IBWF B IJHIFS QSPCBCJMJUZ UP EJTDVTT i)BJUJ &BSUIRVBLFw UIBO UXP VTFST SBOEPNMZ DIPTFO GSPN UIF OFUXPSL 1SPCMFN 'PSNVMBUJPO 'PSNBMMZ XF mSTU HJWF TFWFSBM OFDFTTBSZ EFmOJUJPOT BOE UIFO GPSNVMBUF UIF QSPCMFN PG TPDJBM BDUJPO QSFEJDUJPO 07&37*&8 0.65 friend friend 0.85 friend random 0.7 random random 0.6 0.8 0.55 0.6 0.75 0.5 0.7 0.5 0.45 0.65 0.4 0.4 0.6 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 Twitter Flickr ArnetMiner 'JHVSF "DUJPO DPSSFMBUJPO ɩF YBYJT TUBOET GPS EJĊFSFOU UJNF XJOEPXT iGSJFOEw EFOPUFT UIF MJLFMJIPPE UIBU UXP GSJFOET QFSGPSN BO BDUJPO UPHFUIFS iSBOEPNw SFQSFTFOUT UIF MJLFMJIPPE UIBU UXP SBOEPN VTFST QFSGPSN UIF BDUJPO UPHFUIFS G .V; E/ V V N " TUBUJD TPDJBM OFUXPSL DBO CF SFQSFTFOUFE BT D XIFSF JT UIF TFU PG j jD E V V VTFST BOE ! " JT UIF TFU PG EJSFDUFEVOEJSFDUFE MJOLT CFUXFFO VTFST (JWFO UIJT XF DBO EFmOF UIF VTFST BDUJPO BT GPMMPXT %FmOJUJPO "DUJPO "O BDUJPO y QFSGPSNFE CZ VTFS vi BU UJNF t DBO CF SFQSFTFOUFE BT B USJQMF .y; v ;t/ yt Y t t i PS TIPSUMZ i -FU CF UIF TFU PG BDUJPOT PG BMM VTFST BU UJNF 'VSUIFS XF EFOPUF BMM VTFST BDUJPOT BT UIF BDUJPO IJTUPSZ : .y; vi ;t/ i;t Df g t yi 0; 1 t 8JUIPVU MPTT PG HFOFSBMJUZ XF mSTU DPOTJEFS UIF CJOBSZ BDUJPO t UIBU JT 2f g XIFSF y 1 vi t y 0 i D JOEJDBUFT UIBU VTFS QFSGPSNFE BO BDUJPO BU UJNF BOE i D JOEJDBUFT UIBU UIF VTFS EJE OPU QFSGPSN UIF BDUJPO 4VDI BO BDUJPO MPH DBO CF BWBJMBCMF GSPN NBOZ POMJOF TZTUFNT 'PS yt v FYBNQMF PO 5XJUUFS UIF BDUJPO i DBO CF EFmOFE BT XIFUIFS VTFS i QPTUT B UXFFU NJDSPCMPH BCPVU B TQFDJmD UPQJD FH i)BJUJ &BSUIRVBLFw BU UJNF t 'VSUIFS XF BTTVNF UIBU FBDI VTFS JT BTTPDJBUFE XJUI B OVNCFS PG BUUSJCVUFT BOE UIVT IBWF UIF GPMMPXJOH EFmOJUJPO X t N d t %FmOJUJPO 5JNFWBSZJOH BUUSJCVUF NBUSJY -FU CF BO " BUUSJCVUF NBUSJY BU UJNF i xij JOth XIJDI FWFSZ SPX Y DPSSFTQPOET UP B VTFS FBDI DPMVNO BO BUUSJCVUF BOE BO FMFNFOU JT UIF j BUUSJCVUF WBMVF PG VTFS vi ɩF BUUSJCVUF NBUSJY EFTDSJCFT VTFSTQFDJmD DIBSBDUFSJTUJDT BOE DBO CF EFmOFE JO EJĊFSFOU XBZT 'PS FYBNQMF PO 5XJUUFS FBDI BUUSJCVUF DBO CF EFmOFE BT B LFZXPSE BOE UIF WBMVF PG BO BUUSJCVUF DBO CF EFmOFE BT UIF GSFRVFODZ PG B LFZXPSE PDDVSSJOH PO B VTFST QPTUFE UXFFUT ɩVT XF DBO EFmOF UIF JOQVU PG PVS QSPCMFN B TFU PG BUUSJCVUF BVHNFOUFE OFUXPSLT %FmOJUJPO "UUSJCVUF BVHNFOUFE OFUXPSL ɩF BUUSJCVUF BVHNFOUFE OFUXPSL JT EFOPUFE BT Gt .V t ;Et ;Xt ;Yt / V t Et D XIFSF JT UIF TFU PG VTFST BOE JT UIF TFU PG MJOLT CFUXFFO VTFST BU UJNF 64&3 #&)"7*03 .0%&-*/( "/% 13&%*$5*0/ t t t BOE X SFQSFTFOUT UIF BUUSJCVUF NBUSJY PG BMM VTFST JO UIF OFUXPSL BU UJNF t BOE Y SFQSFTFOUT UIF TFU PG BDUJPOT PG BMM VTFST BU UJNF t #BTFE PO UIF BCPWF DPODFQUT XF DBO EFmOF UIF QSPCMFN PG TPDJBM BDUJPO QSFEJDUJPO (JWFO B TFSJFT PG T UJNFEFQFOEFOU BUUSJCVUF BVHNFOUFE OFUXPSLT UIF HPBM JT UP MFBSO B NPEFM UIBU DBO CFTU mU UIF SFMBUJPOTIJQT CFUXFFO UIF WBSJPVT GBDUPST BOE UIF VTFS BDUJPOT .PSF QSFDJTFMZ XF IBWF UIF GPMMPXJOH 1SPCMFN 4PDJBM BDUJPO QSFEJDUJPO (JWFO B TFSJFT PG T UJNFEFQFOEFOU BUUSJCVUF BVHNFOUFE Gt .V t ;Et ;Xt ;Yt / t 1; ;T OFUXPSLT f D g XIFSF 2f ### g UIF HPBM PG TPDJBM BDUJPO QSFEJDUJPO JT UP MFBSO B NBQQJOH GVODUJPO f . G1;:::;GT 1 ;VT ;ET ;XT / Y T : W f ! g ! /PUF UIBU JO UIJT HFOFSBM GPSNVMBUJPO XF BMMPX UIF HSBQI TUSVDUVSF UP FWPMWF PWFS UJNF BOE BMTP BSCJUSBSZ EFQFOEFODZ GSPN UIF QBTU 5P IBWF B USBDUBCMF QSPCMFN UP XPSL XJUI XF NPEFM UIF UJNFEFQFOEFODZ CZ JOUSPEVDJOH B MBUFOU TUBUF GPS FBDI VTFS .PSF TQFDJmDBMMZ UIFJS BDUJPOT BSF HFOFSBUFE CZ UIFJS MBUFOU TUBUFT XIJDI BSF EFQFOEFOU PO UIFJS OFJHICPST TUBUFT BU UJNF t BOE t 1 $ $IBMMFOHFT BOE 4PMVUJPO ɩVT UIF QSPCMFN CFDPNFT IPX UP FĊFDUJWFMZ BOE FċDJFOUMZ QSFEJDU UIF EZOBNJD VTFST BDUJPOT ɩJT QSPCMFN JT OPOUSJWJBM BOE QPTFT B TFU PG VOJRVF DIBMMFOHFT 'JSTU UIF TPDJBM OFUXPSL EBUB FH OFUXPSL TUSVDUVSF BOE TPDJBM BDUJPOT BSF WFSZ OPJTZ 6TFST QFSGPSNJOH UIF TBNF BDUJPO NBZ OPU IBWF UIF TBNF QSFGFSFODF UPXBSET UIBU BDUJPO -JLFXJTF VTFST XIP EJE OPU QFSGPSN UIF BDUJPO EP OPU NFBO UIFZ IBWF OP JOUFSFTUT UPXBSET UIF BDUJPO 4FDPOE VTFS CFIBWJPST BSF IJHIMZ UJNFEFQFOEFOU 'PS FYBNQMF UIF JOnVFODF PG B VTFS PO BOPUIFS TUSPOHMZ EFQFOET PO UIFJS IJTUPSJD JOUFSBDUJPOT ɩJSE VTFST BDUJPOT BSF VTVBMMZ DPSSFMBUFE *O BEEJUJPO BT SFBM TPDJBM OFUXPSLT BSF HFUUJOH MBSHFS XJUI UIPVTBOET PS NJMMJPOT PG VTFST *U JT JNQPSUBOU UP EFWFMPQ UIF NPEFM UIBU DBO TDBMF XFMM UP SFBM MBSHF EBUB TFUT *O UIJT TFDUJPO XF USZ UP TZTUFNBUJDBMMZ JOWFTUJHBUF UIF QSPCMFN PG TPDJBM BDUJPO QSFEJD UJPO <> 8F PċDJBMMZ GPSNVMBUF UIF QSPCMFN PG TPDJBM BDUJPO QSFEJDUJPO BOE QSPQPTF B VOJmFE NPEFM /PJTF 5PMFSBOU 5JNFWBSZJOH 'BDUPS (SBQI .PEFM /55'(. 8F QSFTFOU BO FċDJFOU BMHPSJUIN GPS NPEFM MFBSOJOH BOE EFWFMPQ B EJTUSJCVUFE JNQMFNFOUBUJPO CBTFE PO .1* .FTTBHF 1BTTJOH *OUFSGBDF UP TDBMF VQ UP SFBM MBSHF OFUXPSLT 8F DPOEVDU FYQFSJNFOUT PO UISFF EJĊFSFOU EBUB TFUT 5XJUUFS 'MJDLS BOE "SOFU.JOFS &YQFSJNFOUBM SFTVMUT TIPX UIBU UIF QSPQPTFE /55 '(. NPEFM DBO BDIJFWF B CFUUFS QFSGPSNBODF GPS UIF BDUJPO QSFEJDUJPO UIBO TFWFSBM BMUFSOBUJWF NPEFMT "1130"$) '3".&803, '03 40$*"- "$5*0/ 13&%*$5*0/ 5P TVNNBSJ[F GPS NPEFMJOH BOE QSFEJDUJOH TPDJBM BDUJPOT XF IBWF UIF GPMMPXJOH JOUVJUJPOT "1130"$) '3".&803, '03 40$*"- "$5*0/ 13&%*$5*0/ 'JHVSF (SBQIJDBM SFQSFTFOUBUJPO PG UIF /55'(. NPEFM &BDI DJSDMF TUBOET GPS B VTFST MBUFOU zt t BDUJPO TUBUF i BU UJNF JO UIF OFUXPSL XIJDI JT VTFE UP DIBSBDUFSJ[F UIF JOUFOUJPO EFHSFF PG UIF VTFS UP QFSGPSN yt t UIF BDUJPO UIF MBUFOU TUBUF JT BTTPDJBUFE XJUI UIF BDUJPO i B WFDUPS PG BUUSJCVUFT Yi BOE EFQFOET PO GSJFOET IJTUPSJD t 1 t !vi vi t g.:/ BDUJPOT [' BOE DPSSFMBUFT XJUI GSJFOET BDUJPOT [' BU UJNF EFOPUFT B GBDUPS GVODUJPO UP SFQSFTFOU UIF GSJFOET JOnVFODF PO B VTFST BDUJPO hi .:/ SFQSFTFOUT B GBDUPS EFmOFE PO VTFS vi T BUUSJCVUFT BOE hij .:/ SFQSFTFOUT B GBDUPS UP DBQUVSF UIF DPSSFMBUJPO CFUXFFO VTFST BDUJPOT VTFST BDUJPOT BU UJNF t BSF JOnVFODFE CZ UIFJS GSJFOET IJTUPSJD BDUJPOT UJNF t %FmOJUJPO yi t -BUFOU BDUJPO TUBUF 'PS FBDI VTFST BDUJPO XF EFmOF B DPOUJOVPVT MBUFOU z Œ0; 1 yi TUBUF i 2 XIJDI DPSSFTQPOET UP B DPNCJOBUJPO PG UIF PCTFSWFE BDUJPO BOE B QPTTJCMF CJBT UP EFTDSJCF UIF BDUVBM JOUFOUJPO EFHSFF PG UIF VTFS UP QFSGPSN UIF BDUJPO 'JHVSF TIPXT UIF HSBQIJDBM TUSVDUVSF PG UIF /55'(. NPEFM "O BDUJPO PG VTFS vi BU t yt zt UJNF JF i JT NPEFMFE CZ VTJOH B DPOUJOVPVT MBUFOU BDUJPO TUBUF i XIJDI JT EFQFOEFOU PO t 1 v v !vi i i GSJFOET IJTUPSJD BDUJPOTt [' XIFSF & SFQSFTFOUTt GSJFOET PG VTFS JO UIF OFUXPSL VTFST BD vi i UJPO DPSSFMBUJPO [' BOE VTFST BUUSJCVUFT Y 4QFDJmDBMMZ JO UIF /55'(. NPEFM FBDI EJTDSFUF BDUJPO JT NBQQFE JOUPt UIF MBUFOU TUBUF TQBDF BOE UIF BDUJPO CJBTt JT NPEFMFE VTJOH B GBDUPS GVODUJPO y 1 z vi 'PS FYBNQMF GPS i D B TNBMM WBMVF PG JUT DPSSFTQPOEJOH i TVHHFTUT UIBU B VTFS IBT B MPX yt zt JOUFOUJPO UP QFSGPSN UIF BDUJPO UIVT B MBSHF BDUJPO CJBT j i $ i j /FYU JOnVFODF CFUXFFO VTFST JT NPEFMFE VTJOH UIF MBUFOU TUBUFT CBTFE PO UIF TBNF BTTVNQUJPO BT JO ).. <> BOE ,BMNBO 'JM UFST <> MBUFOU TUBUFT PG VTFST BDUJPOT BU UJNF t BSF DPOEJUJPOBMMZ JOEFQFOEFOU PG BMM UIF QSFWJPVT 64&3 #&)"7*03 .0%&-*/( "/% 13&%*$5*0/ t 1 TUBUFT HJWFO UIF MBUFOU TUBUFT BU UJNF $ 'JOBMMZ BDUJPOT DPSSFMBUJPO JT BMTP NPEFMFE JO UIF MBUFOU TUBUF TQBDF " .BSLPW SBOEPN mFME JT EFmOFE UP NPEFM UIF EFQFOEFODZ DPSSFMBUJPO BNPOH UIF DPOUJOVPVT MBUFOU TUBUFT %JĊFSFOU GSPN UIF USBEJUJPOBM .BSLPW SBOEPN mFME NPEFM FH $3' <> ).. <> ,BMNBO 'JMUFST <> UIF /55.3' NPEFM VTFT B DPOUJOVPVT WBSJBCMF UP EF TDSJCF UIF MBUFOU TUBUF BOE VUJMJ[FT B DPNCJOBUJPO PG NVMUJWBSJBUF (BVTTJBO GVODUJPO BOE .BSLPW SBOEPN mFME UP JODPSQPSBUF CPUI UJNFJOUFS BOE UJNFJOUSB EFQFOEFODZ CFUXFFO VTFST BDUJPOT /PX XF FYQMBJO UIF QSPQPTFE /55'(. NPEFM JO EFUBJM (JWFO B TFSJFT PG BUUSJCVUF Gt .V t ;Et ;Xt ;Yt / ;t 1; ;T V V 1 V 2 ::: V T ; V BVHNFOUFE OFUXPSLT ( Df D g 2f ### g BOE D [ [ [ j jD N XF DBO EFmOF UIF KPJOU EJTUSJCVUJPO PWFS UIF BDUJPOT : HJWFO ( BT T N p. / f .yt zt /f .zt t 1 /f .zt t ; t /; i i i !vi i vi i :j( D j j[' j[' Y t 1 i 1 YD YD vi vi XIFSF OPUBUJPO & SFQSFTFOUT OFJHICPST PG JO UIF TPDJBM OFUXPSL ɩF KPJOU QSPCBCJMJUZ IBT UISFF UZQFT PG GBDUPS GVODUJPOT DPSSFTQPOEJOH UP UIF JOUVJUJPOT XF IBWF EJTDVTTFE 4QFDJmDBMMZ t t f .y z / vi yi t BDUJPO CJBT GBDUPS i j i SFQSFTFOUT UIF QPTUFSJPS QSPCBCJMJUZ PG VTFS T BDUJPO BU UJNF t zt HJWFO UIF DPOUJOVPVT MBUFOU TUBUF i f .zt t 1 / v t i !vi i t JOnVFODF GBDUPS j[' SFnFDUT GSJFOET JOnVFODF PO VTFS T BDUJPO BU UJNF BOE f .zt t ; t / t i vi i t DPSSFMBUJPO GBDUPS j[' Y EFOPUFT UIF DPSSFMBUJPO CFUXFFO VTFST BDUJPO BU UJNF ɩF UISFF GBDUPST DBO CF JOTUBOUJBUFE JO EJĊFSFOU XBZT SFnFDUJOH PVS QSJPS LOPXMFEHF GPS EJĊFSFOU BQQMJDBUJPOT *O UIJT DIBQUFS XF XJMM HJWF B HFOFSBM EFmOJUJPO GPS UIF UISFF GBDUPST 'PS f .yt zt / UIF BDUJPO CJBT GBDUPS i j i XF EFmOF JU VTJOH B (BVTTJBO GVODUJPO t t 2 t t 1 .yi zi / f .yi zi / $ ; j D p2"/ 2 FYQf$ 2/ 2 g XIFSF / JT B WBSJBODF UP DPOUSPM UIF CJBT BOE JUT WBMVF DBO CF MFBSOFE VTJOH BO &.TUZMF BMHPSJUIN PS QSFEFmOFE FNQJSJDBMMZ /PUF UIBU JG XF POMZ DPOTJEFS UIF CJOBSZ BDUJPO UIF CJBT GBDUPS DBO CF BMTP EFmOFE CBTFE PO B #FSOPVMMJ EJTUSJCVUJPO f .zt t 1 / N N M t 1 i !vi ! 'PS JOnVFODF GBDUPS j[' XF mSTU EFmOFt BO1 CJOBSZ " NBUSJY UP EFTDSJCF t 1 mij! 1 vi vj UIF TPDJBM OFUXPSL BU UJNF $ XIFSF UIF FMFNFOU t D1 SFQSFTFOUT UIBU VTFS BOE IBWF eij E m 0 B SFMBUJPOTIJQ JO UIF TPDJBM OFUXPSL JF 2 BOE ij! D JOEJDBUFT UIFSF JT OP SFMBUJPOTIJQ CFUXFFO vi BOE vj (JWFO UIJT XF DBO GPSNBMMZ EFmOF UIF JOnVFODF GBDUPS BT 1 N f .zt t 1 / & mt 1g .zt ;zt 1/ ; i !vi j i ji! ji i j! j[' D Z1 FYQf g j 1 XD "1130"$) '3".&803, '03 40$*"- "$5*0/ 13&%*$5*0/ t t 1 t t 1 gji.zi ;zj! / zi zj! &ji XIFSt 1F JT B GVODUJPO EFmOFE PO UIF MBUFOU TUBUFT PG UXP VTFST BOE XIFO m 1 vj vi ji! D SFQSFTFOUT UIF JOnVFODF EFHSFF PG PO 'PS FYBNQMF HJWFO B IJHIFS JOnVFODF &ji UIF BDUJPO PG VTFS vj JT NPSF MJLFMZ UP JOEVDF VTFS vi UP CFIBWF JO B TJNJMBS XBZ Z1 JT B j i OPSNBMJ[BUJPO GBDUPS 8IFO D XF SFGFS UP UIF JOnVFODF BT TFMGJOnVFODF XIJDI BDUVBMMZ DIBSBDUFSJ[FT UIF EFQFOEFODZ PG UIF VTFST BDUJPO PO IJT PXO QSFWJPVT TUBUF ɩF DPSSFMBUJPO GBDUPS DBO CF OBUVSBMMZ NPEFMFE JO B .BSLPW SBOEPN mFME ɩFSFGPSF CZ UIF GVOEBNFOUBM UIFPSFN PG SBOEPN mFMET XF DBO EFmOF UIF DPSSFMBUJPO GBDUPS BT 1 N f .zt t ; / . ˇ mt h .zt ;zt / i vi i ij ij ij i j j[' Y D Z2 FYQf j 1 D d X t t ˛khk.z ;x // ; C i ik g k 1 XD h .zt ;zt / v v XIFSF ij i j JT B GFBUVSF GVODUJPO UP DBQUVSF UIF DPSSFMBUJPO CFUXFFO VTFS i BOE j BU UJNF t h .zt ;xt / v k x d k i ik JT B GFBUVSF GVODUJPO EFmOFE PO VTFS i BOE UIF UI BUUSJCVUF ik JT UIF OVN CFS PG BUUSJCVUFT ˇij BOE ˛k BSF SFTQFDUJWFMZ XFJHIUT PG UIF UXP GVODUJPOT BOE Z2 JT BHBJO B OPSNBMJ[BUJPO GBDUPS 'JOBMMZ CZ JOUFHSBUJOH &RVBUJPOT JOUP &RVBUJPO XF DBO PCUBJO UIF GPMMPX JOH KPJOU QSPCBCJMJUZ T N t t 2 T N N 1 .yi zi / t 1 t t 1 p. / $ &ij m g.z ;z / :j( D Z FYQf 2/2 C ji! i j! t 1 i 1 t 1 i 1j 1 XD XD XD XD XD T N N T N d t t t t t ˇij m hij .z ;z / ˛ h .z ;x / ; C ij i j C k k i ik g t 1 i 1j 1 t 1 i 1 k 1 XD XD XD XD XD XD 2 N T Z .2"/ / "2 Z1Z2 XIFSF D ' -FBSOJOH /55'(. JT UP FTUJNBUF B QBSBNFUFS DPOmHVSBUJPO D . zi ; ˛k ; ˇij ; &ij / Y f g f g f g f g GSPN B HJWFO IJTUPSJD BDUJPO MPH UIBU NBYJNJ[FT UIF MPHMJLFMJIPPE .'/ p# . / PCKFDUJWF GVODUJPO O D MPH :j( JF ' ? .'/: D BSH NBY O .0%&- -&"3/*/( ɩFSF BSF UXP DIBMMFOHFT UP TPMWF UIF PCKFDUJWF GVODUJPO 'JSTU BT UIF OFUXPSL TUSVDUVSF JO UIF TPDJBM OFUXPSL DBO CF BSCJUSBSZ NBZ DPOUBJO DZDMFT USBEJUJPOBM NFUIPET TVDI BT +VODUJPO 5SFF <> BOE #FMJFG 1SPQBHBUJPO <> DBOOPU SFTVMU JO BO FYBDU TPMVUJPO 4FDPOE UP DBMDVMBUF UIF OPSNBMJ[BUJPO 64&3 #&)"7*03 .0%&-*/( "/% 13&%*$5*0/ GBDUPS Z JU JT OFDFTTBSZ UP HVBSBOUFF UIBU UIF EFOPNJOBUPS PG &RVBUJPO JF UIF FYQPOFOUJBM : GVODUJPO FYQf g JT JOUFHSBCMF #BTFE PO UIFTF DPOTJEFSBUJPOT XF JOTUBOUJBUF UIF GBDUPS GVODUJPOT g.:/ BOE h.:/ BT GPMMPXT t t 1 t t 1 2 gji.zi ;zj! / .zi zj! / t t D$t $ t 2 hij .zi ;zj / .zi zj / t t D$t $ t 2 hk.z ;x / .z x / : i ik D$i $ ik 8F TFF UIBU BMM PG UIF GBDUPS GVODUJPOT BSF EFmOFE CZ RVBESBUJD GVODUJPOT ɩJT JT CFDBVTF RVBESBUJD FRVBUJPO TBUJTmFT UIF BCPWF UXP SFRVJSFNFOUT JU JT JOUFHSBCMF BOE JU PĊFST UIF QPTTJCJM JUZ UP EFTJHO BO FYBDU TPMVUJPO .PSFPWFS CZ EFmOJOH JO UIJT XBZ UIF JOnVFODF GBDUPS BOE UIF DPSSFMBUJPO GBDUPS DBO CF FMFHBOUMZ FYQMBJOFE XJUI UIF JOGPSNBUJPO EJĊVTJPO UIFPSZ CZ XIJDI UIF BDUJPOT PG VTFST TQSFBE JO UIF TPDJBM OFUXPSL BMPOH UIF SFMBUJPOTIJQT < > .'/ 'JOBMMZ UIF PCKFDUJWF GVODUJPO O DBO CF SFXSJUUFO BT T N t t 2 T N N .yi zi / t 1 t t 1 2 .'/ Z $ &ji m .z z / O D$MPH $f 2/2 C ji! i $ j! t 1 i 1 t 1 i 1j 1 XD XD XD XD XD T N N T N d t t t 2 t t 2 ˇij m .z z / ˛ .z x / C ij i $ j C k i $ ik g t 1 i 1j 1 t 1 i 1 k 1 XD XD XD XD XD XD XIFSF T N t t 2 T N N .yi zi / t 1 t t 1 2 Z C $ &ji m .z z / D FYQf$ 2/2 $ ji! i $ j! Zy Zz t 1 i 1 t 1 i 1j 1 XD XD XD XD XD T N N T N d t t t 2 t t 2 ˇij m .z z / ˛ .z x / dzdy $ ij i $ j $ k i $ ik g t 1 i 1j 1 t 1 i 1 k 1 XD XD XD XD XD XD N T C .2"/ 2/ "2 XIFSF D JT B DPOTUBOU DzF -FBSOJOH "MHPSJUIN ' . zi ; ˛k ; ˇij ; &ij / ɩF UBTL PG NPEFM MFBSOJOH JT UP FTUJNBUF UIF QBSBNFUFST D f g f g f g f g CZ TPMWJOH UIF PCKFDUJWF GVODUJPO &RVBUJPO 'PS UIJT QVSQPTF XF OFFE UP mSTU TPMWF UIF JOUFHSBUJPO Z y : PG "T JT EJTDSFUF XF DBO FBTJMZ JOUFHSBUF PVU UIF mSTU UFSN JO UIF FYQf g GVODUJPO PG &RVB UJPO 'VSUIFSNPSF UP HVBSBOUFF UIBU Z JT JOUFHSBCMF XF NVTU IBWF ˛k > 0; ˇij > 0; &ij >0 *U JT TUJMM EJċDVMU UP TPMWF UIF JOUFHSBUJPO 5P EFBM XJUI UIJT PVS CBTJD JEFB JT UP USBOTGPSN UIF FY : QPOFOUJBM GVODUJPO FYQf g JOUP B NVMUJWBSJBUF (BVTTJBO EJTUSJCVUJPO BOE DBMDVMBUF UIF JOUFHSBUJPO BT GPMMPXT "1130"$) '3".&803, '03 40$*"- "$5*0/ 13&%*$5*0/ 1 T 1 Z Const A ! 2 b A! b c ; D # j j FYQf $ g T N d t c t 1 i 1 k 1 ˛kxik Const A NT NT XIFSF D D D JT B DPOTUBOU JT B " CMPDL USJEJBHPOBM NBUSJY b X˛ NT D X X1 X2 XT NT d BOE D P JT BP EJNFOTJPOP WFDUPS BOE Df W W###W gJT " NBUSJY CZ DPODBUF OBUJOH BMM UJNFWBSZJOH BUUSJCVUF NBUSJDFT UPHFUIFS %FSJWBUJPO PG Z 8F OPX HJWF UIF EFUBJMT PO IPX XF PCUBJO UIF JOUFHSBUJPO PG Z &RVBUJPO DBO CF SFXSJUUFO JO UIF GPSN PG B NVMUJWBSJBUF (BVTTJBO EJTUSJCVUJPO ɩF TUBOEBSE GPSNBUJPO PG UIF JOUFHSBUJPO PG .VMUJWBSJBUF (BVTTJBO %JTUSJCVUJPO JT BT GPMMPXT 1 1 T 1 m .u +/ M ! .u +/ du 1; .2"/ 2 M u FYQf$2 $ $ g D j j Z u + m M m m XIFSF BOE JT B EJNFOTJPO WFDUPS JT B " NBUSJY : ɩF JEFB IFSF JT UP USBOTGPSN UIF FYQPOFOUJBM GVODUJPO FYQf g JO &RVBUJPO JOUP B GPSNBUJPO PG NVMUJWBSJBUF (BVTTJBO EJTUSJCVUJPO 1 T 1 : .z +/ M ! .z +/ c ; FYQf gÁFYQf$2 $ $ $ g XIFSF c JT B WBMVF JOEFQFOEFOU PG z 8JUI GVSUIFS EFSJWBUJPO XF DBO BSSJWF 1 T 1 Z Const A ! 2 b A! b c D #j j FYQf $ g T N d t b X˛˛ c ˛kx A NT NT A XIFSF D D t 1 i 1 k 1 ik JT B " CMPDL USJEJBHPOBM NBUSJY BOE j j DA D D A i t i .t JT EFUFSNJOBOU PG NBUSJYP P ɩF FMFNFOUTP PG JT EFmOFE BT GPMMPXT XF VTF UP EFOPUF C $ 1/ N * GPS TJNQMJDJUZ d N N N N t t t 1 t 1 Ait ;it ˛k ˇij mij ˇjimji "jimji! "ij mijC D k 1 C j 1 C j 1 C j 1 C j 1 XD XD t XDt XD XD Ait ;j t Aj t ;it ˇij mij ˇjimji D D! !t 1 t 1 Ait ;j t 1 Aj t ;it 1 "jimji! "ij mij! : ! D ! D! ! t 2 A t t .z / A t t ɩJT DPOTUSVDUJPO NBUDIFT PVS JOUVJUJPO i ;i SFQSFTFOUT UIF DPFċDJFOU PG i XIJMF i ;j Ait ;j t 1 SFQSFTFOUT UIF DPSSFMBUJPO GBDUPS BOE ! EFTDSJCFT UIF JOnVFODF GBDUPS DzF -FBSOJOH "MHPSJUIN BOE *UT %FSJWBUJPO (JWFO UIJT XF DBO EFTJHO BO &.TUZMF BMHPSJUIN .'/ UP NBYJNJ[F O BT TVNNBSJ[FE JO "MHPSJUIN t &TUFQ mY z BOE VQEBUF BMM ˛ ˇ BOE & VTJOH B HSBEJFOU EFTDFOU NFUIPE t .TUFQ mY ˛ ˇ BOE & UP VQEBUF BMM z CZ TPMWJOH B MJOFBS TZTUFN 64&3 #&)"7*03 .0%&-*/( "/% 13&%*$5*0/ .PSF TQFDJmDBMMZ UIF BMHPSJUIN GPS NPEFM MFBSOJOH QSJNBSJMZ DPOTJTUT PG UXP TUFQT 5P ˛ ˇ & TVNNBSJ[F JO UIF mSTU TUFQ XF mY [ BOE VQEBUF ˛˛;ˇˇ;& BDDPSEJOH UP UIFJS HSBEJFOUT 8F OFFE UP HVBSBOUFF UIBU ˛k;ˇij ;&ij >0 ɩVT DPOWFOUJPOBM HSBEJFOU EFTDFOU DBOOPU CF EJSFDUMZ BQQMJFE UP UIF DPOTUSBJOFE QSPCMFN 8F FNQMPZ B UFDIOJRVF TJNJMBS UP UIBU JO 2JO FU BM <> 4QFDJmDBMMZ .'/ XF mSTU NBYJNJ[F O XJUI SFTQFDU UP UIF MPH GVODUJPO "T B SFTVMU XF HFU T N t t 2 @ Z ˛ ˛ . .z x / MPH / rMPH k D$ k i $ ik C @˛ t 1 i 1 k XDT XD t t 2 @ Z ˇ ˇij . .z z / MPH / rMPH ij D$ i $ j C @ˇ t 1 ij XDT t 1 t t 1 2 @ Z " &ij . m .z z / MPH /; rMPH ij D$ ji! i $ j! C @& t 1 ij XD XIFSF T 1 T N @ Z 1 @ A @b A b 2 MPH j j E ! E xt @˛ D $ 2 A @˛ C @˛ $ ik k j j k k t 1 i 1 1 XD XD .A T / T I XT A 1b bT A 1A 1b D$2 ! W W C ;k ! E $ E ! ! E T N 2 bT A 1X xt C E ! ;k $ ik t 1 i 1 XD XD @ Z 1 @ A @bT A 1b MPH j j E ! E @ˇij D$2 A @ˇij C @ˇij j j 1 T T @A T 1 @A 1 .A! / b A! A! b D$2 W @ˇij W$E @ˇij E @ Z 1 @ A @bT A 1b MPH j j E ! E @&ij D$2 A @&ij C @&ij j j 1 T T @A T 1 @A 1 .A! / b A! A! b; D$2 W @&ij W$E @&ij E M XIFSF UIF OPUBUJPO W XJUI B DPMPO EFOPUFT UIF MPOH DPMVNO WFDUPS GPSNFE CZ DPODBUFOBUJOH UIF DPMVNOT PG NBUSJY M ˛˛;ˇˇˇ;& z *O UIF TFDPOE TUFQ XF mY UP VQEBUF E CZ TPMWJOH B MJOFBS TZTUFN .A I/z y X˛: C E DEC E ' 4PDJBM "DUJPO 1SFEJDUJPO #BTFE PO UIF MFBSOFE QBSBNFUFSTT 1 XF DBO QSFEJDU UIF VTFST GVUVSF y C T 1 BDUJPOT 4QFDJmDBMMZ GPS QSFEJDUJOH B VTFST BDUJPO i BU UJNF C XF mSTU DPNQVUF UIF MBUFOU zT 1 yT 1 TUBUF i C BOE UIFO VTF UIF MBUFOU TUBUF UP JOGFS UIF BDUJPO i C 5P DPNQVUF UIF MBUFOU TUBUF zT 1 i C XF IBWF UIF GPMMPXJOH GPSNVMB "1130"$) '3".&803, '03 40$*"- "$5*0/ 13&%*$5*0/ *OQVU OVNCFS PG JUFSBUJPOT I BOE MFBSOJOH SBUF ( ' . zi ; ˛ ; ˇij ; &ij / 0VUQVU MFBSOFE QBSBNFUFST D f g f kg f g f g z y *OJUJBMJ[F D *OJUJBMJ[F ˛; ˇ; & SFQFBU & 4UFQ mY z MFBSO ˛; ˇ; & i 1 GPS D UP * EP ˛ ; ˇ ; " $PNQVUF HSBEJFOU rMPH k rMPH ij rMPH ij ˛ ˛ ( ˛ 6QEBUF MPH k D MPH k C "rMPH k ˇij ˇij ( ˇ 6QEBUF MPH D MPH C "rMPH ij &ij &ij ( " 6QEBUF MPH D MPH C "rMPH ij FOE . 4UFQ mY ˛; ˇ; & MFBSO z 4PMWF UIF GPMMPXJOH MJOFBS FRVBUJPO .A I/z y X˛ C D C VOUJM DPOWFSHFODF "MHPSJUIN &YQFDUBUJPO NBYJNJ[BUJPO d ˛ x N & mT zT T 1 k 1 k ik j 1 ji ji j z C D C D : i D d N T P k 1 ˛k Pj 1 &j i mji D C D P P )PXFWFS UIF BCPWF FRVBUJPO DBMDVMBUFT UIF MBUFOU TUBUF JOEFQFOEFOUMZ BOE JHOPSF UIF DPS SFMBUJPO CFUXFFO BDUJPOT #Z GVSUIFS DPOTJEFSJOH UIF BDUJPO DPSSFMBUJPO GBDUPS UIBU JT UP DPNQVUF BMM z UPHFUIFS XF DBO TPMWF UIF GPMMPXJOH MJOFBS TZTUFN d N T 1 T T 1 T i; ˛ .z x / &jim .z z / 8 k i C $ ik C ji i C $ j k 1 j 1 X XD D N N T 1 T 1 T 1 T 1 ˇij .z z / ˇji.z z / 0: C i C $ j C C i C $ j C D j 1 j 1 XD XD ɩFO XF DBO QSFEJDU UIF VTFST BDUJPOT y BDDPSEJOH UP UIFJS DPSSFTQPOEJOH MBUFOU TUBUFT z CZ T 1 T 1 T 1 0 zi C z < zi C z y C JG j $ Cj D j $ !j ; i D 1 : ! PUIFSXJTF z z y 1 XIFSF C BOE ! BSF SFTQFDUJWFMZ UIF BWFSBHF TUBUF WBMVFT PG UIF DPSSFTQPOEJOH BDUJPOT D y 0 BOE D JO UIF USBJOJOH EBUB BOE BSF DPNQVUFE CZ 64&3 #&)"7*03 .0%&-*/( "/% 13&%*$5*0/ T N t t t 1 i 1 zi I.yi 0/ z D D D ! D T N t P t 1P i 1 I.yi 0/ T D N D t tD t 1 i 1 zi I.yi 1/ z PD PD D C D T N t P t 1P i 1 I.yi 1/ D D D XIFSF I JT UIF JOEJDBUPS GVODUJPO P P %JTUSJCVUFE /55'(. -FBSOJOH "T B TPDJBM OFUXPSL NBZ DPOUBJO NJMMJPOT PG VTFST BOE IVO ESFET PG NJMMJPOT PG TPDJBM UJFT CFUXFFO VTFST JU JT JNQSBDUJDBM UP MFBSO B /55'(. GSPN B IVHF EBUB VTJOH B TJOHMF NBDIJOF 4QFDJmDBMMZ UIFSF BSF UXP NBKPS QSPCMFNT JO PVS /55'(. NPEFM OBNFMZ NFNPSZ TQBDF BOE DPNQVUJOH UJNF 8F VTF B TQBSTF SFQSFTFOUBUJPO UP TPMWF UIF mSTU QSPCMFN 5P TQFFE VQ UIF DPNQVUJOH XF EFQMPZ UIF MFBSOJOH UBTL PO B EJTUSJCVUFE TZTUFN CBTFE PO UIF .1* .FTTBHF 1BTTJOH *OUFSGBDF .1* JT B NFTTBHFQBTTJOH MJCSBSZ JOUFSGBDF TQFDJmDBUJPO *O UIF NFTTBHFQBTTJOH QBSBMMFM QSPHSBNNJOH NPEFM EBUB JT NPWFE GSPN UIF BEESFTT TQBDF PG POF QSPDFTT UP UIBU PG BOPUIFS QSPDFTT UISPVHI DPPQFSBUJWF PQFSBUJPOT PO FBDI QSPDFTT #BTFE PO UIF NFTTBHF QBTTJOH TDIFNF XF FNQMPZ UIF NBTUFSTMBWF NPEFM ɩBU JT NBTUFS DBO BTTJHO UBTLT UP UIF TMBWFT DPNQVUFST BOE DPNCJOF UIF SFTVMUT JO UIF NBTUFS NBDIJOF 4QFDJmDBMMZ JO PVS MFBSOJOH BMHPSJUIN UIF UJNFDPOTVNJOH TUFQ MJFT JO UIF DBMDVMBUJPO PG ˛ ˇ ˛ A UIF HSBEJFOUT rMPH k rMPH ij rMPH ij XIJDI SFRVJSFT DPNQVUJOH UIF JOWFSTF PG UIF NBUSJY A NT NT /PUF JT B " NBUSJY XIJDI JT UPP1 MBSHF UP CF IFME JO NFNPSZ XIFO EFBM XJUI B MBSHF EBUB ɩVT XF DPNQVUF FBDI DPMVNO PG A! SFTQFDUJWFMZ CZ TPMWJOH UIF GPMMPXJOH MJOFBS FRVBUJPO i Axi bi ; 8 D 1 XIFSF xi SFQSFTFOUT UIF i DPMVNO PG A! BOE bi SFQSFTFOUT B NTEJNFOTJPO WFDUPS XJUI UIF iUI FMFNFOU 1 UIF PUIFS FMFNFOUT 0 ɩVT JO FBDI JUFSBUJPO UIF NBTUFS CSPBEDBTUT UIF QBSBNFUFST UP FBDI TMBWF BOE BTTJHOT UIF UBTLT UP TPMWF &RVBUJPO UP UIF TMBWFT BWFSBHFMZ "MM UIF TBMWF DPNQVUFST DBMDVMBUF A BOE TFOE UIF SFTVMUT CBDL UP UIF NBTUFS ɩF NBTUFS SFEVDFT BMM UIF EJT USJCVUFE SFTVMUT BOE CSPBEDBTUT UIF VQEBUFE QBSBNFUFST UP UIF TMBWFT BHBJO GPS UIF OFYU JUFSBUJPO ɩF EFUBJMFE EFTDSJQUJPO JT JO "MHPSJUIN &7"-6"5*0/ ɩF QSPQPTFE BQQSPBDI GPS TPDJBM BDUJPO QSFEJDUJPO JT WFSZ HFOFSBM BOE DBO CF BQQMJFE UP BOBMZ[F EJĊFSFOU LJOET PG TPDJBM OFUXPSLT *O UIJT TFDUJPO XF QSFTFOU WBSJPVT FYQFSJNFOUT UP FWBMVBUF UIF FĊFDUJWFOFTT BOE FċDJFODZ PG UIF QSPQPTFE BQQSPBDI "MM EBUB TFUT BOE DPEFT BSF QVCMJDMZ BWBJMBCMFņ ņ?iiT,ff `M2iKBM2`XQ`;fbiMif &7"-6"5*0/ *OQVU OVNCFS PG JUFSBUJPOT I BOE MFBSOJOH SBUF ( ' . zi ; ˛ ; ˇij ; &ij / 0VUQVU MFBSOFE QBSBNFUFST D f g f kg f g f g z y *OJUJBMJ[F D *OJUJBMJ[F ˛; ˇ; & SFQFBU .BTUFS CSPBEDBTUT z & 4UFQ mY z MFBSO ˛; ˇ; & i 1 GPS D UP * EP .BTUFS CSPBEDBTUT ˛; ˇ; & ˛ ; ˇ ; " $PNQVUF HSBEJFOU rMPH k rMPH ij rMPH ij FBDI 4MBWFT TFOE CBDL UIF DBMDVMBUJPO SFTVMUT .BTUFS SFEVDFT UIF SFTVMUT .BTUFS 6QEBUF ˛; ˇ; & FOE . 4UFQ mY ˛; ˇ; & MFBSO z .BTUFS 4PMWF UIF GPMMPXJOH MJOFBS FRVBUJPO .A I/z y X˛ C D C VOUJM DPOWFSHFODF "MHPSJUIN 1BSBMMFM FYQFDUBUJPO NBYJNJ[BUJPO &7"-6"5*0/ .&53*$4 %BUB 4FUT 8F QFSGPSN PVS FYQFSJNFOUT PO UISFF EJĊFSFOU HFOSFT PG SFBMXPSME EBUB TFUT 5XJUUFS B NJDSPCMPHHJOH EBUB TFU DSBXMFE GSPN UXJUUFSDPN 'MJDLS B EBUB TFU PG QIPUP TIBSJOH GSPN nJDLSDPN BOE "SOFU.JOFS B QVCMJDBUJPO EBUB TFU GSPN BSOFUNJOFSPSH t 5XJUUFS ɩF EBUB TFU JT DSBXMFE GSPN 5XJUUFS CZ TUBSUJOH GSPN UIF VTFS i$BSFM 1FESF DBSFMQF ESF wŇ POF PG )BJUJBO NPTU QPQVMBS SBEJP %+T XIP VTFE 5XJUUFS UP JOGPSN UIF XPSME BCPVU UIF FBSUIRVBLF XIJDI SBWBHFE IJT DPVOUSZ 8F FYUSBDU BMM GPMMPXFST > 11; 704 PG iDBSFMQF ESFw BOE UIF VTFST IF JT GPMMPXJOH BOE DPOUJOVF UIF QSPDFTT GPS FBDI FYUSBDUFE 5XJUUFS VTFS 8F GVSUIFS DSBXM BMM UXFFUT QPTUFE CZ UIF VTFST BT BUUSJCVUFT 'JOBMMZ B EBUB TFU VTFE GPS BDUJPO QSFEJDUJPO DPOTJTUT PG VTFST UJNF WBSZJOH GPMMPXJOH BOE GPMMPXFE SF MBUJPOTIJQT BOE UXFFUT CMPHT QPTUFE CZ UIF VTFST " MBSHFS EBUB TFU DPOTJTUJOH PG NJMMJPOT PG VTFST JT BMTP QVCMJDMZ BWBJMBCMF t 'MJDLS ɩF EBUB TFU JT DPMMFDUFE CZ $IB FU BM <> XIJDI DPOUBJOT VTFST GSJFOETIJQT CFUXFFO VTFST BOE GBWPSJUF QIPUPT t "SOFU.JOFS *U JT DPMMFDUFE GSPN "SOFU.JOFS <> BOE DPOTJTUT PG SFTFBSDIFST DPBVUIPS SFMBUJPOTIJQ BOE QVCMJDBUJPO QBQFST CZ UIF SFTFBSDIFST Ň?iiT,ffrrrX+ `2HT2/`2X+QKf 64&3 #&)"7*03 .0%&-*/( "/% 13&%*$5*0/ ɩF BDUJPO JO 5XJUUFS JT EFmOFE BT UIF UPQJD FH i)BJUJ &BSUIRVBLFw EJTDVTTFE CZ UIF VTFS .PSF TQFDJmDBMMZ XF TFMFDUFE TFWFSBM WFSZ SFMFWBOU LFZXPSET FH i)BJUJ w iFBSUIRVBLF w BOE iSFTDVFw *G B VTFS QPTUT B UXFFU DPOUBJOJOH UIF UPQJD LFZXPSE XF TBZ UIBU UIF VTFS QFSGPSNT UIF BDUJPO 8F DSBXMFE UIF EBUB GSPN +BOVBSZ UI XIFO UIF )BJUJ &BSUIRVBLF TUSVDL UP +BOVBSZ UI *O UIF 5XJUUFS EBUB XF WJFX POF EBZ BT B UJNF TUBNQ 'PS FYBNQMF JG B VTFS DBMMT GPS B EPOBUJPO GPS )BJUJ IJT GSJFOET NBZ SFTQPOE CZ SFUXFFUJOH JU PS QPTUJOH B TVQQPSUJOH NFTTBHF 'PS 'MJDLS IPXFWFS UIF BDUJPO EBUB JT EFmOFE BT XIFUIFS PS OPU B VTFS BEET B QIPUP UP IJT GBWPSJUF MJTU 'PS FYBNQMF JG B VTFS BEEFE B QIPUP UP IJT GBWPSJUF MJTU IJT GSJFOET NBZ BMTP BEE UIF QIPUP UP UIFJS GBWPSJUFT 8F FYUSBDU UIF IJTUPSJD BDUJPO MPH GSPN UP JO UIF EBUB TFU EJWJEJOH JOUP UJNF TUBNQT EBZT B TUBNQ ɩF BDUJPO PG UIF "SOFU.JOFS EBUB JT EFmOFE BT XIFUIFS B SFTFBSDIFS QVCMJTIFT B QBQFS BU B TQFDJmD WFOVF 'PS FYBNQMF JG B SFTFBSDIFS QVCMJTIFE B QBQFS BU ,%% JU NBZ JOnVFODF IJT DPMMBCPSBUPST UP QVCMJTI QBQFST BU ,%% BT XFMM ɩF EBUB JT TQMJU JOUP UJNF TUBNQT GPS FBDI ZFBS 0O BMM UIF UISFF EBUB TFUT UIF BUUSJCVUFT X JT EFmOFE BT UIF DPOUFOUT PG UXFFUT JOGPSNBUJPO PG QIPUPT PS SFMBUFE QVCMJDBUJPO WFOVFT PG UIF SFTFBSDIFS ɩF DPOUFOU PG FBDI UXFFU JT QSFQSPDFTTFE CZ B SFNPWJOH TUPQXPSET BOE OVNCFST C SFNPWJOH XPSET UIBU BQQFBS MFTT UIBO UISFF UJNFT JO UIF DPSQVT BOE D MPXFSDBTJOH UIF PCUBJOFE XPSET ɩFO GPS FBDI VTFS XF DPNCJOF BMM XPSET JO UIF SFNBJOJOH XPSET JO UIF UXFFUT QPTUFE CZ UIF VTFS BOE DSFBUF UIF BUUSJCVUF WFDUPS CZ UBLJOH XPSET BT GFBUVSFT &WBMVBUJPO .FUSJDT 5P FWBMVBUF PVS NFUIPE XF DPOTJEFS UIF GPMMPXJOH UISFF BOHMFT t 1SFEJDUJPO 8F FWBMVBUF UIF QSPQPTFE NPEFM JO UFSNT PG 1SFDJTJPO 3FDBMM BOE '.FBTVSF BOE DPNQBSF XJUI UIF CBTFMJOF NFUIPET UP WBMJEBUF UIF FĊFDUJWFOFTT PG UIF QSPQPTFE NPEFM t $16 UJNF *U JT UIF FYFDVUJPO FMBQTFE UJNF PG UIF NPEFM MFBSOJOH ɩJT TIPXT UIF TQFFEVQ PG UIF QBSBMMFM JNQMFNFOUBUJPO t $BTF TUVEZ 8F VTF TFWFSBM DBTF TUVEJFT BT UIF BOFDEPUBM FWJEFODF UP GVSUIFS EFNPOTUSBUF UIF FĊFDUJWFOFTT PG PVS NFUIPE 8F DPNQBSF UIF GPMMPXJOH NFUIPET GPS TPDJBM BDUJPO QSFEJDUJPO 47. 6UJMJ[FT VTFST BTTPDJBUFE BUUSJCVUFT BT XFMM BT UIFJS OFJHICPST TUBUFT UP USBJO B DMBTTJ mDBUJPO NPEFM BOE UIFO FNQMPZT UIF DMBTTJmDBUJPO NPEFM UP QSFEJDU VTFST BDUJPOT 'PS 47. XF FNQMPZ 47.MJHIUň XW3/ &NQMPZT B XFJHIUFEWPUF SFMBUJPOBM OFJHICPS DMBTTJmFS UP USBJO B DMBTTJmDBUJPO NPEFM CZ NBLJOH VTF PG OFUXPSL JOGPSNBUJPO *O QSFEJDUJPO UIF SFMBUJPOBM DMBTTJmFS FTUJNBUFT UIF BDUJPO TUBUF PG B VTFS CZ UIF XFJHIUFE NFBO PG IJT OFJHICPST /55'(. 6TFT UIF QSPQPTFE /55'(. NPEFM UP USBJO UIF BDUJPO USBDLJOH NPEFM BOE GVSUIFS VTFT UIF MFBSOFE NPEFM GPS QSFEJDUJPO ň?iiT,ffbpKHB;?iXDQ +?BKbXQ`;f &7"-6"5*0/ 5BCMF 1FSGPSNBODF PG BDUJPO QSFEJDUJPO XJUI EJĊFSFOU BQQSPBDIFT Data set Method Recall Precision F1-Measure SVM 10.41 16.71 13.85 wvRN 0.45 7.89 0.86 Twitter NTT-FGM 26.40 21.14 23.47 SVM 34.48 45.05 39.06 wvRN 60.02 48.81 53.84 Flickr NTT-FGM 56.18 45.80 50.47 SVM 10.19 21.62 13.85 wvRN 14.83 16.39 15.57 ArnetMiner NTT-FGM 31.14 44.28 36.57 "DDPSEJOH UP PVS QSFMJNJOBSZ FYQFSJNFOUT UIF / JO UIF (BVTTJBO EJTUSJCVUJPO EPFT OPU / 1 TJHOJmDBOUMZ JOnVFODF UIF QFSGPSNBODF ɩVT GPS TJNQMJDJUZ XF FNQJSJDBMMZ TFU D "MM UIF BMHPSJUINT BSF JNQMFNFOUFE VTJOH $ BOE BMM FYQFSJNFOUT BSF QFSGPSNFE PO B TFSWFS SVOOJOH 6CVOUV XJUI B ".% 1IFOPN UN 2VBE$PSF 1SPDFTTPS ()[ BOE (# NFNPSZ ɩF EJTUSJCVUFE MFBSOJOH BMHPSJUIN JT JNQMFNFOUFE VOEFS UIF .1* QBSBMMFM QSPHSBNNJOH NPEFMʼn 8F QFSGPSN UIF EJTUSJCVUFE USBJOJOH PO DPNQVUFS OPEFT $16 DPSFT XJUI ".% QSPDFTTPST ()[ BOE (# NFNPSZ JO UPUBM 8F TFU UIF NBYJNVN OVNCFS PG ˛ ˇ & 1e 3 JUFSBUJPOT BT BOE UIF UISFTIPME GPS UIF DIBOHF PG BOE UP $ 13&%*$5*0/ 1&3'03."/$& 0O BMM UIF UISFF EBUB TFUT XF VTF UIF IJTUPSJD VTFST BDUJPOT UP USBJO UIF BDUJPO USBDLJOH NPEFM BOE VTF UIF MFBSOFE NPEFM UP QSFEJDU UIF VTFST BDUJPOT JO UIF MBTU UJNF TUBNQ 5BCMF MJTUT UIF QSFEJDUJPO QFSGPSNBODF PG UIF EJĊFSFOU BQQSPBDIFT PO UIF UISFF EBUB TFUT XJUI UIF GPMMPXJOH PCTFSWBUJPOT 1FSGPSNBODF DPNQBSJTPO 0VS NFUIPE /55'(. DPOTJTUFOUMZ BDIJFWFT CFUUFS QFSGPSNBODF 10 DPNQBSJOH UP UIF CBTFMJOF NFUIPET *O UFSNT PG '.FBTVSF /55'(. DBO BDIJFWF B C JNQSPWFNFOU DPNQBSFE XJUI UIF 47. "U UIF TBNF UJNF /55'(. HJWFT SPCVTU SFTVMUT XIJMF UIF QFSGPSNBODF PG XW3/ JT WFSZ TFOTJUJWF UP UIF EBUB DIBSBDUFSJTUJDT XJUI UIF IJHIFTU ' .FBTVSF PO UIF 'MJDLS EBUB BOE FYUSFNFMZ MPX WBMVF JO UIF 5XJUUFS EBUB ɩJT JT CFDBVTF PO 'MJDLS UIF VTFST BDUJPO PG BEEJOH GBWPSJUF QIPUPT JT NBJOMZ JOnVFODFE CZ IFS GSJFOET BDUJPOT BOE XW3/ DBO CF WJFXFE BT B TJNQMF JOnVFODF NPEFM XIJDI NBLFT XW3/ NPTUMZ QSFEJDUT iw PO 'MJDLS CVU UIF 5XJUUFS OFUXPSL BCPVU i)BJUJ FBSUIRVBLFw JO PVS FYQFSJNFOU JT SFMBUJWFMZ TQBSTF BT B SFTVMU ʼn?iiT,ffrrrXK+bX MHX;Qpf`2b2 `+?fT`QD2+ibfKTB+?kf 64&3 #&)"7*03 .0%&-*/( "/% 13&%*$5*0/ 0.8 NTT−FGM NTT−FGM−I 0.6 NTT−FGM−CI 0.4 0.2 0 Twitter Flickr ArnetMiner 'JHVSF $POUSJCVUJPO PG EJĊFSFOU GBDUPS GVODUJPOT /55'(.* TUBOET GPS PVS NFUIPE CZ JHOPSJOH & 0 UIF JOnVFODF GBDUPS GVODUJPO D BOE /55'(.*$ TUBOET GPS /55'(. CZ JHOPSJOH CPUI JOnVFODF & 0 ˇ 0 GBDUPS BOE DPSSFMBUJPO GBDUPS D D XW3/ PVUQVUT BMM iw 8IJMF PVS BQQSPBDI TIPXT SPCVTU BOE DPOTJTUFOU QFSGPSNBODF PO BMM UIF EBUB TFUT XIJDI JT JNQPSUBOU GPS UIF FYUFOEBCJMJUZ PG UIF NFUIPET 'BDUPS DPOUSJCVUJPO BOBMZTJT /55'(. DBQUVSFT UISFF GBDUPST JOnVFODF DPSSFMBUJPO BOE QFSTPOBM JOUFSFTUTBUUSJCVUFT /FYU XF QFSGPSN BO BOBMZTJT UP FWBMVBUF UIF DPOUSJCVUJPO PG EJĊFSFOU GBDUPST EFmOFE JO PVS NPEFM *O QBSUJDVMBS XF SFNPWF UIPTF GBDUPST POF CZ POF mSTU JOnVFODF GBDUPS GVODUJPO GPMMPXFE CZ UIF DPSSFMBUJPO GBDUPS GVODUJPO BOE UIFO USBJO BOE FWBMVBUF UIF QSFEJDUJPO QFSGPSNBODF PG /55'(. 'JHVSF TIPXT UIF '.FBTVSF TDPSF BGUFS JHOPSJOH UIF GBDUPS GVODUJPOT 8F DBO PCTFSWF DMFBS ESPQ PO UIF QSFEJDUJPO QFSGPSNBODF XIJDI JOEJDBUFT UIBU PVS NFUIPE XPSLT XFMM CZ JOUFHSBUJOH UIF EJĊFSFOU GBDUPST GPS BDUJPO USBDLJOH QSFEJDUJPO BOE FBDI EFmOFE GBDUPS JO PVS NFUIPE DPOUSJCVUFT JNQSPWFNFOU JO UIF QFSGPSNBODF "MTP XF mOE UIBU UIF EFDSFBTF WBSJFT PO EJĊFSFOU EBUB TFUT 0O 5XJUUFS UIFSF JT B WFSZ MPX DPSSFMBUJPO CFUXFFO VTFST BDUJPOT CFDBVTF VTFST NBJOMZ QPTU UXFFUT PO 5XJUUFS CBTFE PO UIFJS QSFWJPVT FYQFSJFODF PS GSJFOET UXFFUT BOE SFMBUJWFMZ BDU JOEFQFOEFOUMZ BU B TBNF UJNF t -BUFOU BDUJPO TUBUFT ɩF MFBSOFE MBUFOU BDUJPO TUBUFT FTTFOUJBMMZ QMBZ B SPMF BT TNPPUIJOH 'JH VSF JMMVTUSBUFT TFWFSBM FYBNQMFT PG UIF MFBSOFE MBUFOU BDUJPO TUBUFT *U DBO CF FBTJMZ TFFO UIBU UIF MFBSOFE MBUFOU TUBUFT EFOPUFE BT UIF SFE DVSWF JT NVDI NPSF TNPPUIJOH UIBO UIF PSJHJOBM EJTDSFUF BDUJPOT EFOPUFE BT UIF CMBDL TUFQ MJOF XIJDI JOEJDBUFT UIBU MBUFOU BDUJPO TUBUFT DBO NPEFM UIF CJBT JO CJOBSZ BDUJPOT ɩJT JT EFTJSBCMF GPS NPTU QSFEJDUJPODMBTTJmDBUJPO UBTLT BOE GVSUIFS DPOmSNT VT UIF BEWBOUBHF PG UIF QSPQPTFE /55'(. NPEFM &''*$*&/$: 1&3'03."/$& 8F OPX FWBMVBUF UIF FċDJFODZ PG PVS BQQSPBDI CZ DPNQBSJOH UIF EJTUSJCVUFE MFBSOJOH BMHPSJUIN XJUI UIF CBTJD POF PO UIF UISFF EBUB TFUT &7"-6"5*0/ 1 1 1 0.5 0.5 0.5 0 0 0 2 4 6 8 10 12 14 2 4 6 8 10 12 2 4 6 8 Twitter Flickr ArnetMiner 'JHVSF &YBNQMF MBUFOU BDUJPO TUBUFT 5BCMF MJTUT UIF $16 UJNF SFRVJSFE GPS MFBSOJOH UIF /55'(. NPEFM PO B TJOHMF NB DIJOF #BTJD /55'(. BOE CZ UIF EJTUSJCVUFE MFBSOJOH BMHPSJUIN VTJOH mWF DPNQVUFS OPEFT FBDI GPVS DPSFT ɩF EJTUSJCVUFE MFBSOJOH BMHPSJUIN UZQJDBMMZ BDIJFWFT B TJHOJmDBOU SFEVDUJPO > 17 PG UIF $16 UJNF 'PS FYBNQMF PO "SOFU.JOFS XF PCUBJO B TQFFEVQ " BOE PO 'MJDLS UIF > 13 EJTUSJCVUFE MFBSOJOH BMHPSJUIN SFTVMUT JO B TQFFEVQ " 5BCMF &ċDJFODZ QFSGPSNBODF PO UIF UISFF EBUB TFUT mWF DPNQVUFS OPEFT FBDI GPVS DPSFT Data Set Basic NTT-FGM Distributed NTT-FGM Twitter 77.7hr 7.0hr Flickr 9.14hr 0.68hr ArnetMiner 100min 6.2min 8F BMTP FWBMVBUF UIF TQFFEVQ PG UIF EJTUSJCVUFE MFBSOJOH BMHPSJUIN VTJOH EJĊFSFOU OVN CFST PG DPNQVUFS OPEFT DPSFT UP FWBMVBUF UIF DPTU PG NFTTBHF QBTTJOH ɩF TQFFEVQ BT TIPXO JO 'JHVSF B JT DMPTF UP UIF QFSGFDU MJOF JO UIF CFHJOOJOH "MUIPVHI JU EFDSFBTFT JO > 10 FWJUBCMZ BT UIF OVNCFS PG DPSFT JODSFBTFT JU TDBMFT WFSZ XFMM XJUI " TQFFEVQ VTJOH UISFBET 8F GVSUIFS BOBMZ[F IPX UIF OFUXPSL TUSVDUVSF BĊFDUT UIF FċDJFODZ PG UIF MFBSOJOH BMHP SJUINE 8F HFOFSBUF B TZOUIFUJD EBUB TFU GPS UIJT FYQFSJNFOUT CZ WBSZJOH UIF EFOTJUZ PG UIF OFUXPSL MPH jV j *U DBO CF TFFO GSPN 'JHVSF C BOE D UIBU BT UIF EFOTJUZ YBYJT JODSFBTFT CPUI CBTJD j j MFBSOJOH BOE UIF EJTUSJCVUFE MFBSOJOH BMHPSJUIN OFFE NPSF $16 UJNF UP USBJO UIF /55'(. 14 15 NPEFM CVU UIF TQFFEVQ PG UIF EJTUSJCVUFE BMHPSJUIN JT DPOTJTUFOUMZ IJHI BCPVU $ " VTJOH UISFBET 26"-*5"5*7& $"4& 456%: /PX XF QSFTFOU UISFF DBTF TUVEJFT UP EFNPOTUSBUF UIF FĊFDUJWFOFTT PG UIF QSPQPTFE NPEFM 64&3 #&)"7*03 .0%&-*/( "/% 13&%*$5*0/ 20 4 perfect CPU time 1 core our method CPU time 5x4 cores 15 3 s) 5 10 2 Speedup (x) Speedup 5 (10 CPU time 1 0 5 10 15 20 1 2 3 4 5 B 4QFFEVQ WT DPSFT C $16 UJNF WT OFUXPSL EFOTJUZ 15 10 Speedup (x) Speedup 5 0 1 2 3 4 5 D 4QFFEVQ WT OFUXPSL EFOTJUZ 'JHVSF 4QFFEVQ SFTVMUT *O HSBQI B XF FWBMVBUF UIF TQFFEVQ WBSJFE XJUI UIF OVNCFS PG DPSFT ɩF YBYJT 1 $16 UJNF DPSF TUBOET GPS UIF OVNCFS PG DPSFT UIF ZBYJT SFQSFTFOUT UIF TQFFEVQ n *O HSBQI C XF FWBMVBUF UIF E $16 UJNF DPSFTE $16 UJNF XJUI EJĊFSFOU OFUXPSL EFOTJUZ EFmOFE BT MPH jV j ɩF YBYJT JT MPH jV j UIF ZBYJT JT UIF SVOOJOH UJNF j j j j E JO TFDPOET *O HSBQI D XF FWBMVBUF UIF TQFFEVQ XJUI EJĊFSFOU OFUXPSL EFOTJUZɩF YBYJT JT MPH jV j UIF ZBYJT j j JT UIF TQFFEVQ i)BJUJ &BSUIRVBLFw ɩF )BJUJ &BSUIRVBLF XBT B EFWBTUBUJOH FBSUIRVBLF MFBWJOH UIF DPVOUSZ JO TIBNCMFT 8F VTF PVS SFTVMUT UP BOBMZ[F QFPQMFT BDUJPOT SFMBUFE UP UIF DBUBTUSPQIF PO 5XJUUFS 5BCMF MJTUT TFWFSBM FYBNQMF UXFFUT BCPVU UIF i)BJUJ &BSUIRVBLFw 8F TFF UIBU UIFTF UXFFUT BSF BCPVU B DBMMGPSEPOBUJPO CZ UIF GBNPVT UFOOJT QMBZFS i4FSFOB 8JMMJBNT TFSFOBKXJMMJBNT w ɩF DBMMGPS NFTTBHF XBT TPPO SFUXFFUFE CZ iBDUTPG'BJUICMPHw BOE iNBEBNFBMJw PO UIFJS PXO NJ DSPCMPHT BOE B CJU MBUFS UIF )BJUJBO SBEJP IPTU iDBSFMQFESFw BEEFE B DPNNFOU PO 4FSFOB 8JMMJBNTT 5XJUUFS ɩFTF 5XJUUFS VTFST BSF POF PG UIF NPTU JOnVFOUJBM VTFST BOE UIFJS BDUJPOT PO i)BJUJ &BSUI RVBLFw RVJDLMZ TQSFBE PO 5XJUUFS XJUI SFUXFFUT BOE SFQMJFT #FDBVTF PG UIJT $BSFM 1FESF SFDFJWFE B TQFDJBM iIVNBOJUBSJBOw BXBSE BU UIF TFDPOE BOOVBM i4IPSUZ "XBSETw JO /FX :PSL 8JUI UIF QSPQPTFE NPEFM XF DBO JEFOUJGZ UIF NPTU JOnVFOUJBM VTFST XIPTF BDUJPOT DBO JOEVDF B MBSHF DBT DBEF GPMMPXJOHT BOE USBDL UIF JOGPSNBUJPO nPXT WJB TPDJBM UJFT XJUI B IJHI JOnVFODF TDPSF PS DPSSFMBUJPO TDPSF *O UIJT XBZ XF DBO VOEFSTUBOE IPX UIF JOnVFODF TQSFBET BNPOH QFPQMF &7"-6"5*0/ 5BCMF "DUJPO USBDLJOH PO 5XJUUFS GPS i)BJUJ &BSUIRVBLFw Date/User Tweet 6:03 PM Jan 16th Tennis pro Roger Federer is joining forces with Rafael Nadal & by extratv @serenajwilliams to raise money for Haiti. http://su.pr/1E3MDU 5:23 AM Jan 17th Hey. Please, check out my foundation website: www.theswf.org by serenajwilliams to help those in Haiti! 6:48 AM Jan 17th RT @SIXTWELVEMAG: RT @serenajwilliams: Hey. Please, by madameali check out my foundation website: www.theswf.org to help those in Haiti! 7:34 AM Jan 17th RT @serenajwilliams: Hey. Please, check out my foundation by actsofFaithblog website: www.theswf.org to help those in Haiti! 2:50 PM Jan 17th @serenajwilliams Through Her 92k Mission has set a goal to con- by carelpedre tribute donations to the victims in #haiti. Visit www.theswf.org and donate 5BCMF 1SFEJDUJPO PO XIP XJMM QVCMJTI PO PS TVCNJU UP ,%% ɩF FYBNQMFT BSF TFMFDUFE GSPN UIF UPQ SFTFBSDIFST QSFEJDUFE CZ UIF /55'(. NPEFM Jiawei Han Christos Faloutsos Philip S. Yu Pedro Domingos Lise Getoor Jon M. Kleinberg Frequent Hang Li ChengXiang Zhai Wei-Ying Ma Lise Getoor Jure Leskovec Qiaozhu Mei Bing Liu Jian Pei Ravi Kumar Huijia Zhu Dimitrios Kotsakos Zi Yang New Noman Mohammed Caimei Lu Quanquan Gu Zhili Guo i1VCMJDBUJPO BU ,%%w 8F DBO BMTP VTF UIF /55'(. NPEFM UP USBDL BOE QSFEJDU XIP XJMM QVCMJTI PS TVCNJU QBQFST UP ,%% 8F USBJO UIF /55'(. NPEFM VTJOH UIF "SOFU.JOFS EBUB CFGPSF BOE VTF UIF MFBSOFE NPEFM UP QSFEJDU UIF MBUFOU BDUJPO TUBUF PG FBDI SFTFBSDIFS BOE mOBMMZ PCUBJO B MJTU PG SFTFBSDIFST SBOLFE CZ UIF MBUFOU TUBUF 5BCMF MJTUT B GFX SFQSFTFOUBUJWF FYBNQMFT TFMFDUFE GSPN UIF UPQ SBOLFE SFTFBSDIFST 8F TFF UIBU PVS BQQSPBDI DBOOPU POMZ mOE TPNF GBNPVT SFTFBSDIFST CVU BMTP EJTDPWFS TPNF iOFXDPNFSTw UP UIF ,%% DPNNVOJUZ ɩF mSTU SPX MJTUT TFWFSBM XFMMFTUBCMJTIFE SFTFBSDIFST XIP IBWF QVCMJTIFE B MPU PO ,%% ɩF TFDPOE SPX TIPXT TFWFSBM iOFXw SFTFBSDIFST XIP IBWF OP QBQFS PS POMZ GFX QBQFST QVCMJTIFE BU ,%% i$PSSFMBUJPO CFUXFFO 3FTFBSDIFSTw #BTFE PO UIF MFBSOFE /55'(. NPEFM XF DBO HFO FSBUF B DPSSFMBUJPOJOnVFODF NBQ GPS CFUUFS VTFS BOBMZTJT 'JHVSF TIPXT BO FYBNQMF DPS SFMBUJPO NBQ CFUXFFO SFTFBSDIFST ɩF TUSFOHUI PG UIF MJOL CFUXFFO UXP SFTFBSDIFST JOEJDBUFT UIF DPSSFMBUJPO TDPSF 8F TFF TPNF SFTFBSDIFST IBWF TUSPOH DPSSFMBUJPO CFDBVTF UIFZ DPBVUIPSFE RVJUF B GFX QBQFST FH +JBXFJ )BO BOE 1IJMJQ :V 8IJMF PVS BQQSPBDI BMTP mOET TPNF SF TFBSDIFST IBWF TUSPOH DPSSFMBUJPO FH 3BWJ ,VNBS BOE $ISJTUPT 'BMPVUTPT BMUIPVHI UIFZ POMZ 64&3 #&)"7*03 .0%&-*/( "/% 13&%*$5*0/ 'JHVSF &YBNQMF DPSSFMBUJPO BOBMZTJT CFUXFFO SFTFBSDIFST ɩF TUSFOHUI SFQSFTFOUT UIF DPSSFMBUJPO TDPSF CFUXFFO UXP SFTFBSDIFST DPBVUIPSFE POF PS UXP QBQFS T ɩF EJTDPWFSFE DPSSFMBUJPO DBO QPUFOUJBMMZ CFOFmU NBOZ BQ QMJDBUJPOT TVDI BT MJOL QSFEJDUJPO .PSF DPSSFMBUJPOJOnVFODF BOBMZTJT SFTVMUT DBO CF GPVOE BU ?iiT,ff `M2iKBM2`XQ`;fbiMif 46.."3: *O UIJT DIBQUFS XF TUVEZ BO JOUFSFTUJOH QSPCMFN PG VTFS CFIBWJPS NPEFMJOH BOE QSFEJDUJPO JO EZOBNJD OFUXPSLT 8F QSPQPTF B OPJTF UPMFSBOU UJNFWBSZJOH GBDUPS HSBQI NPEFM /55'(. UP GPSNBMJ[F UIJT QSPCMFN JO B VOJmFE NPEFM ɩSFF GBDUPS GVODUJPOT BSF EFmOFE UP DBQUVSF UIF JOUVJUJPOT EJTDPWFSFE JO PVS PCTFSWBUJPO BOE BO FċDJFOU BMHPSJUIN JT QSFTFOUFE UP MFBSO UIF USBDL JOH NPEFM " EJTUSJCVUFE MFBSOJOH BMHPSJUIN IBT CFFO JNQMFNFOUFE VOEFS UIF NFTTBHFQBTTJOH QBSBMMFM QSPHSBNNJOH NPEFM 8F FYQFSJNFOU PO UISFF EJĊFSFOU HFOSFT PG EBUB TFUT BOE GVSUIFS QSFTFOU B DBTF TUVEZ PO TPDJBM BDUJPO QSFEJDUJPO VTJOH UIF MFBSOFE /55'(. NPEFM &YQFSJ NFOUBM SFTVMUT PO UISFF EJĊFSFOU UZQFT PG EBUB TFUT EFNPOTUSBUF UIBU UIF QSPQPTFE BQQSPBDI DBO FĊFDUJWFMZ NPEFM UIF TPDJBM BDUJPOT BOE DMFBSMZ PVUQFSGPSNT TFWFSBM BMUFSOBUJWF NFUIPET GPS BDUJPO QSFEJDUJPO ɩF EJTUSJCVUFE MFBSOJOH BMHPSJUIN BMTP IBT B HPPE TDBMBCJMJUZ QFSGPSNBODF $ )"15&3 "SOFU.JOFS %FFQ .JOJOH GPS "DBEFNJD 4PDJBM /FUXPSLT *O UIJT DIBQUFS XF VTF BO POMJOF TZTUFN "SOFU.JOFS <> UP FYQMBJO IPX UIF UFDIOPMPHJFT QSFTFOUFE JO QSFWJPVT TFDUJPOT IFMQ SFBM BQQMJDBUJPOT "SOFU.JOFS JT B TZTUFN BJNJOH UP FYUSBDU BOE EFFQ BOBMZ[F BDBEFNJD TPDJBM OFUXPSLT 4QFDJmDBMMZ JU QSPWJEFT GPVS LFZ GVODUJPOT FY USBDUJPO PG B SFTFBSDIFS TPDJBM OFUXPSL BVUPNBUJDBMMZ GSPN UIF FYJTUJOH 8FC JOUFHSBUJPO PG UIF QVCMJDBUJPOT JOUP UIF TPDJBM OFUXPSL GSPN FYJTUJOH EJHJUBM MJCSBSJFT NPEFMJOH PG UIF XIPMF BDB EFNJD TPDJBM OFUXPSL BOE FYQFSUJTF PSJFOUFE TFBSDI VTJOH TPDJBM OFUXPSL ɩF TZTUFN IBT CFFO JO PQFSBUJPO TJODF 4P GBS JU IBT FYUSBDUFE JOGPSNBUJPO PG NPSF UIBO SFTFBSDIFST BOE QVCMJDBUJPOT GSPN UIF *OUFSOFU ɩF TZTUFN IBT BUUSBDUFE JOEFQFOEFOU *1 BDDFTTFT GSPN DPVOUSJFT BOE SFHJPOT JO UIF XPSME VQ UP 07&37*&8 1SFWJPVTMZ TFWFSBM JTTVFT JO BDBEFNJD TPDJBM OFUXPSL IBWF CFFO JOWFTUJHBUFE BOE TZTUFNT XFSF EFWFMPQFE FH .JDSPTPGU "DBEFNJD 4FBSDI ¤ 3FYBJOGP © BOE (PPHMF 4DIPMBSņ )PXFWFS NPTU PG UIF QSPCMFNT BSF JOWFTUJHBUFE TFQBSBUFMZ BOE UIF NFUIPET QSPQPTFE BSF OPU TVċDJFOU GPS NJOJOH UIF XIPMF BDBEFNJD TPDJBM OFUXPSL ɩJT JT CFDBVTF PG UXP SFBTPOT -BDL PG TFNBOUJDCBTFE JOGPSNBUJPO ɩF TPDJBM JOGPSNBUJPO PCUBJOFE TPMFMZ GSPN UIF VTFS FOUFSFE QSPmMF PS FYUSBDUFE CZ VTJOH IFVSJTUJDT JT TPNFUJNFT JODPNQMFUF PS JODPOTJTUFOU 6TFST EP OPU mMM TPNF JOGPSNBUJPO NFSFMZ CFDBVTF UIFZ BSF VOXJMMJOH UP mMM UIF JOGPSNBUJPO -BDL PG B VOJmFE NPEFMJOH BQQSPBDI GPS FċDJFOU NJOJOH UIF TPDJBM OFUXPSL 5SBEJUJPOBMMZ EJĊFSFOU UZQFE JOGPSNBUJPO TPVSDFT JO UIF BDBEFNJD TPDJBM OFUXPSL XFSF NPEFMFE JOEJWJEVBMMZ BOE UIVT EFQFOEFODJFT CFUXFFO UIFN DBOOPU CF DBQUVSFE )PXFWFS EFQFOEFODJFT FWFO TUSPOH EFQFOEFODJFT FYJTU CFUXFFO UIF TPDJBM EBUB )JHI RVBMJUZ TFBSDI TFSWJDFT OFFE UP DPOTJEFS UIF JOUSJOTJD EFQFOEFODJFT CFUXFFO UIF EJĊFSFOU JOGPSNBUJPO TPVSDFT *O "SOFU.JOFS XF USZ UP BEESFTT UIF BCPWF DIBMMFOHFT JO OPWFM BQQSPBDIFT 0VS PCKFDUJWF JO UIJT TZTUFN JT UP BOTXFS GPVS RVFTUJPOT )PX EPFT POF BVUPNBUJDBMMZ FYUSBDUDSFBUF UIF SFTFBSDIFS QSPmMF GSPN UIF FYJTUJOH 8FC )PX EPFT POF JOUFHSBUF UIF FYUSBDUFE JOGPSNBUJPO ?iiT,ff KBM2`XQ`; ¤?iiT,ff + /2KB+X`2b2 `+?XKB+`QbQ7iX+QKf ©IUUQSFYBJOGP ņ?iiT,ffb+?QH `X;QQ;H2X+QK "3/&5.*/&3 %&&1 .*/*/( '03 "$"%&.*$ 40$*"- /&5803,4 'JHVSF "SOFU.JOFS PWFSWJFX ɩF MFGU mHVSF MJTUT UIF NBKPS GVODUJPOBMJUJFT JO "SOFU.JOFS BOE UIF SJHIU mHVSF TIPXT VTFS EJTUSJCVUJPOT JO UIF XPSME JF SFTFBSDIFST QSPmMFT BOE QVCMJDBUJPOT GSPN EJĊFSFOU TPVSDFT )PX EPFT POF NPEFM UIF EJĊFSFOU UZQFE JOGPSNBUJPO TPVSDFT JO B VOJmFE NPEFM )PX EPFT POF QSPWJEF QPXFSFE TFBSDI TFSWJDFT JO UIF DPOTUSVDUFE OFUXPSL 'PS UIF mSTU RVFTUJPO XF FYUFOE '0"' 'SJFOE0G"'SJFOE POUPMPHZ <> BT UIF TDIFNB BOE FNQMPZ B VOJmFE BQQSPBDI CBTFE PO $POEJUJPOBM 3BOEPN 'JFMET $3'T UP FYUSBDU UIF QSP mMF PG B SFTFBSDIFS GSPN UIF 8FC 'PS UIF TFDPOE RVFTUJPO XF JOUFHSBUF UIF FYUSBDUFE SFTFBSDIFS QSPmMFT BOE QVCMJDBUJPOT GSPN POMJOF EJHJUBM MJCSBSJFT 8F QSPQPTF B VOJmFE QSPCBCJMJTUJD GSBNF XPSL GPS EFBMJOH XJUI UIF OBNF BNCJHVJUZ QSPCMFN JO UIF JOUFHSBUJPO 'PS UIF UIJSE RVFTUJPO XF QSPQPTF UISFF HFOFSBUJWF QSPCBCJMJTUJD NPEFMT GPS TJNVMUBOFPVTMZ NPEFMJOH DIBSBDUFSJTUJDT PG EPDVNFOU DPOUFOUT BVUIPS JOUFSFTUT BOE DPOGFSFODF UIFNFT 'PS UIF MBTU RVFTUJPO XF CBTFE PO UIF NPEFMJOH SFTVMUT QSPQPTF TFWFSBM NFUIPET GPS FYQFSUJTF TFBSDI TFBSDIJOH FYQFSUJTF BVUIPST DPOGFSFODFKPVSOBMT BOE QBQFST BTTPDJBUJPO TFBSDI BVUIPS JOUFSFTUT mOEJOH BOE BDBEFNJD TVH HFTUJPO "SDIJUFDUVSF 'JHVSF TIPXT UIF BSDIJUFDUVSF PG UIF TZTUFN ɩF TZTUFN NBJOMZ DPOTJTUT PG mWF NBJO DPNQPOFOUT &YUSBDUJPO 'PDVTFT PO BVUPNBUJDBMMZ FYUSBDUJOH UIF SFTFBSDIFS QSPmMF GSPN UIF 8FC *U mSTU DPMMFDUT BOE JEFOUJmFT POFT SFMFWBOU QBHFT FH IPNFQBHFT PS JOUSPEVDJOH QBHFT GSPN UIF 8FC UIFO VTFT B VOJmFE BQQSPBDI UP FYUSBDU EBUB GSPN UIF JEFOUJmFE EPDVNFOUT *U BMTP FYUSBDUT QVCMJDBUJPOT GSPN POMJOF EJHJUBM MJCSBSJFT VTJOH IFVSJTUJD SVMFT *OUFHSBUJPO *OUFHSBUFT UIF FYUSBDUFE SFTFBSDIFST QSPmMFT BOE UIF FYUSBDUFE QVCMJDBUJPOT *U FNQMPZT UIF SFTFBSDIFS OBNF BT UIF JEFOUJmFS " QSPCBCJMJTUJD GSBNFXPSL IBT CFFO QSPQPTFE UP EFBM XJUI UIF OBNF BNCJHVJUZ QSPCMFN JO UIF JOUFHSBUJPO ɩF JOUFHSBUFE EBUB JT TUPSFE JOUP B SFTFBSDIFS OFUXPSL LOPXMFEHF CBTF 3/,# 4UPSBHF BOE "DDFTT 1SPWJEFT TUPSBHF BOE JOEFYJOH GPS UIF FYUSBDUFEJOUFHSBUFE EBUB JO UIF 3/,# 4QFDJmDBMMZ GPS TUPSBHF JU FNQMPZT +FOB <> B UPPM UP TUPSF BOE SFUSJFWF POUPMPHJDBM 07&37*&8 5. Search Services Hot-topic finding Expert search Author interest finding Paper search Survey paper finding Conference search Academic suggestion Association search 4. Modeling Modeling Academic Social Network 3. Storage and Access Access Interface Indexing Storage RNKB Metadata 2. Integration Name disambiguation 1. Extraction Profile extraction Publication collection Document Collection Papers Web DBLP 'JHVSF "SDIJUFDUVSF PG "SOFU.JOFS EBUB GPS JOEFYJOH JU FNQMPZT UIF JOWFSUFE mMF JOEFYJOH NFUIPE BO FYJTUJOH NFUIPE JO JOGPSNBUJPO SFUSJFWBM <> .PEFMJOH 6UJMJ[FT B HFOFSBUJWF QSPCBCJMJTUJD NPEFM UP TJNVMUBOFPVTMZ NPEFM UIF EJĊFSFOU UZQFE JOGPSNBUJPO TPVSDFT *U FTUJNBUFT B NJYUVSF UPQJD EJTUSJCVUJPO BTTPDJBUFE XJUI UIF EJĊFSFOU JOGPSNBUJPO TPVSDFT "3/&5.*/&3 %&&1 .*/*/( '03 "$"%&.*$ 40$*"- /&5803,4 Fax Research_Interest Phone Affiliation Title Address Postion Publication_venue Email Person Photo Start_page Homepage End_page Name authored_by Publication author Researcher Date Phddate Bsdate Publisher Phduniv Bsuniv Phdmajor Msdate Download_URL Msuniv Bsmajor Msmajor 'JHVSF ɩF TDIFNB PG UIF SFTFBSDIFS QSPmMF 4FBSDI 4FSWJDFT 1SPWJEFT TFWFSBM QPXFSFE TFBSDI TFSWJDFT CBTFE PO UIF NPEFMJOH SFTVMUT FY QFSUJTF BVUIPS TFBSDI QBQFS TFBSDI DPOGFSFODF TFBSDI BOE QFPQMF BTTPDJBUJPO TFBSDI *U BMTP QSPWJEFT PUIFS TFSWJDFT GPS TVQQPSUJOH BEWBODFE BQQMJDBUJPOT JODMVEJOH IPUUPQJD mOEJOH BVUIPS JOUFSFTUJOH mOEJOH TVSWFZ QBQFS mOEJOH BOE BDBEFNJD TVHHFTUJPO 'PS TFWFSBM GFBUVSFT JO UIF TZTUFN FH FYUSBDUJPO PG SFTFBSDIFST QSPmMFT OBNF EJTBNCJHVB UJPO JO UIF JOUFHSBUJPO BDBEFNJD NPEFMJOH BOE TFWFSBM TFBSDI TFSWJDFT JF FYQFSUJTF TFBSDI BOE BTTPDJBUJPO TFBSDI XF QSPQPTF OFX BQQSPBDIFT USZJOH UP PWFSDPNF UIF ESBXCBDLT UIBU FYJTU JO UIF DPOWFOUJPOBM NFUIPET 'PS TPNF PUIFS GFBUVSFT FH TUPSBHF BOE BDDFTT XF VUJMJ[F UIF TUBUF PGUIFBSU NFUIPET ɩJT JT CFDBVTF UIFTF JTTVFT IBWF CFFO JOUFOTJWFMZ JOWFTUJHBUFE QSFWJPVTMZ BOE UIF DPOWFOUJPOBM NFUIPET DBO SFTVMU JO HPPE QFSGPSNBODFT *O UIF SFTU PG UIF CPPL XF XJMM JOUSPEVDF JO EFUBJM UIF DIBMMFOHFT XF BSF EFBMJOH XJUI BOE EFTDSJCF PVS NFUIPET 8F mSTU FYQMBJO PVS BQQSPBDI UP SFTFBSDIFS QSPmMJOH BOE UIFO EFTDSJCF UIF QSPCBCJMJTUJD GSBNFXPSL UP OBNF EJTBNCJHVBUJPO /FYU XF QSPQPTF UISFF HFOFSBUJWF QSPCBCJMJTUJD NPEFMT UP NPEFM UIF DPOTUSVDUFE BDBEFNJD TPDJBM OFUXPSL BOE QSFTFOU TFWFSBM TFBSDI TFSWJDFT QSPWJEFE JO "SOFU.JOFS CBTFE PO UIF NPEFMJOH SFTVMUT 3&4&"3$)&3 130'*-& &953"$5*0/ 8F EFmOF UIF TDIFNB PG UIF SFTFBSDIFS QSPmMF BT TIPXO JO 'JHVSF CZ FYUFOEJOH UIF '0"' POUPMPHZ <> *O UIF QSPmMF QSPQFSUJFT BOE UXP SFMBUJPOT BSF EFmOFE < > *U JT OPOUSJWJBM UP QFSGPSN UIF SFTFBSDIFS OFUXPSL FYUSBDUJPO GSPN UIF 8FC 8F QSPEVDFE TUBUJTUJDT PO SBOEPNMZ TFMFDUFE 1; 000 SFTFBSDIFST 8F PCTFSWFE UIBU 85:62 PG UIF SFTFBSDIFST BSF GBDVMUJFT GSPN VOJWFSTJUJFT BOE 14:38 BSF GSPN DPNQBOZ SFTFBSDI DFOUFST 'PS SFTFBSDIFST GSPN UIF TBNF DPNQBOZ UIFZ PGUFO IBWF B UFNQMBUFCBTFE IPNFQBHF )PXFWFS EJĊFSFOU DPNQBOJFT IBWF BCTPMVUFMZ EJĊFSFOU UFNQMBUFT 'PS SFTFBSDIFST GSPN VOJWFSTJUJFT UIF MBZPVU BOE DPOUFOU PG UIF IPNFQBHFT WBSZ MBSHFMZ EFQFOEJOH PO UIF BVUIPST 8F IBWF BMTP GPVOE UIBU 71:88 PG UIF 3&4&"3$)&3 130'*-& &953"$5*0/ All Token Term Token Term Feature Pattern Feature tive word tive word nary Term If the token contains a base noun phrase ognized by (opencvlibrary.sf.net) The number of “unique color”The number of bits for per pixel #Line break How many line breaks before Content Feature WordMorphologySize Morphology of the word Word in the token The size of the image Positive word If the token contains a pre-defined posi- Negative word If the token contains a pre-defined nega- ALT Words in “alt” attribute of the image Dictionary If the token contains a word in a dictio- Height/width ratio the ratio of height/width of the image Special token If the token contains a special pattern Face detection If the image contains a person face rec- Image formatImage color The format of the image (e.g., ”JPG”) Name If the token contains the researcher name Filename Words in the filename $POUFOU GFBUVSFT QBUUFSO GFBUVSFT BOE UFSN GFBUVSFT BCMF Image Token Standard Token 5 "3/&5.*/&3 %&&1 .*/*/( '03 "$"%&.*$ 40$*"- /&5803,4 1; 000 XFC QBHFT BSF SFTFBSDIFST IPNFQBHFT BOE UIF SFTU BSF QBHFT JOUSPEVDJOH UIF SFTFBSDIFST $IBSBDUFSJTUJDT PG UIF UXP UZQFT PG QBHFT TJHOJmDBOUMZ EJĊFS GSPN FBDI PUIFS 8F BOBMZ[FE UIF DPOUFOU PG UIF XFC QBHFT BOE GPVOE UIBU BCPVU 40 PG UIF QSPmMF QSPQFS UJFT BSF QSFTFOUFE JO UBCMFT PS MJTUT BOE BCPVU 60 BSF QSFTFOUFE JO OBUVSBM MBOHVBHF UFYU ɩJT BMTP NFBOT B NFUIPE XJUIPVU VTJOH UIF HMPCBM DPOUFYU JOGPSNBUJPO JO UIF QBHF XPVME CF JOFĊFDUJWF " TUBUJTUJDBM TUVEZ BMTP VOWFJMT UIBU TUSPOH EFQFOEFODJFT FYJTU CFUXFFO EJĊFSFOU QSPmMF QSPQFSUJFT 'PS FYBNQMF UIFSF BSF 1; 325 DBTFT 14:54 JO PVS EBUB UIBU FYUSBDUJPO PG UIF QSPQFSUZ OFFET UP VTF UIF FYUSBDUJPO SFTVMUT PG UIF PUIFS QSPQFSUJFT "O JEFBM NFUIPE TIPVME DPOTJEFS QSPDFTTJOH BMM UIF TVCUBTLT UPHFUIFS " 6/*'*&% "1130"$) 50 130'*-*/( ɩF QSPQPTFE BQQSPBDI DPOTJTUT PG UISFF TUFQT SFMFWBOU QBHF JEFOUJmDBUJPO QSFQSPDFTTJOH BOE UBHHJOH *O SFMFWBOU QBHF JEFOUJmDBUJPO HJWFO B SFTFBSDIFS OBNF XF mSTU HFU B MJTU PG XFC QBHFT CZ B TFBSDI FOHJOF XF VTFE (PPHMF "1* BOE UIFO JEFOUJGZ UIF IPNFQBHFJOUSPEVDJOH QBHF VTJOH B DMBTTJmFS 8F VTF 4VQQPSU 7FDUPS .BDIJOFT 47. <> BT UIF DMBTTJmDBUJPO NPEFM BOE EFmOF GFBUVSFT TVDI BT XIFUIFS UIF UJUMF PG UIF QBHF DPOUBJOT UIF QFSTPO OBNF BOE XIFUIFS UIF 63- BEESFTT QBSUMZ DPOUBJOT UIF QFSTPO OBNF ɩF QFSGPSNBODF PG UIF DMBTTJmFS JT 92:39 JO UFSNT PG 'NFBTVSF *O QSFQSPDFTTJOH " XF TFQBSBUF UIF UFYU JOUP UPLFOT BOE # XF BTTJHO QPTTJCMF UBHT UP FBDI UPLFO ɩF UPLFOT GPSN UIF CBTJD VOJUT BOE UIF QBHFT GPSN UIF TFRVFODFT PG VOJUT JO UIF UBHHJOH QSPCMFN *O UBHHJOH HJWFO B TFRVFODF PG VOJUT XF EFUFSNJOF UIF NPTU MJLFMZ DPSSF TQPOEJOH TFRVFODF PG UBHT CZ VTJOH B USBJOFE UBHHJOH NPEFM ɩF UZQF PG UIF UBHT DPSSFTQPOET UP UIF QSPQFSUZ EFmOFE JO 'JHVSF *O UIJT DIBQUFS BT UIF UBHHJOH NPEFM XF NBLF VTF PG $POEJUJPOBM 3BOEPN 'JFMET $3'T <> /FYU XF EFTDSJCF UIF TUFQT " BOE # JO EFUBJM " 8F JEFOUJGZ UPLFOT JO UIF 8FC QBHF VTJOH IFVSJTUJDT 8F EFmOF mWF UZQFT PG UPLFOT TUBOEBSE XPSE TQFDJBM XPSE JNBHF UPLFO UFSN BOE QVODUVBUJPO NBSL 4UBOEBSE XPSET BSF VO JHSBN XPSET JO OBUVSBM MBOHVBHF 4QFDJBM XPSET <> JODMVEF FNBJM 63- EBUF OVNCFS QFS DFOUBHF XPSET DPOUBJOJOH TQFDJBM TZNCPMT FH i1I%w BOE i/&5w VOOFDFTTBSZ UPLFOT FH i w BOE iw FUD 8F JEFOUJGZ TQFDJBM XPSET CZ VTJOH SFHVMBS FYQSFTTJPOT JNBHF UPLFOT BSF JNBHF UBHT JO UIF )5.- mMF 8F JEFOUJGZ JU CZ QBSTJOH UIF )5.- mMF 5FSNT BSF CBTF OPVO QISBTFT FYUSBDUFE GSPN UIF XFC QBHFT 8F FNQMPZFE B UPPM CBTFE PO UFDIOPMPHJFT QSPQPTFE JO 9VO FU BM <> # 8F BTTJHO UBHT UP FBDI UPLFO CBTFE PO UIF UPLFO UZQF 'PS FYBNQMF GPS TUBOEBSE XPSE XF BTTJHO BMM QPTTJCMF UBHT FBDI UBH SFQSFTFOUJOH B QSPQFSUZ 'PS TQFDJBM XPSE XF BTTJHO UBHT 1PTJUJPO "ċMJBUJPO &NBJM "EESFTT 1IPOF 'BY #TEBUF .TEBUF BOE 1IEEBUF 'PS JNBHF UPLFO XF BTTJHO UXP UBHT 1IPUP BOE &NBJM BO FNBJM JT MJLFMZ UP CF TIPXO BT BO JNBHF *O UIJT XBZ FBDI UPLFO DBO CF BTTJHOFE XJUI TFWFSBM QPTTJCMF UBHT 6TJOH UIF UBHT XF DBO QFSGPSN NPTU PG UIF QSPmMJOH QSPDFTTJOH DPOEVDUJOH TVCUBTLT EFmOFE JO 'JHVSF DzF $3' .PEFM 8F FNQMPZ $POEJUJPOBM 3BOEPN 'JFMET $3' BT UIF UBHHJOH NPEFM $3' JT B DPOEJUJPOBM QSPCBCJMJUZ PG B TFRVFODF PG MBCFMT Y HJWFO B TFRVFODF PG PCTFSWBUJPOT UPLFOT X 3&4&"3$)&3 130'*-& &953"$5*0/ 5BCMF 1FSGPSNBODFT PG SFTFBSDIFS QSPmMJOH Unified Unified NT SVM Amilcare Profile Prec. Rec. F1 Prec. Rec. F1 Prec. Rec. F1 Prec. Rec. F1 Photo 90.32 88.09 89.11 89.22 88.19 88.64 87.99 89.98 88.86 97.44 52.05 67.86 Position 77.53 63.01 69.44 73.99 57.67 64.70 78.62 55.12 64.68 37.50 61.71 46.65 Affiliation 84.21 82.97 83.52 74.09 70.42 72.16 78.24 70.04 73.86 42.68 81.38 55.99 Phone 89.78 92.58 91.10 74.86 83.08 78.72 77.91 81.67 79.71 55.79 72.63 63.11 Fax 92.51 89.35 90.83 73.03 57.49 64.28 77.18 54.99 64.17 84.62 79.28 81.86 Email 81.21 82.22 80.35 81.66 70.32 75.47 93.14 69.18 79.37 51.82 72.32 60.38 Address 87.94 84.86 86.34 77.66 72.88 75.15 86.29 69.62 77.04 55.68 76.96 64.62 Bsuniv 74.44 62.94 67.38 64.08 53.16 57.56 86.06 46.26 59.54 21.43 20.00 20.69 Bsmajor 73.20 58.83 64.20 67.78 53.68 59.18 85.57 47.99 60.75 53.85 18.42 27.45 Bsdate 62.26 47.31 53.49 50.77 34.58 40.59 68.64 18.23 28.49 17.95 16.67 17.28 Msuniv 66.51 51.78 57.55 59.81 40.06 47.49 89.38 34.77 49.78 15.00 8.82 11.11 Msmajor 69.29 59.03 63.35 69.91 56.56 61.92 86.47 49.21 62.10 45.45 20.00 27.78 Msdate 57.88 43.13 48.96 48.11 36.82 41.27 68.99 19.45 30.07 30.77 25.00 27.59 Phduniv 71.22 58.27 63.73 60.19 48.23 53.11 82.41 43.82 57.01 23.40 14.29 17.74 Phdmajor 77.55 62.47 67.92 71.13 51.52 59.30 91.97 44.29 59.67 68.57 42.11 52.17 Phddate 67.92 51.17 57.75 50.53 36.91 42.49 73.65 29.06 41.44 39.13 15.79 22.50 Overall 84.98 81.90 83.37 75.04 69.41 72.09 81.66 66.97 73.57 48.60 59.36 53.44 P.Y X/ Yi Y Y JF j <> "MM DPNQPOFOUT PG BSF BTTVNFE UP SBOHF PWFS B mOJUF MBCFM BMQIBCFU BT UIF QSPQFSUJFT EFmOFE JO 'JHVSF ɩF DPOEJUJPOBM QSPCBCJMJUZ JT GPSNBMJ[FE BT 1 P.y x/ . &j tj .e; y e;x/ +ksk.v; y v; x//; j D Z.x/ FYQ j C j e;j X Xv;k x y y e y v y XIFSF JT B EBUB TFRVFODF JT B MBCFM TFRVFODF BOE j BOE j BSF UIF TFU PG DPNQPOFOUT PG BTTPDJBUFE XJUI FEHF e BOE WFSUFY v JO UIF EBUB TFRVFODF SFTQFDUJWFMZ tj BOE sk BSF GFBUVSF GVOD UJPOT QBSBNFUFST &j BOE +k BSF DPFċDJFOUT SFTQFDUJWFMZ DPSSFTQPOEJOH UP UIF GFBUVSF GVODUJPOT tj BOE sk BOE BSF UP CF FTUJNBUFE GSPN UIF USBJOJOH EBUB BOE Z.x/ JT UIF OPSNBMJ[BUJPO GBDUPS *O UBHHJOH B USBJOFE $3' NPEFM JT VTFE UP mOE UIF TFRVFODF PG UBHT Y # IBWJOH UIF IJHIFTU Y Y P.Y X/ MJLFMJIPPE # D NBY j XJUI UIF 7JUFSCJ BMHPSJUIN *O USBJOJOH UIF $3' NPEFM JT CVJMU XJUI MBCFMFE EBUB BOE CZ NFBOT PG BO JUFSBUJWF BMHPSJUIN CBTFE PO .BYJNVN -JLFMJIPPE &TUJNBUJPO 'FBUVSF %FmOJUJPO ɩSFF UZQFT PG GFBUVSFT XFSF EFmOFE DPOUFOU GFBUVSFT QBUUFSO GFBUVSFT BOE UFSN GFBUVSFT ɩF GFBUVSFT XFSF EFmOFE GPS EJĊFSFOU LJOET PG UPLFOT 5BCMF TIPXT UIF EFmOFE GFBUVSFT 8F DBO FBTJMZ JODPSQPSBUF UIF EFmOFE GFBUVSFT JOUP UIF $3' NPEFM CZ EFmOJOH #PPMFBO WBMVFE GFBUVSF GVODUJPOT 'JOBMMZ GFBUVSFT XFSF VTFE JO PVS FYQFSJNFOUT "3/&5.*/&3 %&&1 .*/*/( '03 "$"%&.*$ 40$*"- /&5803,4 130'*-& &953"$5*0/ 1&3'03."/$& 'PS FWBMVBUJOH PVS VOJmFE QSPmMJOH NFUIPE XF SBOEPNMZ DIPTF 1; 000 SFTFBSDIFS OBNFT JO UP UBM GSPN PVS SFTFBSDIFS OFUXPSL CBTF 8F VTFE UIF NFUIPE EFTDSJCFE JO 4FDUJPO UP mOE UIF SFTFBSDIFST IPNFQBHFT PS JOUSPEVDJOH QBHFT *G UIF NFUIPE DBOOPU mOE B XFC QBHF GPS B SF TFBSDIFS XF SFNPWF UIF SFTFBSDIFS OBNF GSPN UIF EBUB TFU 8F mOBMMZ PCUBJOFE XFC QBHFT 4FWFO IVNBO BOOPUBUPST DPOEVDUFE BOOPUBUJPO PO UIF XFC QBHFT " TQFD XBT DSFBUFE UP HVJEF UIF BOOPUBUJPO QSPDFTT 'PS EJTBHSFFNFOUT JO UIF BOOPUBUJPO XF DPOEVDUFE iNBKPSJUZ WPUJOHw ɩF BOOPUBUFE EBUB TFU BOE UIF BOOPUBUJPO TQFDJmDBUJPO BSF QVCMJDMZ BWBJMBCMFŇ *O UIF FYQFSJNFOUT XF DPOEVDUFE FWBMVBUJPOT JO UFSNT PG QSFDJTJPO SFDBMM BOE 'NFBTVSF GPS EFmOJUJPOT PG UIF NFBTVSFT TFF GPS FYBNQMF WBO 3JKTCFSHFO <> 8F EFmOFE CBTFMJOFT GPS SFTFBSDIFS QSPmMF FYUSBDUJPO 8F VTF UIF SVMF MFBSOJOH BOE UIF DMBTTJmDBUJPO CBTFE BQQSPBDI BT CBTFMJOFT 'PS UIF GPSNFS BQQSPBDI XF2 FNQMPZFE UIF "NJMDBSF TZTUFN <> ɩF TZTUFN JT CBTFE PO B SVMF JOEVDUJPO BMHPSJUIN DBMMFE LP 'PS UIF MBUFS BQQSPBDI XF USBJO B DMBTTJmFS GPS JEFOUJGZJOH UIF WBMVFT PG FBDI QSPQFSUZ 8F FNQMPZFE 4VQQPSU 7FDUPS .BDIJOFT 47. <> BT UIF DMBTTJmDBUJPO NPEFM 5P UFTU IPX EFQFOEFODJFT CFUXFFO EJĊFSFOU UZQFT PG QSPQFSUJFT BĊFDU QSPmMJOH XF BMTP DPO EVDUFE FYQFSJNFOUT VTJOH UIF VOJmFE NPEFM CZ SFNPWJOH UIF USBOTJUJPO GFBUVSFT 6OJmFE@/5 5BCMF TIPXT UIF mWFGPME DSPTTWBMJEBUJPO SFTVMUT 0VS NFUIPE DMFBSMZ PVUQFSGPSNT UIF 29:93 9:80 CBTFMJOF NFUIPET C BOE C SFTQFDUJWFMZ JO UFSNT PG 'TDPSF 8F DBO BMTP TFF UIBU 11:28 UIF QFSGPSNBODF PG UIF VOJmFE NFUIPE EFDSFBTFT $ CZ ' XIFO SFNPWJOH UIF USBOTJUJPO GFBUVSFT 6OJmFE@/5 8F IBWF JNQMFNFOUFE UIF QSPQPTFE QSPmMJOH BQQSPBDIFT JO "SOFU.JOFS #Z FNQMPZJOH UIF QSPQPTFE QSPmMJOH BQQSPBDIFT XF IBWF FYUSBDUFE NPSF UIBO NJMMJPO SFTFBSDIFS QSPmMFT 'JHVSF TIPXT BO FYBNQMF SFTFBSDIFS QSPmMF 8F TFF UIBU JO UIF UPQ PG UIF QSPmMF QBHF TPNF CBTJD JOGPSNBUJPO FH QFSTPO QIPUP QPTJUJPO BOE BċMJBUJPO PG UIF SFTFBSDIFS IBT CFFO DPSSFDUMZ FYUSBDUFE GSPN UIF IPNFQBHF #FMPX JT UIF SFTFBSDI JOUFSFTU BOE FWPMVUJPO PG UIF SFTFBSDI JOUFSFTU EJTDPWFSFE CZ PVS JOUFSFTU BOBMZTJT BQQSPBDI ɩF SJHIU TJEF PG UIF QBHF TIPXT UIF TPDJBM HSBQI PG UIF SFTFBSDIFS CBTFE PO IJT DPBVUIPS SFMBUJPOTIJQT /".& %*4".#*(6"5*0/ 8F JOUFHSBUFE UIF QVCMJDBUJPO EBUB GSPN FYJTUJOH POMJOF EBUB TPVSDFT JODMVEJOH %#-1 CJCMJ PHSBQIZ ň "$. ʼn BOE PUIFST DPWFST NPSF UIBO NJMMJPO QBQFST GSPN NBKPS DPNQVUFS TDJFODF QVCMJDBUJPO WFOVFT *O FBDI EBUB TPVSDF BVUIPST BSF JEFOUJmFE CZ UIFJS OBNFT 'PS JOUFHSBUJOH UIF SFTFBSDIFS QSPmMFT BOE UIF QVCMJDBUJPOT EBUB XF VTF SFTFBSDIFS OBNFT BOE UIF BVUIPS OBNFT BT UIF JEFOUJmFS ɩF QSPDFTT JOFWJUBCMZ IBT UIF BNCJHVPVT QSPCMFN Ň?iiT,ff `M2iKBM2`XQ`;fH #@/ i b2ibfT`Q7BHBM;f ň?iiT,ff/#HTXmMB@i`B2`X/2f ʼn/HX +KXQ`; /".& %*4".#*(6"5*0/ 'JHVSF "O FYBNQMF PG SFTFBSDIFS QSPmMF )FSF XF HJWF B GPSNBM EFmOJUJPO PG UIF OBNF EJTBNCJHVBUJPO UBTL JO PVS DPOUFYU (JWFO B a a P p1;p2; ;pn QFSTPO OBNF XF EFOPUF BMM QVCMJDBUJPOT IBWJOH UIF BVUIPS OBNF BT Df g 'PS FBDI QVCMJDBUJPO pi JU IBT TJY BUUSJCVUFT BT TIPXO JO 5BCMF a.0/;a.1/; ;a.u/ a.0/ 'PS UIF BVUIPST PG B QBQFS f i i i g XF DBMM UIF mSTU BVUIPS i BT UIF QSJODJQBM k y1;y2; ;yk BVUIPS BOE UIF PUIFST TFDPOEBSZ BVUIPST 4VQQPTF UIFSF FYJTU BDUVBM SFTFBSDIFST f g IBWJOH UIF OBNF a PVS UBTL JT UIFO UP BTTJHO UIFTF n QVCMJDBUJPOT UP UIFJS SFBM SFTFBSDIFS yh h Œ1; k XIFSF 2 "3/&5.*/&3 %&&1 .*/*/( '03 "$"%&.*$ 40$*"- /&5803,4 5BCMF "UUSJCVUFT PG FBDI QVCMJDBUJPO Attribute Description pi.title title of pi pi.pubvenue published conference/journal of pi pi.year published year of pi pi.abstract abstract of pi (0) (1) (u) pi.authors authors name set of pi, {ai ,ai , ··· ,ai } pi.references references of pi 5BCMF 3FMBUJPOTIJQT CFUXFFO QBQFST RWRelation Name Description r1 w1 Co-Conference pi.pubvenue = pj .pubvenue (r) (s) r2 w2 Co-Author ∃r, s > 0,ai = aj r3 w3 Citation pi cites pj or pj cites pi r4 w4 Constraints Feedbacks supplied by users r5 w5 τ−CoAuthor τ−extension co-authorship (τ>1) 8F EFmOF mWF UZQFT PG SFMBUJPOTIJQT CFUXFFO QBQFST 5BCMF 3FMBUJPOTIJQ r1 SFQSFTFOUT UXP QBQFST BSF QVCMJTIFE BU UIF TBNF WFOVF 3FMBUJPOTIJQ r2 NFBOT UXP QBQFST IBWF B TFDPOEBSZ BVUIPS XJUI UIF TBNF OBNF BOE SFMBUJPOTIJQ r3 NFBOT POF QBQFS DJUFT UIF PUIFS QBQFS 3FMBUJPO TIJQ r4 JOEJDBUFT DPOTUSBJOUCBTFE SFMBUJPOTIJQT TVQQMJFE WJB VTFS GFFECBDLT 'PS JOTUBODF UIF VTFS DBO QSPWJEF UIBU UXP TQFDJmD QBQFST TIPVME CF EJTBNCJHVBUFE UP UIF TBNF BVUIPS 8F VTF BO FY BNQMF UP FYQMBJO SFMBUJPOTIJQ r5 4VQQPTF pi IBT BVUIPST i%BWJE .JUDIFMMw BOE i"OESFX .BSL w BOE pj IBT BVUIPST i%BWJE .JUDIFMMw BOE i'FSOBOEP .VMGPSEw 8F BSF HPJOH UP EJTBNCJHVBUF i%BWJE .JUDIFMMw *G i"OESFX .BSLw BOE i'FSOBOEP .VMGPSEw BMTP DPBVUIPS POF QBQFS UIFO XF TBZ pi BOE pj IBWF B DPBVUIPS SFMBUJPOTIJQ , 4QFDJmDBMMZ UP UFTU XIFUIFS UXP QBQFST IBWF B $DPBVUIPS SFMBUJPOTIJQ XF DPOTUSVDU B #PPMFBOWBMVFE NBUSJY M JO XIJDI BO FMFNFOU JT JG JUT WBMVF JT MBSHFS UIBO PUIFSXJTF M p1;p2; ;pn DG 'JHVSF *O NBUSJY f ### g BSF QVCMJDBUJPOT.0/ XJUI UIF QSJODJQMF BVUIPS OBNF a a1;a2; ;ap pi :authors a i Œ1; n a1;a2; ;ap f ### g JT UIF VOJPO TFU PG BMM n i 2 /PUF UIBU f ### g a.0/ M EPFT OPU JODMVEF UIF QSJODJQMF BVUIPS OBNF i 4VC NBUSJY p JOEJDBUFT UIF SFMBUJPOTIJQ CFUXFFO p1;p2; ;pn Mpa i f ### g BOE JOJUJBMMZ JU JT BO JEFOUJUZ NBUSJY *O TVC NBUSJY BO FMFNFOU PO SPX BOE j aj pi :authors Map DPMVNO JT FRVBM UP JG BOE POMZ JG 2 PUIFSXJTF ɩF NBUSJY JT TZNNFUSJD Mpa Ma a1;a2; ;ap UP 4VC NBUSJY JOEJDBUFT UIF DPBVUIPSTIJQ BNPOH f ### g ɩF WBMVF PO SPX i BOE DPMVNO j JO Ma JT FRVBM UP JG BOE POMZ JG ai BOE aj DPBVUIPS POF QBQFS JO PVS EBUBCBTF p1;p2; ;pn , OPU MJNJUFE JO f ### g PUIFSXJTF ɩFO $DPBVUIPS DBO CF EFmOFE FBTJMZ CBTFE PO M .% 1/ M .% 1/ M .%/M ,>0 C XIFSF C D XJUI /".& %*4".#*(6"5*0/ p1 p2 ... pn a1 ... ap p1 p2 ... pn a1 ... ap p1 1 0 ... 0 1 ... 0 p1 p2 0 1 0 1 p2 Mp Mpa ...... pn 0 1 1 0 pn a1 1 0 1 1 0 1 a1 … ... … Map Ma ap 0 1 0 1 0 1 ap 'JHVSF .BUSJY M GPS r5 SFMBUJPOTIJQ 5BCMF "CCSFWJBUF /BNF EBUB TFU Abbr. Name # Publications #Actual person Abbr. Name # Publications #Actual Person B.Liang 55 13 M.Hong 69 17 H. Xu 189 59 W. Yang 249 78 K. Zhang 320 40 5BCMF 3FBM OBNF EBUB TFU Person Name # Publications #Actual Person Person Name # Publications #Actual Person Cheng Chang 12 3 Gang Wu 40 16 Wen Gao 286 4 Jing Zhang 54 25 Yi Li 42 21 Kuo Zhang 6 2 Jie Tang 21 2 Hui Fang 15 3 Bin Yu 66 12 Lei Wang 109 40 Rakesh Kumar 61 5 Michael Wagner 44 12 Bing Liu 130 11 Jim Smith 33 5 8F FNQJSJDBMMZ TFU UIF XFJHIU GPS FBDI UZQF PG SFMBUJPOTIJQ 'PS FYBNQMF XF BTTJHO SFMB r4 r2 UJPOTIJQ XJUI UIF IJHIFTU XFJHIU 8F BTTJHO% DPBVUIPS SFMBUJPOTIJQ B SFMBUJWFMZ IJHI XFJHIU w5 , w2 w5 w2 BOE BT UIF QPXFS PG JF D DPDPOGFSFODF JT B XFBL SFMBUJPOTIJQ % TP XF BTTJHO w1 w1 w5 0:2 0:7 0:3 1:0 0:7 B TNBMM WBMVF *O PVS FYQFSJNFOUT XF TFU & BT SFTQFDUJWFMZ ɩF QVCMJDBUJPO EBUB XJUI SFMBUJPOTIJQT DBO CF NPEFMFE BT B HSBQI DPNQSJTJOH PG OPEFT BOE FEHFT &BDI BUUSJCVUF PG B QBQFS JT BUUBDIFE UP UIF DPSSFTQPOEJOH OPEF BT B GFBUVSF WFDUPS 'PS UIF WFDUPS XF VTF XPSET BGUFS TUPQ XPSET mMUFSJOH BOE TUFNNJOH JO UIF BUUSJCVUFT PG B QBQFS BT GFBUVSFT BOE VTF PDDVSSJOH UJNFT BT UIF WBMVFT " 6/*'*&% 130#"#*-*45*$ '3".&803, 8F QSPQPTF B QSPCBCJMJTUJD GSBNFXPSL CBTFE PO )JEEFO .BSLPW 3BOEPN 'JFMET ).3' <> XIJDI DBO DBQUVSF EFQFOEFODJFT CFUXFFO PCTFSWBUJPOT IFSF FBDI QBQFS JT WJFXFE BT BO PCTFSWB UJPO ɩF EJTBNCJHVBUJPO QSPCMFN JT DBTU BT BTTJHOJOH B UBH UP FBDI QBQFS XJUI FBDI UBH SFQSF TFOUJOH BO BDUVBM SFTFBSDIFS <> "3/&5.*/&3 %&&1 .*/*/( '03 "$"%&.*$ 40$*"- /&5803,4 4QFDJmDBMMZ XF EFmOF UIF BQPTUFSJPSJ QSPCBCJMJUZ BT UIF PCKFDUJWF GVODUJPO 8F BJNT BU mOEJOH UIF NBYJNVN PG UIF PCKFDUJWF GVODUJPO ɩF mWF UZQFT PG SFMBUJPOTIJQT BSF JODPSQPSBUFE JOUP UIF PCKFDUJWF GVODUJPO "DDPSEJOH UP ).3' UIF DPOEJUJPOBM EJTUSJCVUJPO PG UIF SFTFBSDIFS MBCFMT y HJWFO UIF PCTFSWBUJPO x QBQFS IBT 1 P.y x/ . D.xi ;yh/ .D.xi ;xj / wkrk.xi ;xj ///; j D Z.x/ FYQ $ $ i;h i;j i rk X X¤ X XIFSF D.xi ;yh/ JT UIF EJTUBODF CFUXFFO UIF QBQFS xi BOE UIF SFTFBSDIFS yh BOE D.xi ;xj / JT UIF EJTUBODF CFUXFFO QBQFST xi BOE xj rk.xi ;xj / EFOPUFT B SFMBUJPOTIJQ CFUXFFO xi BOE xj wk JT UIF XFJHIU PG UIF SFMBUJPOTIJQ BOE Z.x/ JT UIF OPSNBMJ[BUJPO GBDUPS DzF &. "MHPSJUIN ɩSFF UBTLT BSF FYFDVUFE CZ UIF &YQFDUBUJPO .BYJNJ[BUJPO NFUIPE MFBSOJOH QBSBNFUFST PG UIF EJTUBODF NFBTVSF SFBTTJHONFOU PG QBQFST UP SFTFBSDIFST BOE UIF VQEBUF PG SFTFBSDIFS SFQSFTFOUBUJWFT yh 8F EFmOF UIF EJTUBODF GVODUJPO D.xi ;xj / BT GPMMPXT xT x i " j T D.xi ;xj / 1 xi A xi xj D $ xi xj XIFSFk k D " k k"k k" q IFSF A JT B QBSBNFUFS NBUSJY 'PS TJNQMJDJUZ XF EFmOF JU BT B EJBHPOBM NBUSJY ɩF &. QSPDFTT DBO CF TVNNBSJ[FE BT GPMMPXT JO UIF &TUFQ HJWFO UIF DVSSFOU SFTFBSDIFS P.Y X/ SFQSFTFOUBUJWFT FWFSZ QBQFS JT SFBTTJHOFE UP UIF SFTFBSDIFS CZ NBYJNJ[F j *O UIF .TUFQ yh P.Y X/ UIF SFTFBSDIFS SFQSFTFOUBUJWF JT SFFTUJNBUFE GSPN UIF BTTJHONFOUT UP NBYJNJ[F j BHBJO BOE UIF EJTUBODF NFBTVSF JT VQEBUFE UP SFEVDF UIF PCKFDUJWF GVODUJPO *O UIF JOJUJBMJ[BUJPO PG PVS &. GSBNFXPSL XF mSTU DMVTUFS QVCMJDBUJPOT JOUP EJTKPJOU HSPVQT CBTFE PO UIF SFMBUJPOTIJQT CFUXFFO UIFN JF JG UXP QVCMJDBUJPOT IBWF B SFMBUJPOTIJQ UIFO UIFZ BSF BTTJHOFE UP UIF TBNF SFTFBSDIFS ɩFSFGPSF XF mSTU HFU & HSPVQT *G & JT FRVBM UP PVS BDUVBM SFTFBSDIFS OVNCFS k UIFO UIFTF HSPVQT BSF VTFE BT PVS JOJUJBM BTTJHONFOU *G & f .yh;xi / D.xi ;yh/ .D.xi ;xj / wkrk.xi ;xj //: D C i i;j i rk X X¤ X ɩF BTTJHONFOU PG B QBQFS JT QFSGPSNFE XIJMF LFFQJOH BTTJHONFOUT PG UIF PUIFS QBQFST mYFE ɩF BTTJHONFOU QSPDFTT JT SFQFBUFE BGUFS BMM QBQFST BSF BTTJHOFE ɩJT QSPDFTT SVOT VOUJM OP QBQFS DIBOHFT JUT BTTJHONFOU CFUXFFO UXP TVDDFTTJWF JUFSBUJPOT /".& %*4".#*(6"5*0/ 100.00 80.00 F1-score (%) F1-score 60.00 40.00 20.00 0.00 Hui Fang Rakesh Michael Bing Liu Jim Smith Lei Wang Bin Yu Kumar Wagner Person name DISTINCT Our Approach 'JHVSF $PNQBSJTPO XJUI FYJTUJOH NFUIPE *O UIF .TUFQ FBDI SFTFBSDIFS SFQSFTFOUBUJWF JT VQEBUFE CZ UIF BSJUINFUJD NFBO PG JUT QPJOUT x i yi h i y W D : h x D i yi h i k P W D k" P ɩFO FBDI QBSBNFUFS amm JO A JT VQEBUFE CZ POMZ QBSBNFUFST PO UIF EJBHPOBM amm @f.yh;xi / D amm ( C @amm XIFSF @f.yh;xi / @D.xi ;yh/ @D.xi ;xj / . wkrk.xi ;xj // @amm D$ @amm $ @amm i i;j i rk X X¤ 2X 2 2 2 T xim xi xjm xj ximxjm xi xj x xj k k"C k k" @D.xi ;xj / " " i " 2 xi xj k k k k $ k k"k k" 2 2 : @amm D xi xj k k"k k" /".& %*4".#*(6"5*0/ 1&3'03."/$& %BUB 4FUT BOE &WBMVBUJPO .FBTVSF 5P FWBMVBUF PVS NFUIPET XF DSFBUFE UXP EBUB TFUT GSPN "SOFU.JOFS OBNFMZ "CCSFWJBUF /BNF EBUB TFU BOE 3FBM /BNF EBUB TFU ɩF mSTU EBUB TFU XBT DPMMFDUFE CZ RVFSZJOH mWF BCCSFWJBUFE OBNFT JO PVS EBUBCBTF "MM UIFTF BCCSFWJBUFE OBNFT BSF HFOFSBUFE CZ TJNQMJGZJOH UIF PSJHJOBM OBNFT UP JUT mSTU OBNF JOJUJBM BOE MBTU OBNF 'PS FYBNQMF i$IFOH $IBOHw JT TJNQMJmFE UP i$ $IBOHw ɩF TJNQMJmDBUJPO GPSN JT QPQVMBS JO CJCMJPHSBQIJD SFDPSET 4UBUJTUJDT PG UIJT EBUB TFU JT TIPXO JO 5BCMF "OPUIFS EBUB TFU JODMVEFT SFBM QFSTPO OBNFT *O UIFTF OBNFT TPNF OBNFT POMZ DPSSF TQPOE UP B GFX QFSTPOT 'PS FYBNQMF i$IFOH $IBOHw DPSSFTQPOET UP UISFF BDUVBM QFSTPOT BOE i8FO (BPw GPVS XIJMF TPNF OBNFT TFFN UP CF QPQVMBS 'PS FYBNQMF UIFSF BSF QFSTPOT XJUI UIF OBNF i+JOH ;IBOHw BOE QFSTPOT GPS i-FJ 8BOHw 4UBUJTUJDT PG UIJT EBUB TFU BSF TIPXO JO 5BCMF "3/&5.*/&3 %&&1 .*/*/( '03 "$"%&.*$ 40$*"- /&5803,4 100.00 80.00 w/o Relationship 60.00 +CoConference 40.00 +Citation +CoAuthor 20.00 All 0.00 Pre. Rec. F1 'JHVSF $POUSJCVUJPO PG SFMBUJPOTIJQT B C D E 'JHVSF %JTUSJCVUJPO BOBMZTJT 'JWF IVNBO BOOPUBUPST DPOEVDUFE EJTBNCJHVBUJPO PO UIF QBQFST " TQFD XBT DSFBUFE UP HVJEF UIF BOOPUBUJPO QSPDFTT &BDI QBQFS JT MBCFMFE XJUI B OVNCFS JOEJDBUJOH UIF BDUVBM QFSTPO ɩF MBCFMJOH XPSL XBT DBSSJFE PVU CBTFE PO UIF QVCMJDBUJPO MJTUT PO UIF BVUIPST IPNFQBHFT BċMJ BUJPOT BOE FNBJM BEESFTTFT 'PS GVSUIFS EJTBHSFFNFOUT JO UIF BOOPUBUJPO XF DPOEVDUFE iNBKPSJUZ WPUJOHw ɩF BOOPUBUFE EBUB TFU DBO CF EPXOMPBEFE IFSFŊ Ŋ?iiT,ff `M2iKBM2`XQ`;f/Bb K#B;m iBQM /".& %*4".#*(6"5*0/ 'SPN UIF TUBUJTUJDT XF IBWF GPVOE UIBU UIF EJTBNCJHVBUJPO SFTVMUT JT FYUSFNFMZ VOCBMBODF 'PS FYBNQMF UIFSF BSF 286 QBQFST BVUIPSFE CZ i8FO (BPw XJUI 282 PG UIFN BVUIPSFE CZ 1SPG 8FO (BP GSPN *OTUJUVUF PG $PNQVUJOH BU $IJOFTF "DBEFNZ PG 4DJFODF BOE POMZ GPVS QBQFST BSF BVUIPSFE CZ UIF PUIFS UISFF i8FO (BPw 8F EFmOFE B CBTFMJOF CBTFE PO UIF IJFSBSDIJDBM DMVTUFSJOH BMHPSJUIN ɩF CBTFMJOF NFUIPE JT TJNJMBS UP UIBU QSPQPTFE CZ 5BO FU BM <> FYDFQU UIBU 5BO FU BM <> BMTP VUJMJ[F B TFBSDI FOHJOF UP IFMQ UIF EJTBNCJHVBUJPO 8F BMTP DPNQBSFE PVS BQQSPBDI XJUI UIF FYJTUJOH XPSL FH :JO FU BM <> *O BMM FYQFSJNFOUT XF TVQQPTF UIBU UIF OVNCFS PG QFSTPO k JT QSPWJEFE FNQJSJDBMMZ 3FTVMUT 8F FWBMVBUFE UIF QFSGPSNBODFT PG PVS NFUIPE BOE UIF CBTFMJOF NFUIPET PO UIF UXP EBUB TFUT 5BCMF TIPXT UIF SFTVMUT *U DBO CF TFFO UIBU PVS NFUIPE DBO TJHOJmDBOUMZ PVUQFSGPSN 4:54 10:75 UIF CBTFMJOF NFUIPE GPS OBNF EJTBNCJHVBUJPO C PO "CCS /BNF EBUB TFU BOE C PO 3FBM /BNF EBUB TFU JO UFSNT PG UIF BWFSBHF 'TDPSF .PSF SFTVMUT XFSF SFQPSUFE JO 5BOH FU BM <> 5BCMF 3FTVMUT PO OBNF EJTBNCJHVBUJPO Baseline Our Approach Data Set Person Name Prec. Rec. F1 Prec. Rec. F1 B. Liang 82.07 76.90 79.07 49.54 100.00 66.26 H. Xu 65.87 59.48 71.27 32.77 100.00 49.37 Abbr. Name K. Zhang 75.67 60.27 67.84 71.03 100.00 83.06 M. Hong 79.24 65.36 71.36 91.32 86.06 88.61 W. Yang 71.30 62.83 66.99 52.48 99.86 68.81 Avg. 74.43 64.47 69.21 59.43 97.18 73.75 Cheng Chang 100.00 100.00 100.00 100.0 100.0 100.0 Wen Gao 96.60 62.64 76.00 99.29 98.59 98.94 Yi Li 86.64 95.12 90.68 70.91 97.50 82.11 Jie Tang 100.0 100.0 100.0 100.0 100.0 100.0 Gang Wu 97.54 97.54 97.54 71.86 98.36 83.05 Jing Zhang 85.00 69.86 76.69 83.91 100.0 91.25 Kuo Zhang 100.0 100.0 100.0 100.0 100.0 100.0 Real Name Hui Fang 100.0 100.0 100.0 100.0 100.0 100.0 Bin Yu 67.22 50.25 57.51 86.53 53.00 65.74 Lei Wang 68.45 41.12 51.38 88.64 89.06 88.85 Rakesh Kumar 63.36 92.41 75.18 99.14 96.91 98.01 Michael Wagner 18.35 60.26 28.13 85.19 76.16 80.42 Bing Liu 84.88 43.16 57.22 88.25 86.49 87.36 Jim Smith 92.43 86.80 89.53 95.81 93.56 94.67 Avg. 82.89 78.51 80.64 90.68 92.12 91.39 "3/&5.*/&3 %&&1 .*/*/( '03 "$"%&.*$ 40$*"- /&5803,4 ɩF CBTFMJOF NFUIPE TVĊFST GSPN UXP EJTBEWBOUBHFT JU DBOOPU UBLF BEWBOUBHF PG SFMB UJPOTIJQT CFUXFFO QBQFST BOE JU SFMJFT PO B mYFE EJTUBODF NFBTVSF 0VS GSBNFXPSL CFOFmUT GSPN UIF BCJMJUZ PG NPEFMJOH EFQFOEFODJFT CFUXFFO BTTJHONFOU SFTVMUT 8F DPNQBSFE PVS BQQSPBDI XJUI UIF BQQSPBDI %*45*/$5 QSPQPTFE JO :JO FU BM <> 8F VTFE UIF QFSTPO OBNFT UIBU XFSF VTFE CPUI JO :JO FU BM <> BOE JO PVS FYQFSJNFOUT GPS DPNQBSJTPOT 'JHVSF TIPXT UIF DPNQBSJTPO SFTVMUT *U DBO CF TFFO UIBU GPS TPNF OBNFT PVS BQQSPBDI TJHOJmDBOUMZ PVUQFSGPSNT %*45*/$5 FH i.JDIBFM 8BHOFSw XIJMF GPS TPNF OBNFT PVS BQQSPBDI VOEFSQFSGPSNT %*45*/$5 FH i#JO :Vw 'FBUVSF $POUSJCVUJPO "OBMZTJT 8F GVSUIFS JOWFTUJHBUFE UIF DPOUSJCVUJPO PG UIF EFmOFE SFMB UJPOT GPS OBNF EJTBNCJHVBUJPO 8F mSTU FWBMVBUFE UIF SFTVMUT PG PVS BQQSPBDI CZ SFNPWJOH BMM , SFMBUJPOT ɩFO XF BEEFE UIF SFMBUJPOT DPDPOGFSFODF DJUBUJPO DPBVUIPS BOE $DPBVUIPS JOUP PVS BQQSPBDI POF CZ POF 'JHVSF TIPXT UIF SFTVMUT iXP 3FMBUJPOTIJQTw EFOPUFT PVS BQQSPBDI XJUIPVU BOZ SFMBUJPOTIJQT i $P$POGFSFODFw EFOPUFT UIF SFTVMUT PG CZ BEEJOH DPDPOGFSFODF SFMB UJPOTIJQT -JLFXJTF GPS UIF PUIFST "U FBDI TUFQ XF PCTFSWFE JNQSPWFNFOUT JO UFSNT PG 'TDPSF 15:65 8F OFFE OPUF UIBU XJUIPVU VTJOH SFMBUJPOT UIF QFSGPSNBODFT ESPQ TIBSQMZ $ PO "CCS 44:72 /BNF BOE $ PO 3FBM /BNF ɩJT DPOmSNT VT UIBU B GSBNFXPSL CZ JOUFHSBUJOH SFMBUJPO TIJQT GPS OBNF EJTBNCJHVBUJPO JT OFFEFE BOE FBDI EFmOFE SFMBUJPOTIJQT JO PVS NFUIPE JT IFMQGVM 24:38 8F DBO BMTP TFF UIBU UIF DPBVUIPS SFMBUJPOTIJQ NBLFT NBKPS DPOUSJCVUJPOT C 0:68 CZ ' UP UIF JNQSPWFNFOUT DPDPOGFSFODF BOE DJUBUJPO NBLF MJNJUFE DPOUSJCVUJPOT C 0:61 13:99 BOE C UP UIF JNQSPWFNFOUT PO QSFDJTJPO CVU DBO PCUBJO JNQSPWFNFOUT C BOE 5:20 C PO SFDBMM %JTUSJCVUJPO "OBMZTJT 'JHVSF TIPXT TFWFSBM UZQJDBM GFBUVSF EJTUSJCVUJPOT JO PVS EBUB TFUT ɩF HSBQIT XFSF HFOFSBUFE VTJOH B EJNFOTJPO SFEVDUJPO NFUIPE EFTDSJCFE JO $BJ FU BM <> ɩF EJTUSJCVUJPOT DBO CF UZQJDBMMZ DBUFHPSJ[FE JOUP QBQFST PG EJĊFSFOU QFSTPOT BSF DMFBSMZ TFQBSBUFE i)VJ 'BOH w JO 'JHVSF B /BNF EJTBNCJHVBUJPO PO UIJT LJOE PG EBUB DBO CF TPMWFE QSFUUZ XFMM CZ PVS BQQSPBDI BOE BT XFMM UIF CBTFMJOF NFUIPE QVCMJDBUJPOT BSF NJYFE UPHFUIFS IPXFWFS UIFSF JT B EPNJOBUF BVUIPS XIP XSJUFT NPTU PG UIF QBQFS FH i#JOH -JV w JO 'JHVSF C PVS BQQSPBDI DBO BDIJFWF B 'TDPSF PG 87:36 IPXFWFS UIF CBTFMJOF NFUIPE SFTVMUT JOUP B MPX BDDVSBDZ 57:22 CZ ' BOE QVCMJDBUJPOT PG EJĊFSFOU BVUIPST BSF NJYFE i+JOH ;IBOHw BOE i:J -J w JO 'JHVSF D BOE E 0VS NFUIPE DBO PCUBJO 92:15 BOE 82:11 JO UFSNT PG ' NFBTVSF XIJMF UIF CBTFMJOF NFUIPE DBO POMZ PCUBJO B SFTVMU 76:69 BOE 90:68 JO UFSNT PG 'NFBTVSF SFTQFDUJWFMZ 'JHVSF TIPXT B TOBQTIPU PG UIF EJTBNCJHVBUJPO SFTVMU ɩF VTFS TFBSDIFT GPS i+JF 5BOHw BOE UIF TZTUFN SFUVSOT UISFF EJĊFSFOU QFSTPOT PO UIF UPQ PG UIF QBHF BOE UIF CBDLHSPVOE TIPXT UIF EFUBJMFE QSPmMF JOGPSNBUJPO PG DIPTFO QFSTPO ɩF NFUIPE SVOT JO BO PČJOF NPEF BOE TP GBS UIF TZTUFN BMSFBEZ HFOFSBUFT UIF EJTBNCJHVBUJPO SFTVMUT GPS NPSF UIBO QFSTPO OBNFT 1MFBTF OPUF UIBU UIJT JT BO POHPJOH QSPKFDU 7JTJUPST TIPVME FYQFDU UIF TZTUFN UP DIBOHF 501*$ .0%&-*/( 'JHVSF "O FYBNQMF SFTVMU PG OBNF EJTBNCJHVBUJPO GPS i+JF 5BOHw ɩFSF BSF UISFF EJĊFSFOU i+JF 5BOHw BVUPNBUJDBMMZ SFDPHOJ[FE CZ UIF QSPQPTFE NFUIPET 501*$ .0%&-*/( *O BDBEFNJD TFBSDI SFQSFTFOUBUJPO PG UIF DPOUFOU PG UFYU EPDVNFOUT BVUIPST JOUFSFTUT BOE DPO GFSFODFT UIFNFT JT B DSJUJDBM JTTVF PG BOZ BQQSPBDI 5SBEJUJPOBMMZ EPDVNFOUT BSF SFQSFTFOUFE CBTFE PO UIF iCBH PG XPSETw #08 BTTVNQUJPO )PXFWFS UIJT SFQSFTFOUBUJPO DBOOPU VUJMJ[F UIF iTF "3/&5.*/&3 %&&1 .*/*/( '03 "$"%&.*$ 40$*"- /&5803,4 NBOUJDw EFQFOEFODJFT CFUXFFO XPSET *O BEEJUJPO JO BDBEFNJD TFBSDI UIFSF BSF EJĊFSFOU UZQFE JOGPSNBUJPO TPVSDFT UIVT IPX UP DBQUVSF UIF EFQFOEFODJFT CFUXFFO UIFN CFDPNFT B DIBMMFOHJOH JTTVF 5P EFBM XJUI UIJT QSPCMFN UPQJD NPEFMT TVDI BT QSPCBCJMJTUJD -BUFOU 4FNBOUJD *OEFYJOH Q-4* <> BOE -BUFOU %JSJDIMFU "MMPDBUJPO -%" <> IBWF CFFO QSPQPTFE #PUI NPEFMT DBO NPEFM UIF EFQFOEFODJFT CFUXFFO XPSET BOE EPDVNFOUT ɩF "VUIPS5PQJD NPEFM JT QSPQPTFE GPS NPEFMJOH UIF DPOUFOU PG EPDVNFOUT BOE UIF JOUFSFTUT PG BVUIPST < > )PXFWFS BMM PG UIF BGPSFNFOUJPOFE NPEFMT DBOOPU CF EJSFDUMZ BQQMJFE UP UIF DPOUFYU PG BDBEFNJD TFBSDI BT UIFZ DBOOPU DBQUVSF BMM JOUSJOTJD EFQFOEFODJFT JO BDBEFNJD TFBSDI TVDI BT EFQFOEFODJFT CFUXFFO QBQFS BOE DPOGFSFODF 8F QSPQPTF B VOJmFE UPQJD NPEFMJOH BQQSPBDI GPS TJNVMUBOFPVTMZ NPEFMJOH DIBSBDUFSJTUJDT PG EPDVNFOUT BVUIPST DPOGFSFODFT BOE EFQFOEFODJFT CFUXFFO UIFN 'PS TJNQMJDJUZ XF VTF DPOGFSFODF UP EFOPUF DPOGFSFODF KPVSOBM BOE CPPL IFSFBGUFS ɩF OPUBUJPOT VTFE IFSF BSF TVNNBSJ[FE BT GPMMPXT " EPDVNFOU d JT B WFDUPS PG Nd XPSET Xd XIFSF FBDI wdi JT DIPTFO GSPN B WPDBCVMBSZ PG TJ[F V B WFDUPS PG Ad BVUIPST Bd DIPTFO GSPN B TFU PG BVUIPST PG TJ[F A BOE B QVCMJTIFE DPOGFSFODF cd " DPMMFDUJPO PG D EPDVNFOUT JT EFmOFE . 1; 1;c1/; ;. D; D;cD/ xdi d CZ % DfX B ### X B g JOEJDBUFT BO BVUIPS DIPTFO GSPN B SFTQPOTJCMF GPS UIF iUI XPSE JO EPDVNFOU d )FSF FBDI BVUIPS JT BTTPDJBUFE XJUI B EJTUSJCVUJPO PWFS UPQJDT ‚ DIPTFO GSPN B TZNNFUSJD Dirichlet.˛/ QSJPS ɩF OVNCFS PG UPQJD JT EFOPUFE BT T 063 130104&% 501*$ .0%&-4 ɩF QSPQPTFE NPEFM JT DBMMFE "VUIPS$POGFSFODF5PQJD "$5 NPEFM .PSF TQFDJmDBMMZ EJG GFSFOU TUSBUFHJFT DBO CF FNQMPZFE UP NPEFM UIF UPQJD EJTUSJCVUJPOT BT TIPXO JO 'JHVSF BOE UIVT UIF JNQMFNFOUFE NPEFMT IBWF EJĊFSFOU JOUVJUJPOT *O 'JHVSF B FBDI BVUIPS JT BTTPDJ BUFE XJUI B NJYUVSF XFJHIUT PWFS UPQJDT BOE FBDI XPSE UPLFO JO B QBQFS BOE B DPOGFSFODF TUBNQ BTTPDJBUFE UP FBDI XPSE UPLFO JT HFOFSBUFE GSPN B TBNQMFE UPQJD *O 'JHVSF C FBDI BVUIPS DPOGFSFODF QBJS JT BTTPDJBUFE XJUI B NJYUVSF XFJHIUT PWFS UIF UPQJDT BOE XPSE UPLFOT BSF UIFO HFOFSBUFE GSPN UIF TBNQMFE UPQJDT *O 'JHVSF D FBDI BVUIPS JT BTTPDJBUFE XJUI UPQJDT BOE FBDI XPSE UPLFO JT HFOFSBUFE GSPN B TBNQMFE UPQJD BOE UIFO B DPOGFSFODF JT HFOFSBUFE GSPN UIF TBNQMFE UPQJDT PG BMM XPSE UPLFOT JO B QBQFS *O UIF SFTU PG UIJT TFDUJPO XF XJMM EFTDSJCF UIF UISFF NPEFMT JO EFUBJM .PEFM 0OF *O UIF mSTU NPEFM UIF DPOGFSFODF JOGPSNBUJPO JT WJFXFE BT B TUBNQ GPS FBDI XPSE XJUI UIF TBNF WBMVF ɩF HFOFSBUJWF QSPDFTT JO UIJT "$5 NPEFM DG 'JHVSF B DBO CF TVN NBSJ[FE BT GPMMPXT 'PS FBDI UPQJD z ESBX .z BOE z SFTQFDUJWFMZ GSPN %JSJDIMFU QSJPST ˇz BOE +z 'PS FBDI XPSE wdi JO EPDVNFOU d t ESBX BO BVUIPS xdi GSPN Bd VOJGPSNMZ 501*$ .0%&-*/( AC T d d d x z w c Nd D , 2 B .PEFM 0OF C .PEFM 5XP D .PEFM ɩSFF 'JHVSF (SBQIJDBM SFQSFTFOUBUJPO PG UIF UISFF "VUIPS$POGFSFODF5PQJD "$5 NPEFMT z ' x ' t ESBX B UPQJD di GSPN B NVMUJOPNJBM EJTUSJCVUJPO xdi TQFDJmD UP BVUIPS di XIFSF JT HFOFSBUFE GSPN B %JSJDIMFU QSJPS ˛ w . t ESBX B XPSE di GSPN NVMUJOPNJBM zdi BOE c t ESBX B DPOGFSFODF TUBNQ di GSPN NVMUJOPNJBM zdi *O UIF HFOFSBUJWF QSPDFTT BMM DPOGFSFODF TUBNQT JO B EPDVNFOU BSF PCTFSWFE BT UIF TBNF BT UIF QVCMJTIFE WFOVF PG UIF EPDVNFOU *O UIJT XBZ UIF QPTUFSJPS EJTUSJCVUJPO PG UPQJDT EFQFOET PO UISFF NPEBMJUJFT BVUIPST XPSET BOE DPOGFSFODFT 1BSBNFUFSJ[BUJPOT JO UIF "$5 NPEFM BSF x d Uniform. d / jB & B 'x ˛ Dirichlet.˛/ di j & .z ˇ Dirichlet.ˇ/ j & z + Dirichlet.+/ j & zdi 'x Multinomial.'x / j di & di wdi .z Multinomial..z / j di & di cdi z Multinomial. z /: j di & di )FODF JO UIJT "$5 NPEFM UIF KPJOU QSPCBCJMJUZ PG XPSET X DPOGFSFODFT D B TFU PG DPSSF TQPOEJOH MBUFOU UPQJDT [ BOE BO BVUIPS NJYUVSF Y JT EFmOFE BT D Nd A T V C n 1 mxz nzv zcd P. ; ; ; ‚;ˆ;‰; / .'xz .zv zcd /; Y [ X Dj B D Ad " d 1 i 1 x 1 z 1 v 1 c 1 YD YD YD YD YD YD XIFSF mxz JT UIF OVNCFS PG UJNFT UIBU UPQJD z IBT CFFO VTFE BTTPDJBUFE XJUI UIF DIPTFO BVUIPS x n w z n zv JT UIF OVNCFS PG UJNFT UIBU XPSE v IBT CFFO HFOFSBUFE CZ UPQJD BOE zcd JT UIF OVNCFS PG UJNFT UIBU DPOGFSFODF cd IBT CFFO HFOFSBUFE CZ UPQJD z "3/&5.*/&3 %&&1 .*/*/( '03 "$"%&.*$ 40$*"- /&5803,4 #Z QMBDJOH B %JSJDIMFU QSJPS PWFS ‚ BOE BOPUIFS UXP PWFS ˆ BOE ‰ BOE DPNCJOJOH UIFN JOUP &RVBUJPO XJUI GVSUIFS JOUFHSBUJOH PWFS ‚ ˆ BOE ‰ XF PCUBJO D Nd A 1 . ˛z/ .mxz ˛z/ P. ; ; ; ˛; ˇ; +; / z z C Y [ X Dj B D Ad " .˛z/ . .mxz ˛z// d 1 i 1 x 1 zP Q z C T YD YD YTD . ˇv/ .nzv ˇv/ Q. +c/ P.nzc +c/ v v C c c C : " .ˇ / . .n ˇ // " .+ / . .n + // z 1 vP v Q v zv v z 1 cP c Q c zc c YD C YD C Q P Q P *U JT JOUSBDUBCMF UP EJSFDUMZ DPNQVUF &RVBUJPO " WBSJFUZ PG BMHPSJUINT IBWF CFFO QSPQPTFE UP DPOEVDU BQQSPYJNBUF JOGFSFODF GPS FYBNQMF WBSJBUJPOBM &. NFUIPET <> (JCCT TBNQMJOH < > BOE FYQFDUBUJPO QSPQBHBUJPO < > 8F DIPTF (JCCT TBNQMJOH GPS JUT FBTZ PG JNQMFNFOUBUJPO "T GPS UIF IZQFSQBSBNFUFST ˛ ˇ BOE + POF DPVME FTUJNBUF UIF PQUJNBM WBMVFT CZ VTJOH B (JCCT &. BMHPSJUIN < > PS B WBSJBUJPOBM &. NFUIPE <> 'PS TPNF BQQMJDBUJPOT UPQJD NPEFMT BSF TFOTJUJWF UP UIF IZQFSQBSBNFUFST BOE JU JT OFDFTTBSZ UP HFU UIF SJHIU WBMVFT GPS UIF IZQFSQBSBNFUFST *O UIF BQQMJDBUJPOT EJTDVTTFE JO UIJT CPPL XF GPVOE UIBU UIF FTUJNBUFE UPQJD NPEFMT BSF OPU WFSZ TFOTJUJWF UP UIF IZQFSQBSBNFUFST ɩVT GPS TJNQMJDJUZ XF UPPL B mYFE WBMVF ˛ 50=T ˇ 0:01 + 0:1 JF D D BOE D *O UIF (JCCT TBNQMJOH QSPDFEVSF XF OFFE UP DBMDVMBUF UIF QPTUFSJPS QSPCBCJMJUZ P.zdi;xdi di; di; ; ;˛;ˇ;+/ j[! Y! X D GPS UIF DIPTFO BVUIPS GPS TBNQMJOH UIF UPQJD GPS FBDI XPSE UPLFO 8F CFHJO XJUI UIF KPJOU QSPCBCJMJUZ PG B EBUB TFU DG &RVBUJPO BOE VTJOH UIF DIBJO SVMF XF DBO PCUBJO UIF DPOEJUJPOBM QSPCBCJMJUZ BT di di d m! ˛z n! ˇw n! +c P.z ;x ; ; ; ;˛;ˇ;+/ xdizdi C di zdiwdi C di zdicd C d ; di di di di di di d j[! Y! X D / .m ˛z/ .n ˇv/ .n +c/ z !xdiz C v !zdiv C c !zdi c C P P P t di XIFSF UIF TVQFSTDSJQU $ EFOPUF B RVBOUJUZ FYDMVEJOH UIF DVSSFOU JOTUBODF UIF UI XPSE UPLFO PS UIF DPOGFSFODF TUBNQ JO UIF dUI EPDVNFOU (JWFO D EPDVNFOUT B TFU PG UPQJDT [ BOE IZQFSQBSBNFUFST ˛ ˇ BOE + UIF SBOEPN WBSJ BCMFT . UIF QSPCBCJMJUZ PG B XPSE HJWFO B UPQJD UIF QSPCBCJMJUZ PG B DPOGFSFODF HJWFO B UPQJD BOE ' UIF QSPCBCJMJUZ PG B UPQJD HJWFO BO BVUIPS DBO CF FTUJNBUFE WJB nzw ˇw . di C di zwdi D v.nzv ˇv/ nzc C+c d C d zcd P D c.nzc +c/ mxz C ˛z 'xz P C : D z .mxz ˛z / 0 0 C 0 P 501*$ .0%&-*/( .PEFM 5XP ɩF TFDPOE NPEFM DG 'JHVSF C JT BO BMUFSOBUJWF NPEFM UP UIF mSTU NPEFM ɩF EJĊFSFODF JT UIBU JU WJFXT UIF DPOGFSFODF BOE BVUIPST JO B EPDVNFOU BT B VOJUFE JOGPSNBUJPO BOE UIVT FBDI QBJS PG BVUIPSDPOGFSFODF JT SFTQPOTJCMF GPS UIF TBNQMFE UPQJDT ɩF HFOFSBUJWF QSPDFTT PG UIJT NPEFM JT GPS FBDI UPQJD z ESBX .z GSPN %JSJDIMFU QSJPST ˇz BOE GPS FBDI XPSE wdi JO EPDVNFOU d .xdi;cd / d ;cd t ESBX BO BVUIPSDPOGFSFODF QBJS GSPN fB g VOJGPSNMZ z ' t ESBX B UPQJD di GSPN B NVMUJOPNJBM EJTUSJCVUJPO .xdicd / TQFDJmD UP BVUIPSDPOGFSFODF QBJS .xdi;cd / XIFSF ' JT HFOFSBUFE GSPN B %JSJDIMFU QSJPS ˛ BOE w . t ESBX B XPSE di GSPN NVMUJOPNJBM zdi 1BSBNFUFSJ[BUJPOT JO UIJT "$5 NPEFM BSF TJNJMBS BT UIPTF JO .PEFM 0OF FYDFQU UIBU XF .x; c/ d ;c DIPTF B QBJS GSPN fB g VOJGPSNMZ BOE XF XJMM OPU TBNQMF UIF DPOGFSFODF TUBNQ JO UIJT NPEFM ɩVT UIF KPJOU QSPCBCJMJUZ PG XPSET X B TFU PG DPSSFTQPOEJOH MBUFOU UPQJDT [ BOE BO BVUIPS NJYUVSF Y JT EFmOFE BT D Nd AC T V 1 m.xc/z nzv P. ; ; ‚;ˆ;‰; ; / '.xc/z .zv ; Y [ Xj B D D Ad cd " d 1 i 1 xc 1 z 1 v 1 YD YD * j j YD YD YD Ad cd XIFSF *j j JT UIF OVNCFS PG BVUIPSDPOGFSFODF QBJST GPS B EPDVNFOU *O QSBDUJDBM JU JT FRVBM UP Ad BT B QBQFS POMZ IBT POF QVCMJDBUJPO WFOVF "HBJO CZ QMBDJOH B %JSJDIMFU QSJPS PWFS ‚ BOE BOPUIFS POF PWFS ˆ BOE QVUUJOH UIFN JOUP &RVBUJPO CZ JOUFHSBUJOH PVU ‚ BOE ˆ XF DBO PCUBJO D Nd AC 1 . ˛z/ .m.xc/z ˛z/ P. ; ; ˛; ˇ; ; / z z C Y [ Xj B D D Ad cd " .˛z/ . .m.xc/z ˛z// d 1 i 1 * j j xc 1 zP Q z C YD YD YD T Q. ˇv/ P .nzv ˇv/ v v C : " .ˇ / . .n ˇ // z 1 vP v Q v zv v YD C Q P 4JNJMBSMZ XF DBO DBMDVMBUF UIF QPTUFSJPS DPOEJUJPOBM QSPCBCJMJUZ P.zdi; .xc/di di; di; d ; ;˛;ˇ/ j[! Y! D! X VTJOH B (JCCT TBNQMJOH QSPDFEVSF BOBMPHPVT UP UIBU JO .PEFM 0OF di di m! ˛zdi n! ˇw P.z ; .xc/ ; ; ; ;˛;ˇ/ .xc/dizdi C zdiwdi C di : di di [ di Y di D d X di di j ! ! ! / .m! ˛z/ v.n!z v ˇv/ z .xc/diz C di C P P "3/&5.*/&3 %&&1 .*/*/( '03 "$"%&.*$ 40$*"- /&5803,4 .PEFM DzSFF *OUVJUJPO PG UIF UIJSE NPEFM DG 'JHVSF D JT EFSJWFE GSPN UIF PCTFSWBUJPO UIBU BVUIPST XSJUF B QBQFS XJUI B UPQJD EJTUSJCVUJPO BOE UIFO UIFZ XBOU UP mOE B SJHIU DPOGFSFODF UP TVCNJU UIF QBQFS ɩVT UIF DPSSFTQPOEJOH HFOFSBUJWF QSPDFTT JT GPS FBDI UPQJD z ESBX .z GSPN %JSJDIMFU QSJPST ˇz GPS FBDI XPSE wdi JO EPDVNFOU d t ESBX BO BVUIPS xdi GSPN Bd VOJGPSNMZ z ' x ' t ESBX B UPQJD di GSPN B NVMUJOPNJBM EJTUSJCVUJPO xdi TQFDJmD UP BVUIPS di XIFSF JT HFOFSBUFE GSPN B %JSJDIMFU QSJPS ˛ BOE w . t ESBX B XPSE di GSPN NVMUJOPNJBM zdi 2 cd z1 Nd N.(>,;/ / , ESBX B DPOGFSFODF GSPN W VTJOH B OPSNBM MJOFBS NPEFM XIFSF JT B WFDUPS SFDPSEJOH UIF OPSNBMJ[FE OVNCFS PG UJNFT PG FBDI UPQJD TBNQMFE GSPN EPDVNFOU d Nd , .1=Nd / i 1 zdi 8F EFmOF JU BT WD D j j P *O UIJT NPEFM UIF DPOGFSFODF DPNFT GSPN B OPSNBM MJOFBS NPEFM ɩF DPWBSJBUFT JO UIJT NPEFM BSF UIF FNQJSJDBM GSFRVFODJFT PG UIF UPQJDT JO UIF EPDVNFOU ɩF SFHSFTTJPO DPFċDJFOUT PO UIPTF GSFRVFODJFT DPOTUJUVUF ( /PUF UIBU XF JHOPSF UIF JOUFSDFQU UFSN XIJDI JT VTFE UP HVBSBOUFF BEEJOH B DPWBSJBUF FRVBM UP POF CFDBVTF JO PVS NPEFM , BMXBZT TVN UP POF ɩVT UIF EJĊFSFODF PG QBSBNFUFSJ[BUJPOT PG UIJT NPEFM GSPN .PEFM 0OF JT UIBU UIF DPOGFSFODF TUBNQ JT TBNQMFE GSPN B OPSNBM MJOFBS EJTUSJCVUJPO BGUFS BMM UPQJDT XFSF TBNQMFE GPS XPSE UPLFOT JO B EPDVNFOU "DDPSEJOHMZ UIF KPJOU QSPCBCJMJUZ PG XPSET X DPOGFSFODF TUBNQT c B TFU PG DPSSFTQPOEJOH MBUFOU UPQJDT [ BOE BO BVUIPS NJYUVSF Y JT EFmOFE BT D Nd A T V 2 2 1 mxz nzv P. ; ; ; ‚;ˆ;(;/ ; / .P.cd z1 Nd ;(;/ / 'xz .zv /: Y [ X Dj B D j W Ad " d 1 i 1 x 1 z 1 v 1 YD YD YD YD YD 'PS DPNQVUJOH UIF BCPWF FRVBUJPO VTJOH (JCCT TBNQMJOH UIFSF JT B TMJHIU EJĊFSFODF2 GSPN UIBU JO .PEFM 0OF BOE .PEFM 5XP BT XF BMTP OFFE UP FTUJNBUF UIF WBMVFT PG ( BOE / 8F VTF B (JCCT &. BMHPSJUIN GPS UIJT NPEFM *O UIF &TUFQ GPS TBNQMJOH UIF UPQJD GPS FBDI XPSE UPLFO UIF QPTUFSJPS QSPCBCJMJUZ P.zdi;xdi di; di;cd ; ;˛;ˇ/ j[! Y! X JT DBMDVMBUFE CZ 2 P.zdi;xdi di; di;cd ; ;˛;ˇ;(;/ / j[di! Y! X di / m! ˛z n! ˇw P.c z ;(;/ 2/ xdizdi C di zdiwdi C di ; d 1 Nd di di j W .m ˛z/ .n ˇv/ z !xdiz C v !zdiv C P P XIFSF &91&35*4& 4&"3$) .c ' (/2 1 . > / 2 !2)2 P.cd z1 Nd ;(;/ / e ! : j W D p2"/ 2 2 *O UIF .TUFQ HJWFO UIF TBNQMFE UPQJDT [ UIF PQUJNBM ( BOE / DBO CF FTUJNBUFE CZ NBY JNJ[JOH argmx P. ; ; ; ˛;ˇ;(;/ 2/: ';( MPH Y [ X Dj 4QFDJmDBMMZ ( JT VQEBUFE CZ 1 ( .EŒA>A/! EŒA> new D 2 BOE / JT VQEBUFE CZ 2 1 / .1=D/ > >EŒA.EŒA>A/! EŒA> ; new fD D $ D Dg XIFSF EŒ: JT UIF FYQFDUBUJPO PG UIF WBSJBCMFT A JT B NBUSJY PG D T XJUI UIF d UI SPX JT EŒ, Nd D " $ D . .1=Nd / i 1 .di EŒA>A d 1 EŒ,d ,d> T T EŒ,d ,d> N WD D BOE D D JT B " NBUSJY XIFSF JT EF mOFE BT P P Nd Nd 2 EŒ,d , > .1=N /. .di.> .di / d D d dj C EJBHf g i 1 j i i 1 XD X¤ XD .di .di .di XJUI EJBHf g JOEJDBUJOH B NBUSJY XJUI EJBHPOBM BT UIF WFDUPS PG /PUF UIBU EFOPUFT B WFDUPS PG QSPCBCJMJUJFT PG UPQJDT HFOFSBUJOH XPSE wdi 8F PNJUUFE UIF EFUBJMT PG EFSJWBUJPO PG UIF VQEBUF &RVBUJPOT BOE *OUFSFTUFE SFBEFS JT SFGFSSFE UP <> BOE <> 8F FTUJNBUF UIF "$5 NPEFMT JO BO PČJOF NPEF CFGPSF BQQMZJOH JU UP UIF BDBEFNJD TFBSDI O. N T A / ɩF mSTU UXP QSPQPTFE NPEFMT SFTVMU JOUP B DPNQMFYJUZ PG MD Nd Nd XJUI TMJHIU EJĊFSFODFT M N XIFSF JT UIF OVNCFS PG TBNQMJOH UJNFT Nd JT UIF BWFSBHF OVNCFS PG XPSE UPLFOT JO B EPDV A A NFOU BOE Nd JT UIF BWFSBHF OVNCFS PG BVUIPST *O NPTU DBTFT UIF OVNCFS Nd JT OFHMJHJCMF UP UIF ( / 2 mOBM DPNQMFYJUZ ɩF UIJSE NPEFM IBT UP2 FTUJNBUF2 UIF PQUJNBM WBMVFT GPS BOE XIJDI MFBET UP O.MDNd T MD T / EŒA EŒA A B IJHIFS DPNQMFYJUZ N C /PUF UIBU > DBO CF DPNQVUFE JO UIF QSFWJPVT &TUFQ XIJMF JO UIF TBNQMJOH QSPDFTT &91&35*4& 4&"3$) *O BDBEFNJD TFBSDI UIF HPBM JT UP mOE UIF FYQFSUJTF BVUIPST FYQFSUJTF QBQFST BOE FYQFSUJTF DPO GFSFODFT GPS B HJWFO RVFSZ < > #BTFE PO UIF QSPQPTFE "$5 NPEFMT XF DBO DBMDVMBUF UIF MJLFMJIPPE PG UIF B EPDVNFOU NPEFM HFOFSBUJOH B XPSE VTJOH UIF GPMMPXJOH FRVBUJPO XF VTF "$5 .PEFM BT UIF FYBNQMF "3/&5.*/&3 %&&1 .*/*/( '03 "$"%&.*$ 40$*"- /&5803,4 T Ad P 1.w d;';./ P.w z;.z/P.z x;'x/P.x d/; ACT j D j j j z 1 x 1 XD XD XIFSF BMM QSPCBCJMJUJFT PO UIF SJHIU TJEF PG UIF FRVBUJPO BSF FTUJNBUFE JO UIF "$5 NPEFM ɩF MJLFMJIPPE PG BO BVUIPS NPEFM BOE B DPOGFSFODF NPEFM HFOFSBUJOH B XPSE DBO CF TJNJMBSMZ EFmOFE )PXFWFS BT B UPQJD JO UIF -%"TUZMF NPEFM SFQSFTFOU B DPNCJOBUJPO PG XPSET JU NBZ OPU CF BT QSFDJTF BT SFQSFTFOUBUJPO BT XPSET JO OPOUPQJD NPEFMT MJLF UIF MBOHVBHF NPEFM ɩFSFGPSF POMZ VTJOH "$5 JUTFMG GPS NPEFMJOH JT UPP DPBSTF GPS BDBEFNJD TFBSDI <> "DUVBMMZ PVS QSFMJNJOBSZ FYQFSJNFOUT BMTP TIPX UIBU FNQMPZJOH POMZ UIF "$5 PS -%" NPEFMT UP JOGPSNBUJPO SFUSJFWBM IVSUT UIF SFUSJFWBM QFSGPSNBODF 'JOBMMZ XF EFSJWF B DPNCJOBUJPO GPSN PG UIF "$5 NPEFMT BOE UIF MBOHVBHF NPEFM P.w d/ P .w d/ P .w d/; j D LM j " ACT j P .w d/ w d XIFSF LM j JT UIF HFOFSBUJOH QSPCBCJMJUZ PG XPSE GSPN EPDVNFOU CZ UIF MBOHVBHF NPEFM *U JT EFmOFE BT <> N tf .w; d/ N tf .w; / P.w d/ d .1 d / % ; j D Nd & # d C $ Nd & # C j j C j%j d d tf .w; d/ XIFSF j j JT UIF MFOHUI PG EPDVNFOU JT UIF XPSE GSFRVFODZ JF OVNCFS PG XPSET PG w d tf .w; / XPSE JO j%j JT UIF OVNCFS PG XPSE UPLFOT JO UIF XIPMF DPMMFDUJPO BOE % JT UIF XPSE GSFRVFODZ PG XPSE w JO UIF XIPMF DPMMFDUJPO % & JT UIF %JSJDIMFU QSJPS BOE JT DPNNPO UP TFU JU BDDPSEJOH UP UIF BWFSBHF EPDVNFOU MFOHUI JO UIF EPDVNFOU DPMMFDUJPO q P.q d/ P.q d/ …w qP.w d/ 'JOBMMZ HJWFO B RVFSZ j DBO CF DPNQVUFE CZ j D 2 j 4JNJMBSMZ P.q a/ P.q c/ XF DBO EFmOF j GPS BVUIPST BOE j GPS DPOGFSFODFT JO B BOBMPHPVT XBZ P.q a/ P .q a/ P .q a/ j D LM j " ACT j P.q c/ P .q c/ P .q c/ j D LM j " ACT j XIFSF a BOE c JT SFQSFTFOUFE CZ B DPMMFDUJPO PG QBQFST QVCMJTIFE CZ BVUIPS a BOE PO DPOGFSFODF c SFTQFDUJWFMZ %"5" 4&54 "/% &7"-6"5*0/ .&"463&4 8F IBWF DPMMFDUFE B MJTU PG RVFSJFT GSPN UIF RVFSZ MPH PG "SOFU.JOFS GPS FWBMVBUJPO QVSQPTFT 4QFDJmDBMMZ XF TFMFDUFE UIF NPTU GSFRVFOU RVFSJFT GSPN UIF MPH PG "SOFU.JOFS CZ SFNPWJOH PWFSMZ TQFDJmD PS MFOHUIZ RVFSJFT FH i" $POWFSHFOU 4PMVUJPO UP 5FOTPS 4VCTQBDF -FBSOJOHw 8F BMTP OPSNBMJ[FE TJNJMBS RVFSJFT FH i8FC 4FSWJDFw BOE i8FC 4FSWJDFTw UP i8FC 4FSWJDFw 8F DPOEVDUFE PVS FYQFSJNFOUT PO B TVCTFU PG UIF EBUB JODMVEJOH 14; 134 QFSTPOT 10; 716 QBQFST BOE 1; 434 DPOGFSFODFT GSPN "SOFU.JOFS 'PS FWBMVBUJPO JU JT EJċDVMU UP mOE B TUBOEBSE &91&35*4& 4&"3$) EBUB TFU XJUI HSPVOE USVUI "T B SFTVMU XF VTF UIF NFUIPE PG QPPMFE SFMFWBODF KVEHNFOUT <> UPHFUIFS XJUI IVNBO KVEHNFOUT 4QFDJmDBMMZ GPS FBDI RVFSZ XF mSTU QPPMFE UIF UPQ SFTVMUT GSPN UISFF TJNJMBS BDBEFNJD TFBSDI TZTUFNT -JCSB 3FYB BOE "SOFU.JOFS JOUP B TJOHMF MJTU ɩFO UXP GBDVMUJFT BOE mWF HSBEVBUF TUVEFOUT GSPN UIF BVUIPST MBC QSPWJEFE IVNBO KVEHNFOUT 'PVS HSBEF TDPSFT BOE XFSF BTTJHOFE SFTQFDUJWFMZ SFQSFTFOUJOH EFmOJUF FYQFSUJTF FY QFSUJTF NBSHJOBM FYQFSUJTF BOE OPU FYQFSUJTF 'PS FYBNQMF GPS BOOPUBUJOH QFSTPOT BTTFTTNFOUT XFSF DBSSJFE PVU NBJOMZ JO UFSNT PG IPX NBOZ QVCMJDBUJPOT TIFIF IBT QVCMJTIFE SFMBUFE UP UIF HJWFO RVFSZ IPX NBOZ UPQ DPOGFSFODF QBQFST IF PS TIF IBT QVCMJTIFE XIBU EJTUJOHVJTIFE BXBSET TIFIF IBT CFFO BXBSEFE 'JOBMMZ UIF KVEHNFOU TDPSFT XFSF BWFSBHFE UP DPOTUSVDU UIF mOBM USVUI HSPVOE ɩ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mOEJOH GPS i%BUB .JOJOHw ɩF MFGU TJEF MJTUT FYQFSUT SBOLFE CZ UIF QSPQPTFE NFUIPE UIF UPQSJHIU MJTUT SBOLFE QVCMJDBUJPO WFOVFT BOE UIF CPUUPNSJHIU MJTUT SBOLFE QBQFST UIF UISFF CBTFMJOF NFUIPET -%" POMZ NPEFMT EFQFOEFODJFT CFUXFFO EPDVNFOUT BOE XPSET BOE UIVT DBO TVQQPSU POMZ QBQFS TFBSDI XIJMF "5 POMZ NPEFMT EFQFOEFODJFT CFUXFFO EPDVNFOUT XPSET BOE BVUIPST BOE UIVT TVQQPSU QBQFS TFBSDI BOE BVUIPS TFBSDI #PUI PG UIF UXP NFUIPET VOEFSQFSGPSN PVS QSPQPTFE VOJmFE NPEFMT 0VS NPEFMT CFOFmU GSPN UIF BCJMJUZ PG DBQUVSJOH BMM LJOET PG EFQFOEFODJFT BNPOH XPSET QBQFST BVUIPST BOE DPOGFSFODFT 8F DBO BMTP TFF UIBU "$5 PVUQFSGPSNT "$5 BOE "$5 "$5 BDIJFWFT UIF CFTU QFSGPS NBODF JO UFSNT PG 1! BOE BHBJOTU -. Q-4* "$5 BOE "$5 SFTQFDUJWFMZ "5$ TVĊFST GSPN B TQBSTF QSPCMFN XIFO TBNQMJOH B QBJS PG BVUIPSDPOGFSFODF GSPN B EPDVNFOU *O PVS FYQFSJNFOU UIF QPTTJCMF OVNCFS PG QBJST TDBMFT VQ UP NPSF UIBO NJMMJPO XIJDI NBLFT UIF BTTPDJBUFE UPQJDT UP FBDI QBJS JT WFSZ TQBSTF ɩVT UIF FTUJNBUFE UPQJDT &91&35*4& 4&"3$) 5BCMF 1FSGPSNBODFT PG mWF FYQFSU mOEJOH BQQSPBDIFT Method Object P@5 P@10 P@20 R-pre MAP LM Paper 37.5 33.8 32.5 8.7 42.1 Author 55.0 37.5 21.3 49.0 62.8 Conference 47.5 30 19.4 40.8 51.0 Average 46.7 33.8 24.4 32.8 52.0 pLSI Paper 32.5 33.8 30 9.7 40.4 Author 65.0 40.0 22.5 60.4 75.5 Conference 47.5 36.3 21.3 45.1 54.1 Average 48.3 36.7 24.6 38.4 56.7 ACT1 Paper 37.5 40.0 36.9 13.7 43.8 Author 80.0 43.8 23.1 70.0 78.4 Conference 55.0 36.3 20.6 53.1 63.3 Average 57.5 40.0 26.9 45.6 61.8 ACT2 Paper 37.5 28.8 28.1 9.1 41.6 Author 65.0 38.8 23.8 56.6 66.8 Conference 55.0 33.8 20.6 51.6 62.9 Average 52.5 33.8 24.2 39.1 57.1 ACT3 Paper 35.0 37.5 36.3 10.6 43.1 Author 67.5 41.3 24.4 60.7 69.5 Conference 52.5 36.3 20.6 53.1 61.2 Average 52.7 38.3 27.1 41.5 57.9 DBOOPU BDDVSBUFMZ DIBSBDUFSJ[F UIF BVUIPS "T B SFTVMU GPS BVUIPS TFBSDI "$5 VOEFSQFSGPSNT 11:6 "$5 CZ $ JO UFSNT PG ."1 "$5 VOEFSQFSGPSNT "$5 CZ 1! BOE 1! CVU PCUBJOT UIF CFTU QFSGPSNBODF JO UFSNT PG 1! BOE 1! 'PS DPNQBSJTPO QVSQPTFT XF BMTP FWBMVBUFE UIF SFTVMUT SFUVSOFE CZ UXP TJNJMBS TZTUFNT -JCSBNTSBDO BOE 3FYBJOGP ɩF BWFSBHF ."1 PCUBJOFE CZ -JCSB BOE 3FYB PO PVS DPMMFDUFE RVFSJFT BSF SFTQFDUJWFMZ 51:0 BOE 46:2 8F TFF UIBU PVS NFUIPET DMFBSMZ PVUQFSGPSN UIF UXP TZTUFNT 5BCMFT BOE TIPX UIF FYBNQMF PG SFUSJFWFE SFTVMUT GPS UIF RVFSZ i*OGPSNBUJPO &Y USBDUJPOw BOE i4FNBOUJD 8FCw 8F DBO TFF TPNF JOUFSFTUJOH QBUUFSOT 'PS FYBNQMF XF IBWF GPVOE UIBU JO UIF UPQJD GPVOE JO 5BCMF i*48$w IBT UIF IJHIFTU HFOFSBUJWF QSPCBCJMJUZ GSPN UIF UPQJD i4FNBOUJD 8FCw CVU GPS UIF RVFSZ i4FNBOUJD 8FC w JU JT SFUSJFWFE JO UIF TFDPOE QMBDF XIJMF i888w JT SFUVSOFE BT UIF UPQ POF ɩJT JT CFDBVTF NBOZ FYQFSUT PO i4FNBOUJD 8FCw BMTP IBT QVCMJTIFE NBOZ QBQFST PO i888w ɩF DPNCJOBUJPO PG UIF "$5 NPEFM BOE UIF MBOHVBHF NPEFM SFSBOL UIF SFTVMUT PG "$5 NPEFM 'JHVSF TIPXT BO FYBNQMF PG FYQFSU mOEJOH JO "SOFU.JOFS ɩF VTFS USJFT UP mOE FY QFSUT PO i%BUB .JOJOHw ɩF TZTUFN SFUVSOT FYQFSUT SBOLFE CZ UIF QSPQPTFE SBOLJOH NFUIPE *O "3/&5.*/&3 %&&1 .*/*/( '03 "$"%&.*$ 40$*"- /&5803,4 5BCMF 3FUSJFWFE SFTVMUT PG i*OGPSNBUJPO &YUSBDUJPOw CZ "$5 Person Conference Paper Raymond J. Mooney AAAI Multistrategy Learning for Information Extraction Nicholas Kushmerick IJCAI Adaptive Information Extraction: Core Technologies for Information Agents Andrew McCallum ICML Integrating Information to Bootstrap Information Extraction from Web Sites Dayne Freitag ACL Automatically Constructing a Dictionary for Information Extraction Tasks Ellen Riloff SIGIR Machine Learning for Information Extraction in Informal Domains Dan I. Moldovan EACL Collective Information Extraction with Relational Markov Networks Fabio Ciravegna COLING Exploiting Subjectivity Classification to Improve Information Extraction Alexiei Dingli IIWeb Evaluating machine learning for information extraction Daniel S. Weld Machine Learning Multi-level Boundary Classification for Information Extraction Bernd Thomas ECML Adaptive information extraction for document annotation in amilcare 5BCMF 3FUSJFWFE SFTVMUT PG i4FNBOUJD 8FCw CZ "$5 Person Conference Paper Ian Horrocks WWW Metamodeling Architecture of Web Ontology Languages Steffen Staab ISWC Three theses of representation in the semantic web Stefan Decker Description Logics Learning Ontologies for the Semantic Web York Sure IEEE Intelligent Systems DAML+OIL: a Description Logic for the Semantic Web Carole A. Goble ESWC Querying the Semantic Web: A Formal Approach Rudi Studer J. Web Sem. A software framework for matchmaking based on semantic web technology Peter F. Patel-Schneider ESWS The Networked Semantic Desktop Jeff Z. Pan AAAI OilEd: a Reason-able Ontology Editor for the Semantic Web Sergio Tessaris IJCAI A Scalable Framework for the Interoperation of Information Sources Sean Bechhofer IEEE Data Eng. Bull. OntoEdit: Collaborative Ontology Development for the Semantic Web BEEJUJPO UIF UPQSJHIU PG UIF TDSFFO MJTUT SBOLFE QVCMJDBUJPO WFOVFT BOE UIF CPUUPNSJHIU MJTUT SBOLFE QBQFST "TTPDJBUJPO 4FBSDI (JWFO B TPDJBM OFUXPSL UIF BTTPDJBUJPO JT EFmOFE BT BT GPMMPXT G .V; E/ ˛.ai ;aj / ai ;aj V "TTPDJBUJPO (JWFO B TPDJBM OFUXPSL D BO BTTPDJBUJPO 2 JT B TF er ;er ; ;er er E m 1; 2; ;l 1 a RVFODF PG SFMBUJPOT i1 12 lj TBUJTGZJOH m.m 1/ GPS XIFSF i f ### g C 2 D ### $ BOE aj BSF UIF TPVSDF BOE UIF UBSHFU QFSTPOT SFTQFDUJWFMZ 8F BTTVNF UIBU OP QFSTPO XJMM BQQFBS PO B HJWFO BTTPDJBUJPO NPSF UIBO POF UJNF &BDI BTTPDJBUJPO JT BTTJHOFE XJUI B TDPSF SFQSFTFOUJOH JUT HPPEOFTT "TTPDJBUJPO 4FBSDI (JWFO BO BTTPDJBUJPO RVFSZ .ai ;aj / BTTPDJBUJPO TFBSDI JT UP mOE QPTTJCMF ˛k.ai ;aj / ai aj BTTPDJBUJPOT f g GSPN UP BOE SBOL UIF BTTPDJBUJPOT BDDPSEJOH UP UIFJS HPPEOFTT 'SPN UIF EFmOJUJPO XF TFF UIBU UIFSF BSF UXP TVCUBTLT JO BTTPDJBUJPO TFBSDI mOEJOH BTTPDJ BUJPOT CFUXFFO UIF UXP QFSTPOT BOE SBOLJOH UIF BTTPDJBUJPOT (JWFO B MBSHFTDBMF TPDJBM OFUXPSL UP mOE BMM QPTTJCMF BTTPDJBUJPOT JT PCWJPVTMZ BO /1IBSE QSPCMFN *O UIJT QBQFS XF GPDVT PO mOE JOH UIF NPTU iHPPEOFTTw BTTPDJBUJPOT )FODF UIF QSPCMFN CFDPNFT IPX UP FWBMVBUF UIF HPPEOFTT PG BO BTTPDJBUJPO BOE POF LFZ JTTVF JT IPX UP DBMDVMBUF UIF EJTUBODF CFUXFFO UXP QFSTPOT #BTFE PO UIF NPEFMJOH SFTVMUT DG 4FDUJPO XF EFmOF UIF EJTUBODF CFUXFFO BVUIPST ai BOE aj BT UIF &91&35*4& 4&"3$) AAAI 0.295846 IJCAI 0.192995 ICML 0.060567 KDDJAIR 0.058551 ECML 0.046451 0.033006 IIWeb 0.026956 Topic #24 (Model 1) learninginformationextraction 0.043527 0.065259 websemantic 0.033592 textrules 0.011860 relational 0.019311 logicprogramming 0.009376 0.008755 0.010618 0.010618 0.009376 “Information extraction” Raymond J. Mooney 0.010346 Andrew McCallumCraig A. Knoblock 0.004074 0.003492 Nicholas Kushmerick 0.002457 Ellen Riloff 0.002199 William W. CohenDan Roth 0.002134 0.001487 opic #16 (Model 1) “Machine learning” T learningclassification 0.018517 boosting 0.058056 machinefeature 0.015881 classifiers 0.017797 margin 0.013904 selection 0.013904 algorithm 0.013245 kernels 0.012586 0.025086 0.011269 NIPSJMLRICMLCOLTNeural Computation 0.023017 MLSSMachine Learning 0.289761 0.206583 0.010827 0.156389 0.096157 0.011545 Robert E. SchapireYoram SingerThomas 0.004033 G. Dietterich 0.002472 0.003318 Bernhard ScholkopfAlexander J. 0.001496 Smola 0.001301 Ralf SchoknechtMichael I. Jordan 0.001236 0.001106 $POUJOVFT 1) $- $PNQVUBUJPOBM -JOHVJTUJDT +.-3 +PVSOBM PG .BDIJOF -FBSOJOH 3FTFBSDI .-44 .BDIJOF -FBSOJOH 4VNNFS “Semantic web” Topic #10 (Model semanticwebontology 0.068226 knowledgelearning 0.043160 0.041497 framework 0.048847 approach 0.012095 0.013431 basedmanagement 0.011427 0.010090 reasoning 0.010758 0.009502 Steffen StaabEnrico MottaYork SureNenad StojanovicAlexander MaedcheAsuncion 0.005863 Gomez-Perez 0.001694 Frank 0.004365 0.001824 van 0.001824 Harmelen 0.003713 0.001563 ISWCEKAWIEEE Intelligent SystemsCoopIS/DOA/ODBASE 0.071418 0.065594 0.125291 0.122379 K-CAPESWSWWW 0.054674 0.023369 0.016817 'PVS UPQJDT EJTDPWFSFE CZ "$5 NPEFMT PO UIF "SOFU.JOFS QVCMJDBUJPO EBUB TFU &BDI UPQJD JT TIPXO XJUI UIF UPQ Topic #5 (Model 1) languageparsing 0.034820 naturallearning 0.023766 approach 0.019029 grammars 0.015871 0.012712 processing 0.012712 text 0.011923 machineprobabilistic 0.010343 0.011133 0.011923 ACLCOLINGCLANLP 0.234435 CoRR 0.253487 COLING-ACL 0.036814 NAACL 0.060423 0.118136 0.058674 0.035065 Yuji MatsumotoEugene Charniak 0.001389 Rens Bod 0.001323 Brian RoarkSuzanne Stevenson 0.001124 Anoop SarkarClaire Cardie 0.001190 0.001323 0.001058 0.000992 “Natural language processing” BCMF 5 XPSET BOE UIFJS DPSSFTQPOEJOH DPOEJUJPOBMɩF QSPCBCJMJUJFT UJUMFT #FMPX BSF BSF PVS UPQ4DIPPM JOUFSQSFUBUJPO +"*3 PG BVUIPST + UIF BOE "SUJG UPQJDT *OUFMM UPQ 3FT BOE DPOGFSFODFT -/-1 BTTPDJBUFE -FBSOJOH XJUI GPS /BUVSBM FBDI -BOHVBHF UPQJD 1SPDFTTJOH "3/&5.*/&3 %&&1 .*/*/( '03 "$"%&.*$ 40$*"- /&5803,4 information 0.265864 extractioninduction 0.152239 ranking 0.014540 documentagent 0.011651 0.010688 incremental 0.007800 probabilistic 0.006837 boosting 0.009726 incomplete 0.005874 0.005874 AAAIACLICMLIJCAISIGIRCIKM 0.035059 Machine Learning 0.014308 0.021953 0.020861 0.020861 0.020861 0.015400 Ellen RiloffFabio CiravegnaNicholas Kushmerick 0.000690 Stephen SoderlandAndrew 0.000794 McCallum 0.001107 0.000690 Dayne Freitag 0.000586 Wai Lam 0.000586 0.000586 $POUJOVFT learningreinforcement 0.082713 hierarchical 0.212239 machine 0.037838 robocupdiscovery 0.024579 large 0.015400 survey 0.013361 multipleresearch 0.009281 0.007241 0.007241 0.006221 ICMLMachine Learning 0.036264 AAAINIPSRoboCupECML 0.085238 IJCAI 0.030434 0.021105 0.029268 0.016441 0.016441 Thomas G. DietterichPeter 0.001743 StoneAndrew G. BartoSridhar MahadevanRaymond J. Mooney 0.000904 0.000904 Ralf Schoknecht 0.000694 Manuela 0.001428 M. Veloso 0.000485 0.000694 $- $PNQVUBUJPOBM -JOHVJTUJDT +.-3 +PVSOBM PG .BDIJOF -FBSOJOH 3FTFBSDI .-44 .BDIJOF websemanticontologyservice 0.080464 automatic 0.156658 0.053723 applicationsrepresentation 0.028723 0.015788 0.037686 0.014016 querydatabasecontext 0.011890 0.013307 0.011535 ISWCWWWACLAAAIIJCAI 0.028819 ICML 0.022842 Web Intelligence 0.020849 0.013060 0.019219 0.014509 0.013060 Ian HorrocksSteffen StaabRaphael VolzDieter FenselNicholas Kushmerick 0.000421 0.000276 WilliamW.Cohen 0.000408 Carole 0.000303 A. Goble 0.000290 0.000263 0.000250 'PVS UPQJDT EJTDPWFSFE CZ "$5 NPEFMT PO UIF "SOFU.JOFS QVCMJDBUJPO EBUB TFU &BDI UPQJD JT TIPXO XJUI $POUJOVFE Topic#52(Model2) Topic#2(Model2) Topic#30(Model2) Topic#75(Model2) languagenaturalprocessing 0.209963 machine 0.053100 methodology 0.074298 0.012825 management 0.017064 0.012825 booleanbaselearning 0.008585 computer 0.005405 0.004346 0.007525 ACLCLAAAICoRRCICLingICMLMachine 0.028150 Learning 0.014745 0.018401 0.018401 0.017183 0.017183 0.014745 BCMF Raymond J. MooneyEric BrillRolf Schwitter 0.001013 Michael CollinsClaire CardieChristopher D. ManningCynthia 0.000592 A. Thompson 0.000697 0.000592 0.000487 0.000802 0.000592 5 UIF UPQ XPSET BOEFBDI UIFJS UPQJD DPSSFTQPOEJOH ɩF DPOEJUJPOBM UJUMFT-FBSOJOH QSPCBCJMJUJFT 4VNNFS BSF #FMPX 4DIPPM BSF PVS +"*3 UPQ JOUFSQSFUBUJPO + PG "SUJG *OUFMM BVUIPST UIF 3FT BOE BOE UPQJDT UPQ -/-1 -FBSOJOH DPOGFSFODFT GPS /BUVSBM BTTPDJBUFE -BOHVBHF XJUI 1SPDFTTJOH &91&35*4& 4&"3$) ACLAAAI 0.034960 0.034960 IJCAI 0.023339 CIKM 0.017529 SIGIR 0.017529 ICML 0.016560 KDD 0.015592 informationextraction 0.372220 rulesforms 0.200865 answerhybridexecution 0.009606 0.004414 oriented 0.004414 general 0.003548 0.003548 discriminative 0.003548 0.003548 0.003548 Fabio CiravegnaDayne Freitag 0.002432 0.001608 Craig A. Knoblock 0.001505 Ellen Riloff 0.001403 Nicholas Kushmerick 0.001300 Raymond J. Mooney 0.001197 Stephen Soderland 0.001094 learningmachineinduction 0.388622 theories 0.082680 0.045596 tasksscientific 0.009355 noise 0.008512 empirical 0.008512 quantitative 0.006827 0.005984 introduction 0.006827 0.005984 ICMLMachine Learning 0.055566 AAAIIJCAIJMLRECML 0.057446 ACL 0.040523 0.031121 0.020778 0.016077 0.014197 Pat LangleyRaymond J. Mooney 0.003450 0.003963 Russell GreinerNicholas Kushmerick 0.001295 Manuela M. VelosoLarry A. 0.001295 Rendell 0.001295 0.000988 Xindong Wu 0.000988 $- $PNQVUBUJPOBM -JOHVJTUJDT +.-3 +PVSOBM PG .BDIJOF -FBSOJOH 3FTFBSDI .-44 .BDIJOF websemanticservicesdocuments 0.251191 search 0.282681 0.005733 0.067097 collaborative 0.004118 incremental 0.004118 soccer 0.004925 actionsnamed 0.004118 0.004118 0.004118 Steffen Staab 0.002003 Ian HorrocksEnrico MottaRaphael Volz 0.002003 0.001187 0.001084 Carole A. GobleKatia P. Sycara 0.001493 Nicholas Kushmerick 0.001391 0.000982 ISWCWWWACLIEEE Intelligent SystemsAAAI 0.021603 RuleMLWeb Intelligence 0.055665 0.024292 0.015328 0.022499 0.018017 0.015328 'PVS UPQJDT EJTDPWFSFE CZ "$5 NPEFMT PO UIF "SOFU.JOFS QVCMJDBUJPO EBUB TFU &BDI UPQJD JT TIPXO XJUI $POUJOVFE ACLCLCoRR 0.046487 ICML 0.020983 CICLing 0.022142 0.018665 0.019824 NIPSCOLING 0.014027 0.015187 Topic #20 (Model 3) Topic #34 (Model 3) Topic #15 (Model 3) Topic #58 (Model 3) languageprocessing 0.209132 0.090411 naturalconceptual 0.013293 role 0.081279 syntacticinformation 0.010249 0.011263 computer 0.013293 identifying 0.009234 0.009234 multiple 0.008219 BCMF Eric BrillClaire CardieChristopher D. ManningHugo 0.000904 LiuAndres MontoyoRaymond J. Mooney 0.000904 0.001847 0.000799 0.000799 0.000799 Rens Bod 0.000694 5 UIF UPQ XPSET BOEFBDI UIFJS UPQJD DPSSFTQPOEJOH ɩF DPOEJUJPOBM UJUMFT-FBSOJOH QSPCBCJMJUJFT 4VNNFS BSF #FMPX 4DIPPM BSF PVS +"*3 UPQ JOUFSQSFUBUJPO + PG "SUJG *OUFMM BVUIPST UIF 3FT BOE BOE UPQJDT UPQ -/-1 -FBSOJOH DPOGFSFODFT GPS /BUVSBM BTTPDJBUFE -BOHVBHF XJUI 1SPDFTTJOH "3/&5.*/&3 %&&1 .*/*/( '03 "$"%&.*$ 40$*"- /&5803,4 TZNNFUSJD ,- EJWFSHFODF CFUXFFO UIF UPQJDT EJTUSJCVUJPO DPOEJUJPOFE PO FBDI PG UIF BVUIPST T 'ai z 'aj z sKL.ai ;aj / .'ai zlog 'aj zlog /; D 'a z C 'a z z 1 j i XD XIFSF 'az JT DBMDVMBUFE CZ &RVBUJPO 8F VTF UIF BDDVNVMBUFE WBMVF PG EJTUBODFT CFUXFFO BVUIPST PO BO BTTPDJBUJPO QBUI BT UIF TDPSF PG UIF BTTPDJBUJPO 8F DBMM UIF BTTPDJBUJPO XJUI UIF TNBMMFTU TDPSF BT UIF TIPSUFTU BTTPDJBUJPO BOE PVS HPBM JT UP mOE UIF OFBSTIPSUFTU BTTPDJBUJPOT #Z OFBSTIPSUFTU BTTPDJBUJPOT XF NFBO .1 $/ BTTPDJBUJPOT XIPTF TDPSFT BSF XJUIJO B GBDUPS PG C PG UIF TDPSF PG UIF TIPSUFTU BTTPDJBUJPO GPS TPNF VTFSEFmOFE $>0 8F GPSNBMJ[F UIF BTTPDJBUJPO TFBSDI QSPCMFN BT UIBU PG OFBSTIPSUFTU BTTPDJBUJPOT BOE FN QMPZ B UXP TUBHF BQQSPBDI UP mOE UIF OFBSTIPSUFTU BTTPDJBUJPOT 4IPSUFTU BTTPDJBUJPO mOEJOH *U BJNT BU mOEJOH TIPSUFTU BTTPDJBUJPOT GSPN BMM QFSTPOT a V aj aj ai 2 n JO UIF OFUXPSL UP UIF UBSHFU QFSTPO UIF TDPSF PG UIF TIPSUFTU BTTPDJBUJPO GSPN UP aj JT EFOPUFE BT Lmin *O B HSBQI UIF TIPSUFTU QBUI CFUXFFO UXP OPEFT DBO CF GPVOE VTJOH UIF TUBUFPGUIFBSU BMHPSJUINT GPS FYBNQMF %JKLTUSB BMHPSJUIN )PXFWFS XF BSF EFBMJOH XJUI B MBSHFTDBMF2 TPDJBM OFUXPSL UIF DPOWFOUJPOBM %JKLTUSB BMHPSJUIN SFTVMUT JO B IJHI UJNF DPNQMFYJUZ PG O.n / 8F VTF B IFBQCBTFE %JKLTUSB BMHPSJUIN UP RVJDLMZ mOE UIF TIPSUFTU BTTPDJBUJPOT UIBU DBO BDIJFWF B DPNQMFYJUZ PG O.nlogn/ /FBSTIPSUFTU BTTPDJBUJPOT mOEJOH #BTFE PO UIF TIPSUFTU BTTPDJBUJPO TDPSF Lmin >0 GPVOE JO 4UFQ BOE B QSFEFmOFE QBSBNFUFS $ UIF BMHPSJUIN SFRVJSFT FOVNFSBUJPO PG BMM BTTP .1 $/Lmin DJBUJPOT UIBU BSF MFTT UIBO C CZ B EFQUImSTU TFBSDI 8F DPOTUSBJO UIF MFOHUI PG BO BTTPDJBUJPO UP CF MFTT UIBO B QSFEFmOFE UISFTIPME ɩJT MFOHUI SFTUSJDUJPO DBO SFEVDF UIF DPN QVUBUJPOBM DPTU BOE FBDI BTTPDJBUJPO TDPSF JT DBMDVMBUFE CZ TVNNJOH UIF EJTUBODFT DPNQVUFE CZ &RVBUJPO CFUXFFO BVUIPST PO UIF BTTPDJBUJPO 'JOBMMZ BMM BTTPDJBUJPOT BSF SBOLFE CBTFE PO UIF TDPSFT BDDPSEJOH UP UIF QPMJDZ PG iUIF MPXFS UIF CFTUw 5BCMF 1FSGPSNBODFT PG BTTPDJBUJPO TFBSDI 4FDPOE Test Set Method Total Time Avg. Time Brute Force 483,708 483.71 Average Two-stage Baseline 1,161,441 1161.44 Our Approach 2,941 2.94 "TTPDJBUJPO 4FBSDI 1FSGPSNBODF "T UIFSF JT OP B TUBOEBSE EBUB TFU GPS FWBMVBUJOH UIF BTTPDJBUJPO TFBSDI )FSF XF GPDVT PO FWBMVBUJOH UIF FĊFDUJWFOFTT PG UIF QSPQPTFE BQQSPBDI 8F DSFBUFE UFTU TFUT FBDI PG UIFN DPOUBJOJOH 369o1; 000 BTTPDJBUJPO RVFSJFT JF QFSTPO QBJST "O BTTPDJBUJPO RVFSZ JT DPNQPTFE PG B TPVSDF QFSTPO BOE B UBSHFU QFSTPO ɩF UFTU TFUT XFSF DSFBUFE BT GPMMPXT 8F SBOEPNMZ TFMFDUFE 1; 000 QFSTPO QBJST GSPN UIF SFTFBSDIFS OFUXPSL BOE DSFBUFE UIF mSTU UFTU TFU 'PS UIF PUIFS FJHIU UFTU TFUT XF DPMMFDUFE QFSTPO "$"%&.*$ 40$*"- /&5803, .*/*/( 'JHVSF "O FYBNQMF SFTVMU PG BEWJTPSBEWJTFF SFMBUJPOTIJQ NJOJOH MJTUT PG EJĊFSFOU SFTFBSDI BSFBT FH %BUB .JOJOH %. BOE 4FNBOUJD 8FC 48 BOE TFMFDUFE QFSTPO QBJST GSPN EJĊFSFOU SFTFBSDI BSFBT 8F VTF UIF BWFSBHF SVOOJOH UJNF PO B UFTU TFU UP FWBMVBUF PVS BQQSPBDI BOE UP DPNQBSF XJUI PUIFS NFUIPET 3VOOJOH UJNFT EP OPU JODMVEF UIF UJNF SFRVJSFE UP MPBE UIF TPDJBM OFUXPSL BOE PVUQVU UIF BTTPDJBUJPOT 8F VTFE UIF NFUIPE PG CSVUF GPSDF FOVNFSBUJPO BT UIF CBTFMJOF *O UIJT NFUIPE XF EJSFDUMZ DPOEVDUFE EFQUImSTU TFBSDI PO UIF TPDJBM OFUXPSL UP mOE BTTPDJBUJPOT XJUI MFOHUI MFTT UIBO UIF UISFTIPME max@length 8F BMTP EFmOFE B UXPTUBHF NFUIPE BT UIF CBTFMJOF *O UIF mSTU TUBHF PG UIF NFUIPE XF NBLF VTF PG UIF DPOWFOUJPOBM %JKLTUSB BMHPSJUIN <> UP mOE TIPSUFTU QBUIT BOE JO UIF TFDPOE TUBHF XF VTF EFQUImSTU TFBSDI UP mOE BTTPDJBUJPOT XJUI MFOHUI MFTT UIBO UIF UISFTIPME max@length 5BCMF TIPXT UIF SFTVMUT PO UIF UFTU TFUT 8F TFF UIBU PVS BQQSPBDI BDIJFWF IJHI QFSGPS NBODF JO BMM PG UIF BTTPDJBUJPO TFBSDI UBTLT *O UFSNT PG UIF BWFSBHF UJNF PVS BQQSPBDI DBO mOE BTTPDJBUJPOT JO MFTT UIBO T "$"%&.*$ 40$*"- /&5803, .*/*/( 8F OPX JO QBSUJDVMBS EJTDVTT IPX UIF JOUSPEVDFE UFDIOPMPHJFT JO $IBQUFST o BSF BQQMJFE JO "SOFU.JOFS 'PS TPDJBM UJF BOBMZTJT XF BQQMJFE UIF QSPQPTFE VOTVQFSWJTFE NFUIPE 51'( DG 4FDUJPO UP BVUPNBUJDBMMZ JOGFS BEWJTPSBEWJTFF SFMBUJPOTIJQT 'PS TPDJBM JOnVFODF XF VTF "3/&5.*/&3 %&&1 .*/*/( '03 "$"%&.*$ 40$*"- /&5803,4 TFWFSBM DBTF TUVEJFT UP EFNPOTUSBUF IPX FĊFDUJWF UIF UPQJDCBTFE TPDJBM JOnVFODF HSBQIT MFBSOFE CZ UIF NFUIPE QSFTFOUFE JO 4FDUJPO 'PS VTFS NPEFMJOH XF VTF UIF NFUIPE EFTDSJCFE JO 4FDUJPO UP FYUSBDU BVUIPST SFTFBSDI JOUFSFTUT .*/*/( "%7*403"%7*4&& 3&-"5*0/4)*14 8F BQQMJFE UIF JOUSPEVDFE NFUIPE 51'( JO 4FDUJPO UP BOBMZ[F UIF SPMFT PG BVUIPST BOE EJTDPWFS UIF MJLFMZ BEWJTPSBEWJTFF SFMBUJPOTIJQT &YQFSJNFOUBM SFTVMUT TIPX UIBU UIF QSPQPTFE BQQSPBDI JOGFS BEWJTPSBEWJTFF SFMBUJPOTIJQT FċDJFOUMZ BOE BDIJFWFT B TUBUFPGUIFBSU BDDVSBDZ XJUIPVU BOZ TVQFSWJTFE JOGPSNBUJPO 'JHVSF TIPXT UIF SFTVMUT PG JOGFSSJOH BEWJTPS BEWJTFF SFMBUJPOTIJQT GSPN UIF DPBVUIPS OFUXPSL ɩF mHVSF JT UIF FHPOFUXPSL PG UIF DFOUFSFE BVUIPS i+JF 5BOHw ɩF SFE DPMPSFE MJOL JOEJDBUFT UIBU UIF BVUIPS PO UIF PUIFS FOE PG UIF MJOL JT UIF JEFOUJmFE BEWJTPS PG i+JF 5BOHw BOE UIF ZFMMPX DPMPSFE SFMBUJPOTIJQT JOEJDBUF UIPTF BVUIPST PO UIF PUIFS FOE BSF BEWJTFF PG i+JF 5BOH w XIJMF HSFFO DPMPSFE MJOLT JOEJDBUF DPMMFBHVF SFMBUJPOTIJQT "QQMJDBUJPOT &YQFSU mOEJOH BOE #PMF TFBSDI ɩF JEFOUJmFE BEWJTPSBEWJTFF SFMBUJPOTIJQT DBO IFMQ XJUI NBOZ BQQMJDBUJPOT )FSF XF JMMVTUSBUF POF BQQMJDBUJPO PO CPMF TFBSDI <> B TQFDJmD FYQFSU mOEJOH UBTL BJNJOH UP JEFOUJGZ CFTU TVQFSWJTPST BDDPSEJOH UP UIFJS OVSUVSF BCJMJUZ <> JO B TQFDJmD SFTFBSDI mFME ɩF UBTL SFRVJSFT BEWJTPSBEWJTFF SFMBUJPOTIJQT BT JOQVU XIJDI BSF VTVBMMZ VOBWBJMBCMF 5P RVBOUJUBUJWFMZ FWBMVBUF IPX UIF BEWJTPSBEWJTFF SFMBUJPOTIJQT DBO IFMQ CPMF TFBSDI XF DPNQBSF B SFUSJFWBM NFUIPE XJUI BOE XJUIPVU UIPTF SFMBUJPOTIJQT PO B EBUB TFU VTFE JO :BOH FU BM <> 4QFDJmDBMMZ UIF EBUB TFU DPOTJTUT RVFSJFT FH EBUB NJOJOH BOE NBDIJOF MFBSOJOH BOE GPS FBDI RVFSZ UPQSBOLFE SFTFBSDIFST CZ "SOFU.JOFSPSH BSF UBLFO BT DBOEJEBUFT 8F TFOU BO FNBJM UP FBDI PG UIF SFTFBSDIFST BOE BOPUIFS ZPVOH SFTFBSDIFST XIP TUBSU QVCMJTIJOH QBQFST POMZ JO SFDFOU ZFBST > 2003 GPS GFFECBDLT iZFT w PS iOP w PS iOPU TVSFw 'JOBMMZ B MJTU PG CFTU TVQFSWJTPST BSF PSHBOJ[FE GPS FBDI RVFSZ CZ TJNQMZ DPVOUJOH UIF OVNCFS PG iZFTw BOE iOPw GSPN UIF SFDFJWFE GFFECBDLT %FUBJMT DBO CF SFGFSSFE UP JO :BOH FU BM <> 'PS FBTZ DPN QBSJTPO XF EJE OPU VTF UIF MFBSOJOHUPSBOL BQQSPBDI BT SFQPSUFE JO :BOH FU BM <> *OTUFBE XF VTF UIF MBOHVBHF NPEFM -. XIJDI EPFT OPU DPOTJEFS UIF BEWJTPSBEWJTFF SFMBUJPOTIJQT BOE B IFVSJTUJDCBTFE NFUIPE XIJDI TJNQMZ DPNCJOFT UIF MBOHVBHF NPEFM XJUI UIF BEWJTPSBEWJTFF SFMBUJPOTIJQT JEFOUJmFE CZ UIF CBTFMJOF NFUIPE -. 3VMF PS JEFOUJmFE PVS QSPQPTFE BQQSPBDI -. 51'( CZ 1 si ˛ri .1 ˛/ raj ; D C $ Ai aj Ai j j X2 XIFSF ri JT UIF SFMFWBODF TDPSF PCUBJOFE CZ UIF MBOHVBHF NPEFM Ai JT B TFU PG BEWJTFFT PG SFTFBSDIFS ai JEFOUJmFE CZ UIF SVMFCBTFE NFUIPE PS 51'( BOE ˛ JT B QBSBNFUFS UP USBEF PĊ UIF CBMBODF ˛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mDBOUMZ JNQSPWFE 8F DBO BMTP TFF UIBU XJUI B IJHIFS BDDVSBDZ 51'( DMFBSMZ BDIJFWFT B CFUUFS JNQSPWFNFOUT QBSUJDVMBSMZ GPS UIF UPQ UXP SFUSJFWFE SFTVMUT CZ 51'( WT CZ SVMFCBTFE NFUIPE JO UFSNT PG 1! .&"463*/( "$"%&.*$ */'-6&/$& 8F BQQMJFE UIF 5PQJDBM "ċOJUZ 1SPQBHBUJPO 5"1 NFUIPE QSFTFOUFE JO 4FDUJPO UP "SOFU .JOFS UP JEFOUJGZ SFQSFTFOUBUJWF BVUIPST BOE SFQSFTFOUBUJWF QBQFST 5BCMF TIPXT SFQSFTFOUBUJWF OPEFT BVUIPST BOE QBQFST GPVOE CZ PVS BMHPSJUIN PO EJĊFSFOU UPQJDT GSPN UIF DPBVUIPS EBUB TFU BOE UIF DJUBUJPO EBUB TFU ɩF SFQSFTFOUBUJWF TDPSF PG FBDI OPEF JT UIF QSPCBCJMJUZ PG UIF OPEF JOnVFODJOH UIF PUIFS OPEFT PO UIJT UPQJD ɩF QSPCBCJMJUZ j NB.i/ i $ij N 2 [f g JT DBMDVMBUFE CZ i P1 j NB.i/ j $ij 8F DBO TFF TPNF JOUFSFTUJOH SFTVMUT 'PS FYBNQMF TPNF D 2 [f g QBQFST FH i'B$5P BOEP J'B$5w UIBU EP IBWF IBWF B IJHI DJUBUJPO OVNCFS NJHIU CF TFMFDUFE BT UIF SFQSFTFOUBUJWF OPEFT ɩJT JT CFDBVTF PVS BMHPSJUIN DBO JEFOUJGZ UIF JOnVFODFT CFUXFFO QBQFST UIVT DBO EJĊFSFOUJBUF UIF DJUBUJPOT PG UIF UIFPSFUJDBM CBDLHSPVOE PG B QBQFS BOE BO PEE DJUBUJPO JO UIF SFGFSFODF 5BCMF TIPXT GPVS SFQSFTFOUBUJWF BVUIPST BOE SFTFBSDIFST XIP BSF NPTUMZ JOnVFODFE CZ UIFN 5BCMF TIPXT UXP SFQSFTFOUBUJWF QBQFST BOE QBQFST UIBU BSF NPTUMZ JOnVFODF CZ UIF UXP QBQFST 4PNF PUIFS NFUIPE FH UIF TJNJMBSJUZCBTFE CBTFMJOF NFUIPE VTJOH DPTJOF NFUSJD DBO CF BMTP VTFE UP FTUJNBUF UIF JOnVFODF BDDPSEJOH UP UIF TJNJMBSJUZ TDPSF $PNQBSJOH XJUI UIF TJNJMBSJUZCBTFE CBTFMJOF NFUIPE UIF QSFTFOUFE 5"1 NFUIPE IBT TFWFSBM EJTUJODU BEWBOUBHFT 'JSTU TVDI B NFUIPE DBO POMZ NFBTVSF UIF TJNJMBSJUZ CFUXFFO OPEFT CVU DBOOPU UFMM XIJDI OPEF IBT B TUSPOHFS JOnVFODF PO UIF PUIFS POF 4FDPOE UIF NFUIPE DBOOPU UFMM XIJDI OPEFT IBWF UIF "3/&5.*/&3 %&&1 .*/*/( '03 "$"%&.*$ 40$*"- /&5803,4 5BCMF 3FQSFTFOUBUJWF OPEFT EJTDPWFSFE CZ PVS BMHPSJUIN PO UIF DPBVUIPS EBUB TFU BOE UIF DJUBUJPO EBUB TFU Dataset Topic Representative Nodes Data Mining Heikki Mannila, Philip S. Yu, Dimitrios Gunopulos, Jiawei Han, Christos Faloutsos, Bing Liu, Vipin Kumar, Tom M. Mitchell, Wei Wang, Qiang Yang, Xindong Wu, Jeffrey Xu Yu, Osmar R. Zaiane Author Machine Learning Pat Langley, Alex Waibel, Trevor Darrell, C. Lee Giles, Terrence J. Sejnowski, Samy Bengio, Daphne Koller, Luc De Raedt, Vasant Honavar, Floriana Esposito, Bernhard Scholkopf Database System Gerhard Weikum, John Mylopoulos, Michael Stonebraker, Barbara Pernici, Philip S. Yu, Sharad Mehrotra, Wei Sun, V. S. Subrahmanian, Alejandro P. Buchmann, Kian-Lee Tan, Jiawei Han Information Retrieval Gerard Salton, W. Bruce Croft, Ricardo A. Baeza-Yates, James Allan, Yi Zhang, Mounia Lal- mas, Zheng Chen, Ophir Frieder, Alan F. Smeaton, Rong Jin Web Services Yan Wang, Liang-jie Zhang, Schahram Dustdar, Jian Yang, Fabio Casati, Wei Xu, Zakaria Maamar, Ying Li, Xin Zhang, Boualem Benatallah, Boualem Benatallah Semantic Web Wolfgang Nejdl, Daniel Schwabe, Steffen Staab, Mark A. Musen, Andrew Tomkins, Juliana Freire, Carole A. Goble, James A. Hendler, Rudi Studer, Enrico Motta Bayesian Network Daphne Koller, Paul R. Cohen, Floriana Esposito, Henri Prade, Michael I. Jordan, Didier Dubois, David Heckerman, Philippe Smets Data Mining Fast Algorithms for Mining Association Rules in Large Databases, Using Segmented Right- Deep Trees for the Execution of Pipelined Hash Joins, Web Usage Mining: Discovery and Applications of Usage Patterns from Web Data, Discovery of Multiple-Level Association Rules Citation from Large Databases, Interleaving a Join Sequence with Semijoins in Distributed Query Pro- cessing Machine Learning Object Recognition with Gradient-Based Learning, Correctness of Local Probability Propaga- tion in Graphical Models with Loops, A Learning Theorem for Networks at Detailed Stochastic Equilibrium, The Power of Amnesia: Learning Probabilistic Automata with Variable Memory Length, A Unifying Review of Linear Gaussian Models Database System Mediators in the Architecture of Future Information Systems, Database Techniques for the World-Wide Web: A Survey, The R*-Tree: An Efficient and Robust Access Method for Points and Rectangles, Fast Algorithms for Mining Association Rules in Large Databases Web Services The Web Service Modeling Framework WSMF, Interval Timed Coloured Petri Nets and their Analysis, The design and implementation of real-time schedulers in RED-linux, The Self-Serv Environment for Web Services Composition Web Mining Web Usage Mining: Discovery and Applications of Usage Patterns from Web Data, Fast Algo- rithms for Mining Association Rules in Large Databases, The OO-Binary Relationship Model: A Truly Object Oriented Conceptual Model, Distributions of Surfers’ Paths Through the World Wide Web: Empirical Characterizations, Improving Fault Tolerance and Supporting Partial Writes in Structured Coterie Protocols for Replicated Objects Semantic Web FaCT and iFaCT, The GRAIL concept modelling language for medical terminology, Semantic Integration of Semistructured and Structured Data Sources, Description of the RACER System and its Applications, DL-Lite: Practical Reasoning for Rich Dls IJHIFTU JOnVFODFT JO UIF OFUXPSL XIJDI UIF QSFTFOUFE 5"1 BQQSPBDI OBUVSBMMZ IBT UIF DBQBDJUZ UP EP ɩJT QSPWJEFT NBOZ JNNFEJBUF BQQMJDBUJPOT GPS FYBNQMF FYQFSU mOEJOH 8F GVSUIFS DPOEVDU B EZOBNJD JOnVFODF BOBMZTJT 8F VTF %S +JBO 1FJ BT UIF FYBNQMF UP BOBMZ[F IPX UIF JOnVFODFT PG %S 1FJ PO PS CZ IJT DPBVUIPST DIBOHF EVSJOH BOE 5BCMF TIPXT UIF EZOBNJD BOBMZTJT SFTVMU 8F TFF UIBU UIF JOnVFODF FWPMVUJPO VODPWFST UIF HSPXJOH VQ PG %S 1FJ 'PS FYBNQMF JO %S 1FJ JT NBJOMZ JOnVFODFE CZ 1SPG )BO XIJMF IF POMZ IBT MJNJUFE JOnVFODF PO 1SPG )BO "GUFS %S 1FJ TUBSUT JOnVFODJOH TPNF PUIFS SFTFBSDIFST FH $IVO 5BOH BOE 4IJXFJ 5BOH 8IJMF JO %S 1FJ BMSFBEZ CFDPNFT B NBUVSF SFTFBSDIFS BOE IBT NBOZ TUSPOH JOnVFODFT PO PUIFS SFTFBSDIFST "$"%&.*$ 40$*"- /&5803, .*/*/( "O FYBNQMF SFTVMU PG VTFS JOUFSFTU NPEFMJOH 'JHVSF "3/&5.*/&3 %&&1 .*/*/( '03 "$"%&.*$ 40$*"- /&5803,4 5BCMF &YBNQMF PG JOnVFODF BOBMZTJT GSPN UIF DPBVUIPS EBUB TFU ɩFSF BSF UXP SFQSFTFOUBUJWF BVUIPST BOE FYBNQMF MJTU PG SFTFBSDIFST XIP BSF NPTUMZ JOnVFODFE CZ UIFN PO UPQJD iEBUB NJOJOH w BOE UIFJS DPSSFTQPOEJOH JOnVFODFE PSEFS PO UPQJD iEBUBCBTFw BOE iNBDIJOF MFBSOJOHw Topic Data Mining Influencer Jiawei Han Heikki Mannila David Clutter Arianna Gallo Hasan M. Jamil Marcel Holsheimer Influencee K. P. Unnikrishnan Robert Gwadera Ramasamy Uthurusamy Vladimir Estivill-Castro Shiwei Tang Mika Klemettinen Topic Database Influencer Jiawei Han Heikki Mannila David Clutter Vladimir Estivill-Castro Shiwei Tang Marcel Holsheimer Influencee Hasan M. Jamil Robert Gwadera Ramasamy Uthurusamy Mika Klemettinen K. P. Unnikrishnan Arianna Gallo Topic Machine Learning Influencer Jiawei Han Heikki Mannila Hasan M. Jamil Vladimir Estivill-Castro K. P. Unnikrishnan Marcel Holsheimer Influencee Shiwei Tang Mika Klemettinen Ramasamy Uthurusamy Robert Gwadera David Clutter Arianna Gallo .0%&-*/( 3&4&"3$)&3 */5&3&454 8F BQQMJFE UIF NFUIPE QSFTFOUFE JO 4FDUJPO UP "SOFU.JOFS UP NPEFM BVUIPST SFTFBSDI JOUFSFTUT ɩF CBTJD JEFB JT UP VTF UIF QSFEJDUJPO NPEFM UP QSFEJDU XIP XJMM CF JOUFSFTUFE JO XIJDI QSFEFmOFE UPQJDT 'JHVSF TIPXT BO FYBNQMF SFTVMU PG VTFS JOUFSFTU NPEFMJOH ɩF NJEEMF PG UIF mHVSF TIPXT UIF BVUIPST SFTFBSDI JOUFSFTUT BOE JOUFSFTU DIBOHFT PWFS UJNF $0/$-64*0/4 *O UIJT DIBQUFS XF JOUSPEVDF B TZTUFN"SOFU.JOFSGPS EFFQ NJOJOH PG B SFTFBSDIFS TPDJBM OFUXPSL 8F JOUSPEVDF UIF BSDIJUFDUVSF BOE UIF NBJO GFBUVSFT PG UIF TZTUFN 8F EFTDSJCF JO EFUBJM UIF SFTFBSDI JTTVFT UIBU XF BSF DVSSFOUMZ GPDVTJOH PO BOE QSPQPTFE PVS BQQSPBDIFT UP UIFN 8F IBWF DBSSJFE PVU FYQFSJNFOUT GPS FWBMVBUJOH FBDI PG UIF QSPQPTFE BQQSPBDIFT &YQFSJNFOUBM SFTVMUT JOEJDBUF UIBU UIF QSPQPTFE NFUIPET DBO BDIJFWF IJHI QFSGPSNBODFT *O UIF JNQMFNFOUBUJPO PG "SOFU.JOFS XF IBWF B GFX QSPCMFNT XIJDI OFFE UP CF JOWFTUJ HBUFE JO UIF GVUVSF GPS FYBNQMF FYUSBDUJPO PG NPSF UZQFT PG SFMBUJPOTIJQT *O "SOFU.JOFS XF VTF $0/$-64*0/4 5BCMF &YBNQMF PG JOnVFODF BOBMZTJT SFTVMUT PO UPQJD iEBUB NJOJOHw GSPN UIF DJUBUJPO EBUB TFU ɩFSF BSF UXP SFQSFTFOUBUJWF QBQFST BOE FYBNQMF QBQFS MJTUT UIBU BSF NPTUMZ JOnVFODFE CZ UIFN Influential paper Fast Algorithms for Mining Association Rules in Large Databases Mining Large Itemsets for Association Rules A New Framework For Itemset Generation Efficient Mining of Partial Periodic Patterns in Time Series Database Influenced paper A New Method for Similarity Indexing of Market Basket Data A General Incremental Technique for Maintaining Discovered Associa- tion Rules Influential paper Web Usage Mining: Discovery and Applications of Usage Patterns from Web Data Mining Web Site’s Clusters from Link Topology and Site Hierarchy Predictive Algorithms for Browser Support of Habitual User Activities on the Web Influenced paper A Fine Grained Heuristic to Capture Web Navigation Patterns A Road Map to More Effective Web Personalization: Integrating Domain Knowledge with Web Usage Mining 5BCMF %ZOBNJD JOnVFODF BOBMZTJT GPS %S +JBO 1FJ EVSJOH o %VF UP TQBDF MJNJUBUJPO XF POMZ MJTU DPBVUIPST XIP NPTU JOnVFODF POCZ %S 1FJ JO FBDI UJNF XJOEPX Year Pairwise Influence Influence Jiawei Han (0.4961) 2000 on Dr. Pei Influenced Jiawei Han (0.0082) by Dr. Pei Influence Jiawei Han (0.4045), Ke Wang (0.0418), Jianyong Wang (0.019), 2002 on Dr. Pei Xifeng Yan (0.007), Shiwei Tang (0.0052) Influenced Shiwei Tang (0.436), Hasan M.Jamil (0.4289), Xifeng Yan by Dr. Pei (0.2192), Jianyong Wang (0.1667), Ke Wang (0.0687) Influence Jiawei Han (0.2364), Ke Wang (0.0328), Wei Wang (0.0294), 2004 on Dr. Pei Jianyong Wang (0.0248), Philip S. Yu (0.0156) Influenced Chun Tang (0.5929), Shiwei Tang (0.5426), Hasan M.Jamil by Dr. Pei (0.3318), Jianyong Wang (0.1609), Xifeng Yan (0.1458) Influence Jiawei Han (0.1201), Ke Wang (0.0351), Wei Wang (0.0226), 2006 on Dr. Pei Jianyong Wang (0.018), Ada Wai-Chee Fu (0.0125) Influenced Chun Tang (0.6095), Shiwei Tang (0.6067), Byung-Won On by Dr. Pei (0.4599), Hasan M.Jamil (0.3433), Jaewoo Kang (0.3386) Influence Jiawei Han (0.2202), Ke Wang (0.0234), Ada Wai-Chee Fu 2008 on Dr. Pei (0.0208), Wei Wang (0.011), Jianyong Wang (0.0095) Influenced ZhaoHui Tang (0.654), Chun Tang (0.6494), Shiwei Tang by Dr. Pei (0.5923), Zhengzheng Xing (0.5549), Hasan M.Jamil (0.3333) "3/&5.*/&3 %&&1 .*/*/( '03 "$"%&.*$ 40$*"- /&5803,4 UIF DPBVUIPS SFMBUJPOTIJQ BT UIF SFMBUJPOTIJQ JO B TPDJBM OFUXPSL *O UIF GVUVSF XF XJMM FYUSBDU PUIFS SFMBUJPOTIJQT GPS FYBNQMF UIF SFMBUJPOTIJQ PG DPPSHBOJ[BUJPO BOE DPQSPKFDU FUD *O GVUVSF XPSL XF BMTP QMBO UP JOWFTUJHBUF NPSF NJOJOH JTTVFT GPS FYBNQMF IPX UP JOUFHSBUF UIF DJUBUJPO JOGPSNBUJPO JOUP UIF UPQJD NPEFMT $ )"15&3 3FTFBSDI 'SPOUJFST ɩF HFOFSBM QSPCMFN PG NJOJOH LOPXMFEHF MJOLT BOE TPDJBM OFUXPSLT SFQSFTFOUT BO JOUFSFTUJOH SFTFBSDI EJSFDUJPO JO DPNQVUFS TDJFODF ɩFSF BSF TUJMM NBOZ DIBMMFOHFT BOE BMTP QPUFOUJBM GVUVSF EJSFDUJPOT PO UIJT UPQJD )FSF XF MJTU TFWFSBM NBKPS DIBMMFOHFT t #JH EBUB WT TNBMM EBUB #JH EBUB JT POF PG UIF IPUUFTU UFSNT VTFE UPEBZ UP EFTDSJCF UIF FYQPOFOUJBM HSPXUI BOE BWBJMBCJMJUZ PG EBUB PO UIF *OUFSOFU 5FDIOJDBMMZ UIFSF BSF TFWFSBM DIBMMFOHFT BOE BMTP PQQPSUVOJUJFT 'JSTU BT UIF EBUB JT HFOFSBUFE EZOBNJDBMMZ BOE BSSJWFT JO B TUSFBNJOH NBOOFS JU JT OFDFTTBSZ UP EFWFMPQ FċDJFOU BMHPSJUIN GPS JODSFNFOUBMMZ NJOJOH UIF TFNBOUJDT PG MJOLT BOE TPDJBM SFMBUJPOTIJQT JO MBSHF EZOBNJD OFUXPSLT 0O UIF PUIFS IBOE QFPQMF BMTP BSHVF UIBU CJH EBUB NBZ CF OPU UIBU JNQPSUBOU *O NBOZ QSBDUJDBM BQQMJDBUJPOT TNBMM EBUB NJHIU CF TVċDJFOU UP BDIJFWF BO FOPVHI BDDVSBUF QFSGPSNBODF #JH EBUB NBZ POMZ JOUSPEVDF FYUSB DPNQVUBUJPOBM DPTU ɩF DIBMMFOHJOH RVFTUJPO JT XIFO TIPVME XF SFTPSU UP CJH EBUB BOE XIFO TIPVME XF TJNQMZ DPOTJEFS TBNQMFE TNBMM EBUB t .BDSP WT NJDSP "U UIF NBDSPMFWFM TPDJBM OFUXPSL NJOJOH GPDVTFT PO TUVEZJOH UIF HMPCBM QBUUFSOT PG UIF TPDJBM OFUXPSLT BOE BU UIF NJDSPMFWFM JU JT NBJOMZ DPODFSOFE XJUI NPEFMJOH JOEJWJEVBMT CFIBWJPST BOE JOUFSBDUJPOT CFUXFFO VTFST 8IBU JT UIF GVOEBNFOUBM SFMBUJPOTIJQ CFUXFFO UIF UXP UZQFT PG BOBMZTFT 8IFO TIPVME XF DPOTJEFS NBDSPMFWFM BOBMZTJT BOE XIFO NJDSP t (MPCBMJUZ WT MPDBMJUZ .PTU FYJTUJOH XPSLT GPDVT PO TUVEZJOH TPDJBM SFMBUJPOTIJQT JO UIF FOUJSF OFUXPSL )PXFWFS BT NPTU VTFST BOE UIFJS CFIBWJPST BSF JOnVFODFE CZ GSJFOET JO UIFJS MPDBM DJSDMFT *U XPVME CF JOUFSFTUJOH UP TUVEZ IPX TFNBOUJDT PG TPDJBM SFMBUJPOTIJQT DBO CF JOGFSSFE GSPN UIF MPDBMJUZ QFSTQFDUJWF ɩFSF BSF TPNF SFMBUFE SFTFBSDI PO UIJT UPQJD 'PS FYBNQMF .D"VMFZ BOE -FTLPWFD EFWFMPQFE B TFNJTVQFSWJTFE MFBSOJOH GSBNFXPSL GPS BVUPNBUJDBMMZ HSPVQJOH B VTFST GSJFOET JOUP EJĊFSFOU DJSDMFT <> ;IBOH FU BM QSPQPTFE UIF OPUJPO PG TP DJBM JOnVFODF MPDBMJUZ <> ɩFZ mOE UIBU UIF JOnVFODF CFUXFFO VTFST JT TUSPOHMZ DPSSFMBUFE XJUI UIF JOOFS TUSVDUVSF GPSNFE CZ UIFN t $PSSFMBUJPO WT DBVTBMJUZ .PTU FYJTUJOH NFUIPEPMPHJFT POMZ DPOTJEFS DPSSFMBUJPO CFUXFFO WBSJBCMFT )PXFWFS DPSSFMBUJPO JT OPU FRVBM UP DBVTBMJUZ *O NBOZ QSPCMFNT XF NBZ CF NPSF JOUFSFTUFE JO VOEFSTUBOEJOH UIF SFBTPO PG B QIFOPNFOPO SBUIFS UIBO PCTFSWJOH PUIFS DPSSFMBUFE QIFOPNFOB 3&4&"3$) '30/5*&34 t 1SFDJTF WT BQQSPYJNBUJPO 5P QSFDJTFMZ QSPDFTT UIF OFUXPSLFE EBUB JT DPNQVUBUJPOBMMZ DPTUMZ )PXFWFS BT POMJOF OFUXPSLT CFDPNF MBSHFS BOE MBSHFS JU JT OFDFTTBSZ UP mOE TPNF FċDJFOU BMHPSJUINT UP TQFFE VQ UIF QSPDFTT FWFO XJUI TPNF MPTT PO UIF QSFDJTJPO 'SPN UIF BMHP SJUINJD QFSTQFDUJWF JU JT DIBMMFOHJOH UP EFTJHO FĊFDUJWF BMHPSJUINT XJUI UIFPSFUJDBM BQQSPY JNBUJPO HVBSBOUFFT t 4PDJBM UIFPSJFT )PX EPFT POF TFBNMFTTMZ JODPSQPSBUF TPDJBM UIFPSJFT JOUP UIF NJOJOH BMHP SJUINT 5SBEJUJPOBMMZ UIJT QSPCMFN IBT CFFO EFBMU XJUI JO BO BE IPD NBOOFS 'PS FYBNQMF )PQDSPGU FU BM <> BOE 5BOH FU BM <> DPNCJOFE TPDJBM CBMBODF UIFPSZ TPDJBM TUBUVT UIF PSZ BOE TUSVDUVSBM IPMF UIFPSZ JOUP UIF GBDUPS HSBQI NPEFM )PXFWFS JU JT TUJMM OPU DMFBS IPX UP EFWFMPQ B VOJmFE NPEFM TP UIBU UIF PUIFS TPDJBM UIFPSJFT DBO CF FBTJMZ JODPSQPSBUFE .PSF JNQPSUBOUMZ UIF TPDJBM OFUXPSLT BSF WFSZ EZOBNJD ɩF TFNBOUJD PG TPDJBM SFMBUJPOTIJQT NBZ DIBOHF PWFS UJNF *U JT JNQPSUBOU UP DBQUVSF UIF EZOBNJD QBUUFSO BOE JOGFS UIF DIBOHFT PG TPDJBM SFMBUJPOTIJQT t "QQMJDBUJPOT *U IBT NBOZ SFBM BQQMJDBUJPOT CBTFE PO UIF SFTVMUT PG NJOJOH LOPXMFEHF MJOLT BOE TPDJBM UJF 'PS FYBNQMF XF DBO VTF UIF JOGFSSFE TPDJBM UJFT UP IFMQ JOGPSNBUJPO SFDPN NFOEBUJPO JO UIF TPDJBM OFUXPSL "DDPSEJOH UP UIF TPDJBM JOnVFODF UIFPSZ B VTFST DPOOFD UJPOT XJUI EJĊFSFOU TPDJBM UJFT XPVME IBWF WFSZ EJĊFSFOU JOnVFODF PO IFSIJT CFIBWJPST GSPN EJĊFSFOU BTQFDUT " 11&/%*9 " 3FTPVSDFT 8F IBWF EFWFMPQFE B 4PDJBM "OBMZUJD &OHJOF 4"& GPS BOBMZ[JOH BOE NJOJOH MBSHF TPDJBM OFU XPSL ɩF DPSOFSTUPOF PG UIF BOBMZUJD FOHJOF JT B EJTUSJCVUFE HSBQI EBUBCBTF XIJDI QSPWJEFT TUPSBHF GPS UIF OFUXPSLJOH EBUB 0O UPQ PG UIF EBUBCBTF UIFSF BSF UISFF DPSF DPNQPOFOUT OFU XPSL JOUFHSBUJPO TPDJBM OFUXPSL BOBMZTJT BOE EJTUSJCVUFE NBDIJOF MFBSOJOH ɩF UPPMLJU DBO CF EPXOMPBE IFSF ?iiTb,ff;Bi?m#X+QKf +iM2ifb 2/# " 40'58"3& 8F BMTP QSPWJEF B MJTU PG TPGUXBSFT WBSJPVT TPDJBM UJF BOBMZTJT TPDJBM JOnVFODF BOBMZTJT BOE VTFS CFIBWJPS QSFEJDUJPO t 1-1'(. ɩF 1-1'(. NPEFM <> JT EFTJHOFE GPS JOGFSSJOH UIF UZQF PG TPDJBM SFMB UJPOTIJQT JO B QBSUJBMMZ MBCFMFE TPDJBM OFUXPSL ?iiT,ff `M2iKBM2`XQ`;fbQ+B HiB2 t 5SJ'( ɩF 5SJBE 'BDUPS (SBQI NPEFM < > BJNT UP QSFEJDU UIF GPSNBUJPO PG SFDJQSPDBM SFMBUJPOTIJQT BOE UIF GPSNBUJPO PG USJBEJD DMPTVSF ?iiT,ff `M2iKBM2`XQ`;f`2+BT`Q+Biv t 5"1 ɩF 5PQJDBM "ċOJUZ 1SPQBHBUJPO BMHPSJUIN <> JT UP FTUJNBUF UIF UPQJDMFWFM TPDJBM JOnVFODF PO MBSHF OFUXPSLT ?iiT,ff `M2iKBM2`XQ`;fH #@/ i b2ibfbQBM7f t $POnVFODF ɩF $POnVFODF NPEFM <> GPSNBMJ[FT UIF FĊFDUT PG TPDJBM DPOGPSNJUZ JOUP B QSPCBCJMJTUJD GBDUPS HSBQI NPEFM BOE DBO EJTUJOHVJTI BOE RVBOUJGZ UIF FĊFDU PG UIF EJĊFSFOU UZQFT PG DPOGPSNJUJFT ?iiT,ff `M2iKBM2`XQ`;f*QM7Hm2M+2 t /55'(. ɩF /55'(. NPEFM <> GPSNBMJ[FT TPDJBM JOnVFODF DPSSFMBUJPO IP NPQIJMZ BOE VTFST BDUJPO EFQFOEFODZ JOUP B VOJmFE BQQSPBDI BOE EJTUJOHVJTIFT UIFJS FG GFDUT GPS NPEFMJOH BOE QSFEJDUJOH VTFST BDUJPOT JO TPDJBM OFUXPSLT ?iiT,ff `M2iKBM2`XQ`;fbiMif " 3&4063$&4 t "$5 ɩF "VUIPS$POGFSFODF5PQJD <> NPEFM DBO TJNVMUBOFPVTMZ NPEFM UPQJDBM EJT USJCVUJPOT PG QBQFST BVUIPST BOE DPOGFSFODFT PS BOZ UISFF EJĊFSFOU UZQFT PG FOUJUJFT ?iiT,ffF2;X+bXibBM;?m X2/mX+MfDB2i M;fbQ7ir `2f*h@+Q/2XxBT t )*4.BY% ɩF UXP BMHPSJUINT BJN UP EFUFDU UPQL TUSVDUVSBM IPMF TQBOOFST JO MBSHF TDBMF TPDJBM OFUXPSLT 8JUI UIF BMHPSJUINT XF EJTDPWFSFE UIBU XIP TQBO TUSVDUVSBM IPMFT DPOUSPM PG UIF JOGPSNBUJPO EJĊVTJPO PO 5XJUUFS ?iiT,ff `M2iKBM2`XQ`;fbi`m+im` H@?QH2 t 3"*/ ɩF NPEFM DBO KPJOUMZ NPEFM VTFST SPMFT BOE JOGPSNBUJPO EJĊVTJPO *U DBO EJTDPWFS EJĊFSFOU TPDJBM SPMFT BOE BMTP NPEFM IPX VTFST PG EJĊFSFOU TPDJBM SPMFT DPOUSPM UIF JOGPSNB UJPO EJĊVTJPO ?iiT,ff KBM2`XQ`;f#BHH#Q `/f` BM t 8IP"N* ɩF 8IP"N* NPEFM BJNT UP QSFEJDU VTFS EFNPHSBQIJDT CBTFE PO UIFJS DPN NVOJDBUJPO CFIBWJPST ?iiT,ff `M2iKBM2`XQ`;f/2KQ;` T?B+ " %"5" 4&54 8F BMTP QSPWJEF B MJTU PG EBUB TFUT GPS SFTFBSDI PO TPDJBM OFUXPSLT t $JUBUJPO ɩF DJUBUJPO EBUB JT FYUSBDUFE GSPN %#-1 "$. BOE PUIFS TPVSDFT DPOTJTUJOH PG > QBQFST BOE > DJUBUJPO SFMBUJPOTIJQT ɩF EBUB TFU DBO CF VTFE GPS DMVTUFSJOH XJUI OFUXPSL BOE TJEF JOGPSNBUJPO TUVEZJOH JOnVFODF JO UIF DJUBUJPO OFUXPSL mOEJOH UIF NPTU JOnVFOUJBM QBQFST UPQJD NPEFMJOH BOBMZTJT FUD ?iiT,ff `M2iKBM2`XQ`;f+Bi iBQM ?iiT,ff `M2iKBM2`XQ`;fJBM2`L2irQ`F DPOUBJOJOH NPSF JOGPSNBUJPO SFMBUFE UP BV UIPST t 8FJCP ɩJT JT B EZOBNJD 8FJCP OFUXPSLJOH EBUB DPOUBJOJOH NPSF UIBO VTFST GPMMPXJOH SFMBUJPOTIJQT PSJHJOBM UXFFUT BOE SFUXFFUT ɩF EBUBTFU JT VOJRVF BT JU DPOUBJOT BMM UIF EZOBNJD JOGPSNBUJPO ?iiT,ff `M2iKBM2`XQ`;fAM7Hm2M+2HQ+ HBiv t 5FODFOU 8FJCP ɩF EBUBTFU DPOUBJOT UIF EJSFDUFE GPMMPXJOH OFUXPSLT BOE QPTUJOH MPHT PG PWFS NJMMJPO VTFST JO 5FODFOU 8FJCP *O UPUBM XF IBWF VTFST BOE PSJHJOBM QPTUT 8F SFNPWFE PSJHJOBM QPTUT UIBU XFSF SFQPTUFE CZ GFXFS UIBO VTFST BOE VTF UIF SFNBJOJOH PSJHJOBM QPTUT GPS FYQFSJNFOUT ?iiT,ff `M2iKBM2`XQ`;f` BM t 'MJDLS ɩF 'MJDLS EBUBTFU DPOTJTUT PG SBOEPNMZ EPXOMPBEFE JNBHFT QPTUFE CZ VTFST 'PS FBDI JNBHF XF BMTP DPMMFDU JUT UBHT BOE BMM DPNNFOUT *O UPUBM XF IBWF " %"5" 4&54 DPNNFOUT QPTUFE CZ VTFST ?iiT,ff `M2iKBM2`XQ`;f2KQiBQM t /BNF EJTBNCJHVBUJPO ɩF EBUB TFU JT GSPN "SOFUNJOFSPSH DPOTJTUJOH PG NBOVBMMZ MBCFMFE EJTBNCJHVBUJPO SFTVMUT GPS QBQFST BVUIPSFE CZ BVUIPS OBNFT ?iiT,ff `M2iKBM2`XQ`;f/Bb K#B;m iBQM #JCMJPHSBQIZ <> -BEB " "EBNJD BOE &ZUBO "EBS 'SJFOET BOE OFJHICPST PO UIF XFC 4PDJBM /FUXPSLT o %0* 4 <> "SJT "OBHOPTUPQPVMPT 3BWJ ,VNBS BOE .PIBNNBE .BIEJBO *OnVFODF BOE DPSSFMBUJPO JO TPDJBM OFUXPSLT *O ,%% QBHFT o %0* <> $ISJTUPQIF "OESJFV /BOEP EF 'SFJUBT "SOBVE %PVDFU BOE .JDIBFM * +PSEBO "O JOUSPEVDUJPO UP NDND GPS NBDIJOF MFBSOJOH .BDIJOF -FBSOJOH o %0* " <> -BST #BDLTUSPN %BO )VUUFOMPDIFS +PO ,MFJOCFSH BOE 9JBOHZBOH -BO (SPVQ GPSNBUJPO JO MBSHF TPDJBM OFUXPSLT NFNCFSTIJQ HSPXUI BOE FWPMVUJPO *O ,%% QBHFT o %0* <> -BST #BDLTUSPN 3BWJ ,VNBS $BNFSPO .BSMPX +BTNJOF /PWBL BOE "OESFX 5PNLJOT 1SFGFSFOUJBM CFIBWJPS JO POMJOF HSPVQT *O 84%. QBHFT o %0* <> -BST #BDLTUSPN BOE +VSF -FTLPWFD 4VQFSWJTFE SBOEPN XBMLT QSFEJDUJOH BOE SFD PNNFOEJOH MJOLT JO TPDJBM OFUXPSLT *O 84%. QBHFT o %0* <> 3JDBSEP #BF[B:BUFT BOE #FSUIJFS 3JCFJSP/FUP .PEFSO *OGPSNBUJPO 3FUSJFWBM "$. 1SFTT <> /PSNBO 5+ #BJMFZ DzF .BUIFNBUJDBM DzFPSZ PG *OGFDUJPVT %JTFBTFT BOE JUT "QQMJDBUJPOT -PO EPO)JHI 8ZDPNCF $IBSMFT (SJċO <> &ZUBO #BLTIZ %FBO &DLMFT 3POH :BO BOE *UBNBS 3PTFOO 4PDJBM JOnVFODF JO TPDJBM BEWFSUJTJOH FWJEFODF GSPN mFME FYQFSJNFOUT *O &$ QBHFT o %0* <> "MCFSU-ÈT[MØ #BSBCÈTJ BOE 3ÏLB "MCFSU &NFSHFODF PG TDBMJOH JO SBOEPN OFUXPSLT 4DJ FODF o %0* TDJFODF #*#-*0(3"1): <> 4VHBUP #BTV .JLIBJM #JMFOLP BOE 3BZNPOE + .PPOFZ " QSPCBCJMJTUJD GSBNFXPSL GPS TFNJTVQFSWJTFE DMVTUFSJOH *O 1SPDFFEJOHT PG UIF 5FOUI "$. 4*(,%% *OUFSOBUJPOBM $PO GFSFODF PO ,OPXMFEHF %JTDPWFSZ BOE %BUB .JOJOH ,%% QBHFT o %0* <> 7ÈDMBW #FMBL 4BNBOUIB -BN BOE $POPS )BZFT $SPTTDPNNVOJUZ JOnVFODF JO EJTDVTTJPO GPSB *O *$84. QBHFT o <> %BWJE . #MFJ BOE +PO % .D"VMJĊF 4VQFSWJTFE UPQJD NPEFMT *O 1SPDFFEJOHT PG UIF UI /FVSBM *OGPSNBUJPO 1SPDFTTJOH 4ZTUFNT /*14 <> %BWJE . #MFJ "OESFX : /H BOE .JDIBFM * +PSEBO -BUFOU EJSJDIMFU BMMPDBUJPO +.-3 o <> 1IJMJQ #POBDJDI 'BDUPSJOH BOE XFJHIUJOH BQQSPBDIFT UP TUBUVT TDPSFT BOE DMJRVF JEFOUJmDBUJPO +PVSOBM PG .BUIFNBUJDBM 4PDJPMPHZ o %0* 9 <> 1IJMJQ #POBDJDI 1PXFS BOE DFOUSBMJUZ " GBNJMZ PG NFBTVSFT DzF "NFSJDBO +PVSOBM PG 4PDJPMPHZ o %0* <> 1IJMJQ #POBDJDI BOE 1BVMFUUF -MPZE &JHFOWFDUPSMJLF NFBTVSFT PG DFOUSBMJUZ GPS BTZNNFUSJD SFMBUJPOT 4PDJBM /FUXPSLT o %0* 4 <> 3PCFSU . #POE $ISJTUPQIFS + 'BSJTT +BTPO + +POFT "EBN % * ,SBNFS $BNFSPO .BS MPX +BJNF & 4FUUMF BOE +BNFT ) 'PXMFS " NJMMJPOQFSTPO FYQFSJNFOU JO TPDJBM JOnV FODF BOE QPMJUJDBM NPCJMJ[BUJPO /BUVSF o %0* OBUVSF <> %BO #SJDLMFZ BOE -JCCZ .JMMFS 'PBG WPDBCVMBSZ TQFDJmDBUJPO *O /BNFTQBDF %PDVNFOU IUUQYNMOTDPNGPBG 4FQUFNCFS <> $ISJT #VDLMFZ BOE &MMFO . 7PPSIFFT 3FUSJFWBM FWBMVBUJPO XJUI JODPNQMFUF JOGPSNBUJPO *O 4*(*3 QBHFT o %0* <> 3POBME 4 #VSU 4USVDUVSBM )PMFT DzF 4PDJBM 4USVDUVSF PG $PNQFUJUJPO )BSWBSE 6OJWFSTJUZ 1SFTT <> %FOH $BJ 9JBPGFJ )F BOE +JBXFJ )BO 4QFDUSBM SFHSFTTJPO GPS EJNFOTJPOBMJUZ SFEVDUJPO *O 5FDIOJDBM 3FQPSU 6*6$%$43 6*6$ <> .BSZ &MBJOF $BMJĊ BOE 3BZNPOE + .PPOFZ 3FMBUJPOBM MFBSOJOH PG QBUUFSONBUDI SVMFT GPS JOGPSNBUJPO FYUSBDUJPO *O 1SPDFFEJOHT PG "TTPDJBUJPO GPS UIF "EWBODFNFOU PG "SUJmDJBM *OUFMMJHFODF """* QBHFT o #*#-*0(3"1): <> +FSFNZ + $BSSPMM *BO %JDLJOTPO $ISJT %PMMJO %BWF 3FZOPMET "OEZ 4FBCPSOF BOE ,FWJO 8JMLJOTPO +FOB *NQMFNFOUJOH UIF TFNBOUJD XFC SFDPNNFOEBUJPOT *O 888 QBHFT o %0* <> .FFZPVOH $IB "MBO .JTMPWF BOE ,SJTIOB 1 (VNNBEJ " NFBTVSFNFOUESJWFO BOBMZTJT PG JOGPSNBUJPO QSPQBHBUJPO JO UIF nJDLS TPDJBM OFUXPSL *O 888 QBHFT o %0* <> 8FJ $IFO $IJ 8BOH BOE :BKVO 8BOH 4DBMBCMF JOnVFODF NBYJNJ[BUJPO GPS QSFWBMFOU WJSBM NBSLFUJOH JO MBSHFTDBMF TPDJBM OFUXPSLT *O ,%% QBHFT o %0* <> 8FJ $IFO :BKVO 8BOH BOE 4JZV :BOH &ċDJFOU JOnVFODF NBYJNJ[BUJPO JO TPDJBM OFU XPSLT *O ,%% QBHFT o %0* <> 'BCJP $JSBWFHOB "O BEBQUJWF BMHPSJUIN GPS JOGPSNBUJPO FYUSBDUJPO GSPN XFCSFMBUFE UFYUT *O 1SPDFFEJOHT PG UIF *+$"* 8PSLTIPQ PO "EBQUJWF 5FYU &YUSBDUJPO BOE .JOJOH "VHVTU <> "BSPO $MBVTFU $SJTUPQIFS .PPSF BOE . & + /FXNBO )JFSBSDIJDBM TUSVDUVSF BOE UIF QSFEJDUJPO PG NJTTJOH MJOLT JO OFUXPSLT /BUVSF o .BZ %0* OBUVSF <> $PSJOOB $PSUFT BOE 7MBEJNJS 7BQOJL 4VQQPSUWFDUPS OFUXPSLT .BDIJOF -FBSOJOH o %0* " <> %BWJE $SBOEBMM %BO $PTMFZ %BOJFM )VUUFOMPDIFS +PO ,MFJOCFSH BOE 4JEEIBSUI 4VSJ 'FFECBDL FĊFDUT CFUXFFO TJNJMBSJUZ BOE TPDJBM JOnVFODF JO POMJOF DPNNVOJUJFT *O ,%% QBHFT o %0* <> %BWJE + $SBOEBMM -BST #BDLTUSPN %BO $PTMFZ %BOJFM )VUUFOMPDIFS 4JEEIBSUI 4VSJ BOE BOE +PO ,MFJOCFSH *OGFSSJOH TPDJBM UJFT GSPN HFPHSBQIJD DPJODJEFODFT 1/"4 o %FDFNCFS <> /JDL $SBTXFMM "SKFO 1 EF 7SJFT BOE *BO 4PCPSPĊ 0WFSWJFX PG UIF USFD FOUFSQSJTF USBDL *O 53&$ $POGFSFODF /PUFCPPL QBHFT o <> +BNFT " %BWJT BOE 4BNVFM -FJOIBSEU ɩF TUSVDUVSF PG QPTJUJWF JOUFSQFSTPOBM SFMBUJPOT JO TNBMM HSPVQT *O + #FSHFS FEJUPS 4PDJPMPHJDBM DzFPSJFT JO 1SPHSFTT WPM QBHFT o )PVHIUPO .JČJO <> "CJS %F /JMPZ (BOHVMZ BOE 4PVNFO $IBLSBCBSUJ %JTDSJNJOBUJWF MJOL QSFEJDUJPO VTJOH MPDBM MJOLT OPEF GFBUVSFT BOE DPNNVOJUZ TUSVDUVSF *O *$%. QBHFT o %0* *$%. #*#-*0(3"1): <> +FĊSFZ %FBO BOE 4BOKBZ (IFNBXBU .BQSFEVDF 4JNQMJmFE EBUB QSPDFTTJOH PO MBSHF DMVT UFST *O 04%* QBHFT o %0* <> . %FVUTDI BOE ) # (FSBSE " TUVEZ PG OPSNBUJWF BOE JOGPSNBUJPOBM TPDJBM JOnVFODFT VQPO JOEJWJEVBM KVEHNFOU +PVSOBM PG "COPSNBM BOE 4PDJBM 1TZDIPMPHZ o %0* I <> $ISJTUPQIFS 1 %JFIM (BMJMFP /BNBUB BOE -JTF (FUPPS 3FMBUJPOTIJQ JEFOUJmDBUJPO GPS TPDJBM OFUXPSL EJTDPWFSZ *O """* QBHFT o <> -BVSB %JFU[ 4UFĊFO #JDLFM BOE 5PCJBT 4DIFĊFS 6OTVQFSWJTFE QSFEJDUJPO PG DJUBUJPO JOnVFODFT *O *$.- QBHFT o %0* <> ÐFS 8 %JKLTUSB " OPUF PO UXP QSPCMFNT JO DPOOFYJPO XJUI HSBQIT /VNFSJTDIF .BUIFNBUJL o %0* #' <> 1FUFS 4IFSJEBO %PEET 3PCZ .VIBNBE BOE %VODBO + 8BUUT "O FYQFSJNFOUBM TUVEZ PG TFBSDI JO HMPCBM TPDJBM OFUXPSLT 4DJFODF o %0* TDJ FODF <> 1FESP %PNJOHPT BOE .BUU 3JDIBSETPO .JOJOH UIF OFUXPSL WBMVF PG DVTUPNFST *O ,%% QBHFT o %0* <> :PO %PVSJTCPVSF 'JMJQQP (FSBDJ BOE .BSDP 1FMMFHSJOJ &YUSBDUJPO BOE DMBTTJmDB UJPO PG EFOTF DPNNVOJUJFT JO UIF XFC *O 888 QBHFT o %0* <> /BUIBO &BHMF "MFY 4BOEZ 1FOUMBOE BOE %BWJE -B[FS *OGFSSJOH TPDJBM OFUXPSL TUSVDUVSF VTJOH NPCJMF QIPOF EBUB 1/"4 %0* @ <> %BWJE &BTMFZ BOE +PO ,MFJOCFSH /FUXPSLT $SPXET BOE .BSLFUT 3FBTPOJOH BCPVU B )JHIMZ $POOFDUFE 8PSME $BNCSJEHF 6OJWFSTJUZ 1SFTT %0* $#0 <> 1&SEPT BOE " 3FOZJ 0O UIF FWPMVUJPO PG SBOEPN HSBQIT 1VCMJDBUJPOT PG UIF .BUIFNBUJDBM *OTUJUVUF PG UIF )VOHBSJBO "DBEFNZ PG 4DJFODFT o <> .JDIBMJT 'BMPVUTPT 1FUSPT 'BMPVUTPT BOE $ISJTUPT 'BMPVUTPT 0O QPXFSMBX SFMB UJPOTIJQT PG UIF JOUFSOFU UPQPMPHZ *O 4*($0.. QBHFT o %0* <> (FSIBSE 'JTDIFS 6TFS PEFMJOH JO IVNBOoDPNQVUFS JOUFSBDUJPO 6TFS .PEFMJOH BOE 6TFS "EBQUFE *OUFSBDUJPO o %0* " #*#-*0(3"1): <> +BNFT ) 'PXMFS BOE /JDIPMBT " $ISJTUBLJT %ZOBNJD TQSFBE PG IBQQJOFTT JO B MBSHF TPDJBM OFUXPSL MPOHJUVEJOBM BOBMZTJT PWFS ZFBST JO UIF GSBNJOHIBN IFBSU TUVEZ *O #SJUJTI .FEJDBM +PVSOBM %0* CNKB <> #SFOEBO + 'SFZ BOE %FMCFSU %VFDL .JYUVSF NPEFMJOH CZ BċOJUZ QSPQBHBUJPO *O 1SP DFFEJOHT PG UIF UI /FVSBM *OGPSNBUJPO 1SPDFTTJOH 4ZTUFNT /*14 QBHFT o <> -JTF (FUPPS BOE #FO 5BTLBS *OUSPEVDUJPO UP 4UBUJTUJDBM 3FMBUJPOBM -FBSOJOH ɩF .*5 1SFTT <> ;PVCJO (IBISBNBOJ BOE .JDIBFM * +PSEBO 'BDUPSJBM IJEEFO NBSLPW NPEFMT .BDIJOF -FBSOJOH o %0* " <> . (JSWBO BOE . & + /FXNBO $PNNVOJUZ TUSVDUVSF JO TPDJBM BOE CJPMPHJDBM OFUXPSLT 1/"4 o <> "NJU (PZBM 'SBODFTDP #PODIJ BOE -BLT 7 4 -BLTINBOBO " EBUBCBTFE BQ QSPBDI UP TPDJBM JOnVFODF NBYJNJ[BUJPO 1SPD 7-%# &OEPX o %0* <> "NJU (PZBM 'SBODFTDP #PODIJ BOE -BLT 74 -BLTINBOBO -FBSOJOH JOnV FODF QSPCBCJMJUJFT JO TPDJBM OFUXPSLT *O 84%. QBHFT o %0* <> .BSL (SBOPWFUUFS ɩF TUSFOHUI PG XFBL UJFT "NFSJDBO +PVSOBM PG 4PDJPMPHZ o %0* <> ɩPNBT - (SJċUIT BOE .BSL 4UFZWFST 'JOEJOH TDJFOUJmD UPQJDT *O 1/"4 QBHFT o %0* QOBT <> 3FUP (SPC .JDIBFM ,VIO 3PHFS 8BUUFOIPGFS BOE .BSUJO 8JS[ $MVFTUS .PCJMF TPDJBM OFUXPSLJOH GPS FOIBODFE HSPVQ DPNNVOJDBUJPO *O (3061 %0* <> %BOJFM (SVIM 3 (VIB %BWJE -JCFO/PXFMM BOE "OESFX 5PNLJOT *OGPS NBUJPO EJĊVTJPO UISPVHI CMPHTQBDF *O 888 QBHFT o %0* <> 3 (VIB 3BWJ ,VNBS 1SBCIBLBS 3BHIBWBO BOE "OESFX 5PNLJOT 1SPQBHBUJPO PG USVTU BOE EJTUSVTU *O 888 QBHFT o %0* <> 3PHFS (VJNFSË BOE .BSUB 4BMFT1BSEP .JTTJOH BOE TQVSJPVT JOUFSBDUJPOT BOE UIF SFDPO TUSVDUJPO PG DPNQMFY OFUXPSLT 1SPDFFEJOHT PG UIF /BUJPOBM "DBEFNZ PG 4DJFODFT o %0* QOBT #*#-*0(3"1): <> )POHMFJ (VP )VJKJB ;IV ;IJMJ (VP 9JBP9VO ;IBOH BOE ;IPOH 4V "EESFTT TUBO EBSEJ[BUJPO XJUI MBUFOU TFNBOUJD BTTPDJBUJPO *O ,%% QBHFT o %0* <> + . )BNNFSTMFZ BOE 1 $MJĊPSE .BSLPW mFME PO mOJUF HSBQIT BOE MBUUJDFT 6OQVCMJTIFE NBOVTDSJQU <> .PIBNNBE "M )BTBO BOE .PIBNNFE + ;BLJ " TVSWFZ PG MJOL QSFEJDUJPO JO TPDJBM OFUXPSLT *O 4PDJBM /FUXPSL %BUB "OBMZUJDT QBHFT o ,MVXFS "DBEFNJD 1VCMJTIFST %0* @ <> 5BIFS ) )BWFMJXBMB 5PQJDTFOTJUJWF QBHFSBOL *O 1SPDFFEJOHT PG UIF UI *O UFSOBUJPOBM $POGFSFODF PO 8PSME 8JEF 8FC 888 QBHFT o %0* 5,%& <> 4JNPO 4 )BZLJO ,BMNBO 'JMUFSJOH BOE /FVSBM /FUXPSLT +PIO 8JMFZ 4POT *OD /FX :PSL %0* <> $SFJHIUPO )FBVLVMBOJ BOE ;PVCJO (IBISBNBOJ %ZOBNJD QSPCBCJMJTUJD NPEFMT GPS MBUFOU GFBUVSF QSPQBHBUJPO JO TPDJBM OFUXPSLT *O *$.- WPMVNF QBHFT o <> (FPSFZ & )JOUPO " GBTU MFBSOJOH BMHPSJUIN GPS EFFQ CFMJFG OFUT /FVSBM $PNQVUBUJPO o %0* OFDP <> ɩPNBT )PGNBOO 1SPCBCJMJTUJD MBUFOU TFNBOUJD JOEFYJOH *O 4*(*3 QBHFT o %0* <> +PIO )PQDSPGU 5JBODIFOH -PV BOE +JF 5BOH 8IP XJMM GPMMPX ZPV CBDL SF DJQSPDBM SFMBUJPOTIJQ QSFEJDUJPO *O $*,. QBHFT o %0* <> (MFO +FI BOE +FOOJGFS 8JEPN 4DBMJOH QFSTPOBMJ[FE XFC TFBSDI *O 888 QBHFT o %0* <> ' 7 +FOTFO "O *OUSPEVDUJPO UP #BZFTJBO /FUXPSLT 4QSJOHFS7FSMBH /FX :PSL <> (FPSHF ,BSZQJT BOE 7JQJO ,VNBS .F5JT 6OTUSDUVSFE (SBQI 1BSUJUJPOJOH BOE 4QBSTF .B USJY 0SEFSJOH 4ZTUFN 7FSTJPO 4FQUFNCFS <> )JTBTIJ ,BTIJNB BOE /BPLJ "CF " QBSBNFUFSJ[FE QSPCBCJMJTUJD NPEFM PG OFUXPSL FWPMVUJPO GPS TVQFSWJTFE MJOL QSFEJDUJPO *O *$%. QBHFT o %0* *$%. <> &MJIV ,BU[ ɩF UXPTUFQ nPX PG DPNNVOJDBUJPO BO VQUPEBUF SFQPSU PG BO IZQPUIFTJT *O &OJT BOE $PY FET .BSLFUJOH $MBTTJDT QBHFT o #*#-*0(3"1): <> &MJIV ,BU[ BOE 1BVM 'FMJY -B[BSTGFME 1FSTPOBM *OnVFODF ɩF 'SFF 1SFTT /FX :PSL <> -FP ,BU[ " OFX TUBUVT JOEFY EFSJWFE GSPN TPDJPNFUSJD BOBMZTJT 1TZDIPNFUSJLB o %0* #' <> ) $ ,FMNBO $PNQMJBODF JEFOUJmDBUJPO BOE JOUFSOBMJ[BUJPO ɩSFF QSP DFTTFT PG BUUJUVEF DIBOHF +PVSOBM PG $POnJDU 3FTPMVUJPO o %0* <> %BWJE ,FNQF +PO ,MFJOCFSH BOE ²WB 5BSEPT .BYJNJ[JOH UIF TQSFBE PG JOnVFODF UISPVHI B TPDJBM OFUXPSL *O ,%% QBHFT o %0* <> .BTBIJSP ,JNVSB BOE ,B[VNJ 4BJUP 5SBDUBCMF NPEFMT GPS JOGPSNBUJPO EJĊVTJPO JO TPDJBM OFUXPSLT *O 1,%% QBHFT o %0* @ <> $ISJTUJOF ,JTT BOE .BSUJO #JDIMFS *EFOUJmDBUJPO PG JOnVFODFST NFBTVSJOH JOnV FODF JO DVTUPNFS OFUXPSLT %FDJTJPO 4VQQPSU 4ZTUFNT o %0* KETT <> +PO ,MFJOCFSH 5FNQPSBM EZOBNJDT PG POMJOF JOGPSNBUJPO TUSFBNT *O %BUB 4USFBN .BO BHFNOU 1SPDFTTJOH )JHITQFFE %BUB 4QSJOHFS <> %BWJE ,SBDLIBSEU DzF 4USFOHUI PG 4USPOH 5JFT DzF *NQPSUBODF PG 1IJMPT JO /FUXPSLT BOE 0SHBOJ[BUJPO *O /JUJO /PISJB BOE 3PCFSU ( &DDMFT &ET /FUXPSLT BOE 0SHBOJ[BUJPOT )BSWBSE #VTJOFTT 4DIPPM 1SFTT $BNCSJEHF <> 'SBOL 3 ,TDIJTDIBOH #SFOEBO + 'SFZ BOE )BOT BOESFB -PFMJHFS 'BDUPS HSBQIT BOE UIF TVNQSPEVDU BMHPSJUIN *&&& 50*5 o %0* <> +ÏSÙNF ,VOFHJT BOE +ÚSH 'MJFHF 1SFEJDUJOH EJSFDUFE MJOLT VTJOH OPOEJBHPOBM NBUSJY EF DPNQPTJUJPO *O *$%. QBHFT o %0* *$%. <> +ÏSÙNF ,VOFHJT BOE "OESFBT -PNNBU[TDI -FBSOJOH TQFDUSBM HSBQI USBOTGPSNBUJPOT GPS MJOL QSFEJDUJPO *O *$.- QBHFT o %0* <> +PIO % -BĊFSUZ "OESFX .D$BMMVN BOE 'FSOBOEP $ / 1FSFJSB $POEJUJPOBM SBOEPN mFMET 1SPCBCJMJTUJD NPEFMT GPS TFHNFOUJOH BOE MBCFMJOH TFRVFODF EBUB *O *$.- QBHFT o #*#-*0(3"1): <> 1 ' -B[BSTGFME BOE 3 , .FSUPO 'SJFOETIJQ BT B TPDJBM QSPDFTT " TVCTUBOUJWF BOE NFUIPEPMPHJDBM BOBMZTJT *O . #FSHFS 5 "CFM BOE $ ) 1BHF &ET 'SFFEPN BOE $POUSPM JO .PEFSO 4PDJFUZ 7BO /PTUSBOE /FX :PSL QBHFT o <> 1BVM 'FMJY -B[BSTGFME #FSOBSE #FSFMTPO BOE )B[FM (BVEFU DzF 1FPQMFT $IPJDF )PX UIF 7PUFS .BLFT VQ )JT .JOE JO B 1SFTJEFOUJBM $BNQBJHO $PMVNCJB 6OJWFSTJUZ 1SFTT /FX :PSL <> $POSBE -FF #PCP /JDL 6MSJL #SBOEFT BOE 1ÈESBJH $VOOJOHIBN -JOL QSFEJDUJPO XJUI TPDJBM WFDUPS DMPDLT *O ,%% QBHFT o %0* <> 7JODFOU -FSPZ #FSLBOU #BSMB $BNCB[PHMV BOE 'SBODFTDP #PODIJ $PME TUBSU MJOL QSF EJDUJPO *O ,%% QBHFT o %0* <> +VSF -FTLPWFD %BOJFM )VUUFOMPDIFS BOE +PO ,MFJOCFSH 1SFEJDUJOH QPTJUJWF BOE OFH BUJWF MJOLT JO POMJOF TPDJBM OFUXPSLT *O 888 QBHFT o %0* <> +VSF -FTLPWFD %BOJFM )VUUFOMPDIFS BOE +PO ,MFJOCFSH 4JHOFE OFUXPSLT JO TPDJBM NFEJB *O $)* QBHFT o %0* <> +VSF -FTLPWFD "OESFBT ,SBVTF $BSMPT (VFTUSJO $ISJTUPT 'BMPVUTPT +FBOOF 7BO#SJFTFO BOE /BUBMJF (MBODF $PTUFĊFDUJWF PVUCSFBL EFUFDUJPO JO OFUXPSLT *O ,%% QBHFT o %0* <> +VSF -FTLPWFD ,FWJO + -BOH "OJSCBO %BTHVQUB BOE .JDIBFM 8 .BIPOFZ 4UBUJTUJDBM QSPQFSUJFT PG DPNNVOJUZ TUSVDUVSF JO MBSHF TPDJBM BOE JOGPSNBUJPO OFUXPSLT *O 888 QBHFT o %0* <> %BWJE -JCFO/PXFMM BOE +PO . ,MFJOCFSH ɩF MJOLQSFEJDUJPO QSPCMFN GPS TPDJBM OFU XPSLT +"4*45 o %0* BTJ <> 3ZBO -JDIUFOXBMUFS BOE /JUFTI 7 $IBXMB 7FSUFY DPMMPDBUJPO QSPmMFT TVCHSBQI DPVOUJOH GPS MJOL BOBMZTJT BOE QSFEJDUJPO *O 888 QBHFT o %0* <> 3ZBO -JDIUFOXBMUFS +BLF 5-VTTJFS BOE /JUFTI 7 $IBXMB /FX QFSTQFDUJWFT BOE NFUIPET JO MJOL QSFEJDUJPO *O ,%% QBHFT o %0* <> -V -JV +JF 5BOH +JBXFJ )BO BOE 4IJRJBOH :BOH -FBSOJOH JOnVFODF GSPN IFUFSPHF OFPVT TPDJBM OFUXPSLT %BUB .JOJOH BOE ,OPXMFEHF %JTDPWFSZ o %0* T #*#-*0(3"1): <> 5JBODIFOH -PV BOE +JF 5BOH .JOJOH TUSVDUVSBM IPMF TQBOOFST UISPVHI JOGPSNBUJPO EJG GVTJPO JO TPDJBM OFUXPSLT *O 888 QBHFT o <> 5JBODIFOH -PV +JF 5BOH +PIO )PQDSPGU ;IBOQFOH 'BOH BOE 9JBPXFO %JOH -FBSOJOH UP QSFEJDU SFDJQSPDJUZ BOE USJBEJD DMPTVSF JO TPDJBM OFUXPSLT 5,%% BDDFQUFE %0* <> 4PGVT " .BDTLBTTZ BOE 'PTUFS 1SPWPTU " TJNQMF SFMBUJPOBM DMBTTJmFS *O 8PSLTIPQ PO .VMUJ3FMBUJPOBM %BUB .JOJOH JO DPOKVODUJPO XJUI ,%% <> 4IPCIJU .BUIVS .BSTIBMM 4DPUU 1PPMF 'FOJPTLZ 1F×B.PSB .BSL )BTFHBXB +PIOTPO BOE /PTIJS 4 $POUSBDUPS %FUFDUJOH JOUFSBDUJPO MJOLT JO B DPMMBCPSBU JOH HSPVQ VTJOH NBOVBMMZ BOOPUBUFE EBUB 4PDJBM /FUXPSLT o %0* KTPDOFU <> +VMJBO .D"VMFZ BOE +VSF -FTLPWFD -FBSOJOH UP EJTDPWFS TPDJBM DJSDMFT JO FHP OFUXPSLT *O /*14 8PSLTIPQ PO 4PDJBM /FUXPSL BOE 4PDJBM .FEJB "OBMZTJT <> . .D1IFSTPO - 4NJUI-PWJO BOE +. $PPL #JSET PG B GFBUIFS )PNPQIJMZ JO TPDJBM OFUXPSLT "OOVBM 3FWJFX PG 4PDJPMPHZ QBHFT o %0* BO OVSFWTPD <> "EJUZB ,SJTIOB .FOPO BOE $IBSMFT &MLBO " MPHMJOFBS NPEFM XJUI MBUFOU GFBUVSFT GPS EZBEJD QSFEJDUJPO *O *$%. QBHFT o %0* *$%. <> 4UBOMFZ .JMHSBN ɩF TNBMM XPSME QSPCMFN 1TZDIPMPHZ 5PEBZ o <> ɩPNBT .JOLB &TUJNBUJOH B EJSJDIMFU EJTUSJCVUJPO *O 5FDIOJRVF 3FQPSU IUUQSFTFBSDINJDSPTPGUDPN NJOLBQBQFSTEJSJDIMFU <> ɩPNBT .JOLB BOE +PIO -BĊFSUZ &YQFDUBUJPOQSPQBHBUJPO GPS UIF HFOFSBUJWF BTQFDU NPEFM *O 6"* QBHFT o <> #IBSBUI ,VNBS .PIBO ɩF CFTU OVSUVSFST JO DPNQVUFS TDJFODF SFTFBSDI *O 4%. QBHFT o <> ,FWJO 1 .VSQIZ :BJS 8FJTT BOE .JDIBFM * +PSEBO -PPQZ CFMJFG QSPQBHBUJPO GPS BQ QSPYJNBUF JOGFSFODF "O FNQJSJDBM TUVEZ *O 6"* QBHFT o <> 4FUI " .ZFST $IFOHVBOH ;IV BOE +VSF -FTLPWFD *OGPSNBUJPO EJĊVTJPO BOE FYUFSOBM JOnVFODF JO OFUXPSLT *O ,%% QBHFT o %0* <> . & + /FXNBO $MVTUFSJOH BOE QSFGFSFOUJBM BUUBDINFOU JO HSPXJOH OFUXPSLT 1IZTJDBM 3FWJFX & %0* 1IZT3FW& #*#-*0(3"1): <> . & + /FXNBO 'BTU BMHPSJUIN GPS EFUFDUJOH DPNNVOJUZ TUSVDUVSF JO OFUXPSLT 1IZTJDBM 3FWJFX & %0* 1IZT3FW& <> 4BUPTIJ 0ZBNB ,PIFJ )BZBTIJ BOE )JTBTIJ ,BTIJNB $SPTTUFNQPSBM MJOL QSFEJDUJPO *O *$%. QBHFT o %0* *$%. <> -BXSFODF 1BHF 4FSHFZ #SJO 3BKFFW .PUXBOJ BOE 5FSSZ 8JOPHSBE ɩF QBHFSBOL DJUBUJPO SBOLJOH #SJOHJOH PSEFS UP UIF XFC 5FDIOJDBM 3FQPSU 4*%-81 4UBOGPSE 6OJWFSTJUZ <> 'SBHLJTLPD 1BQBEPQPVMPT .BLTJN ,JUTBL . «OHFMFT 4FSSBOP .BSJÈO #PHV OÈ BOE %NJUSJ ,SJPVLPW 1PQVMBSJUZ WFSTVT 4JNJMBSJUZ JO (SPXJOH /FUXPSLT /BUVSF o 4FQ %0* OBUVSF <> "MFYBOESJO 1PQFTDVM BOE -ZMF ) 6OHBS 4UBUJTUJDBM SFMBUJPOBM MFBSOJOH GPS MJOL QSFEJDUJPO *O *+$"* 8PSLTIPQ PO -FBSOJOH 4UBUJTUJDBM .PEFMT GSPN 3FMBUJPOBM %BUB WPM QBHF <> 5BP 2JO 5JF : -JV 9V % ;IBOH %F 4 8BOH BOE )BOH -J (MPCBM SBOLJOH VTJOH DPOUJOVPVT DPOEJUJPOBM SBOEPN mFMET *O /*14 .*5 1SFTT <> &NJMF 3JDIBSE /JDPMBT #BTLJPUJT ɩFPEPSPT &WHFOJPV BOE /JDPMBT 7BZBUJT -JOL EJTDPW FSZ VTJOH HSBQI GFBUVSF USBDLJOH *O /*14 QBHFT o <> .BUUIFX 3JDIBSETPO BOE 1FESP %PNJOHPT .JOJOH LOPXMFEHFTIBSJOH TJUFT GPS WJSBM NBSLFUJOH *O ,%% QBHFT o %0* <> .JDIBM 3PTFO;WJ ɩPNBT (SJċUIT .BSL 4UFZWFST BOE 1BEISBJD 4NZUI ɩF BVUIPS UPQJD NPEFM GPS BVUIPST BOE EPDVNFOUT *O 6"* QBHFT o <> .BBZBO 3PUI "TTBG #FO%BWJE %BWJE %FVUTDIFS (VZ 'MZTIFS *MBO )PSO "SJ -FJDIU CFSH /BUZ -FJTFS :PTTJ .BUJBT BOE 3PO .FSPN 4VHHFTUJOH GSJFOET VTJOH UIF JNQMJDJU TPDJBM HSBQI *O ,%% QBHFT o %0* <> ,B[VNJ 4BJUP 3ZPIFJ /BLBOP BOE .BTBIJSP ,JNVSB 1SFEJDUJPO PG JOGPSNBUJPO EJĊV TJPO QSPCBCJMJUJFT GPS JOEFQFOEFOU DBTDBEF NPEFM *O ,&4 QBHFT o %0* @ <> 1VSOBNSJUB 4BSLBS BOE "OESFX 8 .PPSF %ZOBNJD TPDJBM OFUXPSL BOBMZTJT VT JOH MBUFOU TQBDF NPEFMT 4*(,%% &YQMPSBUJPO /FXTMFUUFS o %0* <> 4BMWBUPSF 4DFMMBUP "OBTUBTJPT /PVMBT BOE $FDJMJB .BTDPMP &YQMPJUJOH QMBDF GFBUVSFT JO MJOL QSFEJDUJPO PO MPDBUJPOCBTFE TPDJBM OFUXPSLT *O ,%% QBHFT o %0* #*#-*0(3"1): <> 3PTTBOP 4DIJGBOFMMB "MBJO #BSSBU $JSP $BUUVUP #FOKBNJO .BSLJOFT BOE 'JMJQQP .FOD[FS 'PMLT JO GPMLTPOPNJFT TPDJBM MJOL QSFEJDUJPO GSPN TIBSFE NFUBEBUB *O 84%. QBHFT o %0* <> +FSSZ 4DSJQQT 1BOH/JOH 5BO BOE "CEPM)PTTFJO &TGBIBOJBO .FBTVSJOH UIF FĊFDUT PG QSFQSPDFTTJOH EFDJTJPOT BOE OFUXPSL GPSDFT JO EZOBNJD OFUXPSL BOBMZTJT *O ,%% QBHFT o %0* <> #VSS 4FUUMFT BOE .BSL $SBWFO "O BOBMZTJT PG BDUJWF MFBSOJOH TUSBUFHJFT GPS TFRVFODF MB CFMJOH UBTLT *O &./-1 QBHFT o <> 9JBPMJO 4IJ +VO ;IV 3VJ $BJ BOE -FJ ;IBOH 6TFS HSPVQJOH CFIBWJPS JO POMJOF GPSVNT *O ,%% QBHFT o %0* <> 9JO 4IVBJ :JOH %JOH +FSPNF #VTFNFZFS 4IBOTIBO $IFO :VZJO 4VO BOE +JF 5BOH .PEFMJOH JOEJSFDU JOnVFODF PO UXJUUFS *+48*4 o %0* KTXJT <> (FPSHF 4JNNFM 4PDJPMPHJDBM DzFPSZ UI FE .D(SBX )JMM /FX :PSL <> 1BSBH 4JOHMB BOE .BUUIFX 3JDIBSETPO :FT UIFSF JT B DPSSFMBUJPO GSPN TPDJBM OFU XPSLT UP QFSTPOBM CFIBWJPS PO UIF XFC *O 888 QBHFT o %0* <> 1 4NPMFOTLZ *OGPSNBUJPO QSPDFTTJOH JO EZOBNJDBM TZTUFNT GPVOEBUJPOT PG IBSNPOZ UIF PSZ 1BSBMMFM %JTUSJCVUFE 1SPDFTTJOH &YQMPSBUJPOT JO UIF .JDSPTUSVDUVSF PG $PHOJUJPO WPM 'PVOEBUJPOT QBHFT o <> 3JDIBSE 4QSPBU "MBO 8 #MBDL 4UBOMFZ $IFO 4IBOLBS ,VNBS .BSJ 0TUFOEPSG BOE $ISJTUPQIFS 3JDIBSET /PSNBMJ[BUJPO PG OPOTUBOEBSE XPSET $PNQVUFS 4QFFDI -BOHVBHF QBHFT o %0* DTMB <> .BSL 4UFZWFST 1BEISBJD 4NZUI BOE ɩPNBT (SJċUIT 1SPCBCJMJTUJD BVUIPS UPQJD NPEFMT GPS JOGPSNBUJPO EJTDPWFSZ *O ,%% QBHFT o %0* <> $IFOIBP 5BO -JMMJBO -FF +JF 5BOH -POH +JBOH .JOH ;IPV BOE 1JOH -J 6TFSMFWFM TFOUJNFOU BOBMZTJT JODPSQPSBUJOH TPDJBM OFUXPSLT *O ,%% QBHFT o %0* <> $IFOIBP 5BO +JF 5BOH +JNFOH 4VO 2VBO -JO BOE 'FOHKJBP 8BOH 4PDJBM BDUJPO USBDLJOH WJB OPJTF UPMFSBOU UJNFWBSZJOH GBDUPS HSBQIT *O ,%% QBHFT o %0* WJ #*#-*0(3"1): <> :FF 'BO 5BO .JO:FO ,BO BOE %POHXPO -FF 4FBSDI FOHJOF ESJWFO BVUIPS EJTBN CJHVBUJPO *O 1SPDFFEJOHT PG UIF UI "$.*&&&$4 +PJOU $POGFSFODF PO %JHJUBM -JCSBSJFT +$%- QBHFT o %0* <> +JF 5BOH "$. 'POH #P 8BOH BOE +JOH ;IBOH " VOJmFE QSPCBCJMJTUJD GSBNFXPSL GPS OBNF EJTBNCJHVBUJPO JO EJHJUBM MJCSBSZ *&&& 5,%& o %0* 5,%& <> +JF 5BOH 3VPNJOH +JO BOE +JOH ;IBOH " UPQJD NPEFMJOH BQQSPBDI BOE JUT JOUFHSBUJPO JOUP UIF SBOEPN XBML GSBNFXPSL GPS BDBEFNJD TFBSDI *O *$%. QBHFT o %0* *$%. <> +JF 5BOH 5JBODIFOH -PV BOE +PO ,MFJOCFSH *OGFSSJOH TPDJBM UJFT BDSPTT IFUFSPHFOFPVT OFUXPSLT *O 84%. QBHFT o %0* <> +JF 5BOH +JNFOH 4VO $IJ 8BOH BOE ;J :BOH 4PDJBM JOnVFODF BOBMZTJT JO MBSHFTDBMF OFUXPSLT *O ,%% QBHFT o %0* <> +JF 5BOH 4FO 8V BOE +JNFOH 4VO $POnVFODF $POGPSNJUZ JOnVFODF JO MBSHF TPDJBM OFUXPSLT *O ,%% QBHFT o %0* <> +JF 5BOH -JNJO :BP %VP ;IBOH BOE +JOH ;IBOH " DPNCJOBUJPO BQQSPBDI UP XFC VTFS QSPmMJOH "$. 5,%% o %0* <> +JF 5BOH %VP ;IBOH BOE -JNJO :BP 4PDJBM OFUXPSL FYUSBDUJPO PG BDBEFNJD SFTFBSDIFST *O *$%. QBHFT o %0* *$%. <> +JF 5BOH +JOH ;IBOH 3VPNJOH +JO ;J :BOH ,FLF $BJ -J ;IBOH BOE ;IPOH 4V 5PQJD MFWFM FYQFSUJTF TFBSDI PWFS IFUFSPHFOFPVT OFUXPSLT .BDIJOF -FBSOJOH +PVSOBM o %0* T <> +JF 5BOH +JOH ;IBOH -JNJO :BP +VBO[J -J -J ;IBOH BOE ;IPOH 4V "SOFUNJOFS &Y USBDUJPO BOE NJOJOH PG BDBEFNJD TPDJBM OFUXPSLT *O ,%% QBHFT o %0* <> -FJ 5BOH BOE )VBO -JV 3FMBUJPOBM MFBSOJOH WJB MBUFOU TPDJBM EJNFOTJPOT *O ,%% QBHFT o %0* <> 8FOCJO 5BOH )POHMFJ ;IVBOH BOE +JF 5BOH -FBSOJOH UP JOGFS TPDJBM UJFT JO MBSHF OFU XPSLT *O &$.-1,%% QBHFT o %0* @ #*#-*0(3"1): <> #FOKBNJO 5BTLBS .JOH 'BJ 8POH 1JFUFS "CCFFM BOE %BQIOF ,PMMFS -JOL QSFEJDUJPO JO SFMBUJPOBM EBUB *O /*14 <> :FF 8IZF 5FI .JDIBFM * +PSEBO .BUUIFX + #FBM BOE %BWJE . #MFJ )JFSBSIJDBM EJSJDIMFU QSPDFTTFT *O 5FDIOJDBM 3FQPSU %FQBSUNFOU PG 4UBUJTUJDT 6$ #FSLFMFZ <> $+ WBO 3JKTCFSHFO *OGPSNBUJPO 3FUSJFWBM #VUUFSXPSUIT -POEPO <> $IBP 8BOH 7FOV 4BUVMVSJ BOE 4SJOJWBTBO 1BSUIBTBSBUIZ -PDBM QSPCBCJMJTUJD NPEFMT GPS MJOL QSFEJDUJPO *O *$%. QBHFT o %0* *$%. <> $IJ 8BOH +JBXFJ )BO :VOUBP +JB +JF 5BOH %VP ;IBOH :JOUBP :V BOE +JOHZJ (VP .JOJOH BEWJTPSBEWJTFF SFMBUJPOTIJQT GSPN SFTFBSDI QVCMJDBUJPO OFUXPSLT *O ,%% QBHFT o %0* <> %BTIVO 8BOH %JOP 1FESFTDIJ $IBPNJOH 4POH 'PTDB (JBOOPUUJ BOE "MCFSU-ÈT[MØ #BSBCÈTJ )VNBO NPCJMJUZ TPDJBM UJFT BOE MJOL QSFEJDUJPO *O ,%% QBHFT o %0* <> 4UBOMFZ 8BTTFSNBO BOE ,BUIFSJOF 'BVTU 4PDJBM /FUXPSL "OBMZTJT .FUI PET BOE "QQMJDBUJPOT $BNCSJEHF 6OJWFSTJUZ 1SFTT $BNCSJEHF %0* $#0 <> %VODBO + 8BUUT BOE 4UFWFO ) 4USPHBU[ $PMMFDUJWF EZOBNJDT PG TNBMMXPSME OFUXPSLT /BUVSF o %0* <> .BY 8FCFS DzF /BUVSF PG 4PDJBM "DUJPO JO 3VODJNBO 8(8FCFS 4FMFDUJPOT JO 5SBOTMBUJPO $BNCSJEHF 6OJWFSTJUZ 1SFTT <> 9JOH 8FJ BOE 8 #SVDF $SPGU -EBCBTFE EPDVNFOU NPEFMT GPS BEIPD SFUSJFWBM *O 1SPDFFEJOHT PG UIF UI "$. 4*(*3 *OUFSOBUJPOBM $POGFSFODF PO *OGPSNBUJPO 3FUSJFWBM 4* (*3 QBHFT o %0* <> (BSZ . 8FJTT .JOJOH XJUI SBSJUZ " VOJGZJOH GSBNFXPSL 4*(,%% &YQMPSBUJPOT /FXTMFUUFS QBHFT o %0* <> .BY 8FMMJOH BOE (FPĊSFZ & )JOUPO " OFX MFBSOJOH BMHPSJUIN GPS NFBO mFME CPMU[ NBOO NBDIJOFT *O 1SPDFFEJOHT PG *OUFSOBUJPOBM $POGFSFODF PO "SUJmDJBM /FVSBM /FUXPSL *$"// QBHFT o %0* @ <> 8JN 8JFHFSJODL 7BSJBUJPOBM BQQSPYJNBUJPOT CFUXFFO NFBO mFME UIFPSZ BOE UIF KVODUJPO USFF BMHPSJUIN *O 6"* QBHFT o #*#-*0(3"1): <> 4FO 8V +JNFOH 4VO BOE +JF 5BOH 1BUFOU QBSUOFS SFDPNNFOEBUJPO JO FOUFSQSJTF TPDJBM OFUXPSLT *O 84%. QBHFT o %0* <> 4IBPNFJ 8V + . )PGNBO 8 " .BTPO BOE % + 8BUUT 8IP TBZT XIBU UP XIPN PO UXJUUFS *O 888 QBHFT o %0* <> &OEPOH 9VO $IBOHOJOH )VBOH BOE .JOH ;IPV " VOJmFE TUBUJTUJDBM NPEFM GPS UIF JEFOUJmDBUJPO PG FOHMJTI CBTFOQ *O 1SPDFFEJOHT PG DzF UI "OOVBM .FFUJOH PG UIF "TTPDJBUJPO GPS $PNQVUBUJPOBM -JOHVJTUJDT "$- QBHFT o <> :BOH :BOH +JF 5BOH $BOF 8JOHLJ -FVOH :J[IPV 4VO 2JDPOH $IFO +VBO[J -J BOE 2JBOH :BOH 3BJO 4PDJBM SPMFBXBSF JOGPSNBUJPO EJĊVTJPO *O """* <> ;J :BOH +JOHZJ (VP ,FLF $BJ +JF 5BOH +VBO[J -J -J ;IBOH BOE ;IPOH 4V 6OEFS TUBOEJOH SFUXFFUJOH CFIBWJPST JO TPDJBM OFUXPSLT *O $*,. QBHFT o %0* <> ;J :BOH +JF 5BOH #P 8BOH +JOHZJ (VP +VBO[J -J BOE 4POHDBO $IFO &YQFSUCPMF 'SPN FYQFSU mOEJOH UP CPMF TFBSDI *O 1SPDFFEJOH PG UIF UI "$. 4*(,%% *OUFSOBUJPOBM $POGFSFODF PO ,OPXMFEHF %JTDPWFSZ BOE %BUB .JOJOH ,%% <> +POBUIBO 4 :FEJEJB 8JMMJBN 5 'SFFNBO BOE :BJS 8FJTT (FOFSBMJ[FE CFMJFG QSPQBHBUJPO *O /*14 QBHFT o <> 9JBPYJO :JO +JBXFJ )BO BOE 1IJMJQT :V 0CKFDU EJTUJODUJPO %JTUJOHVJTIJOH PCKFDUT XJUI JEFOUJDBM OBNFT *O 1SPDFFEJOHT PG *&&& SE *OUFSOBUJPOBM $POGFSFODF PO %BUB &OHJOFFSJOH *$%& QBHFT o %0* *$%& <> ;IJKVO :JO .BOJTI (VQUB 5JN 8FOJOHFS BOE +JBXFJ )BO -JOLSFD B VOJmFE GSBNFXPSL GPS MJOL SFDPNNFOEBUJPO XJUI VTFS BUUSJCVUFT BOE HSBQI TUSVDUVSF *O 888 QBHFT o %0* <> $IFOHYJBOH ;IBJ BOE +PIO -BĊFSUZ " TUVEZ PG TNPPUIJOH NFUIPET GPS MBOHVBHF NPE FMT BQQMJFE UP BE IPD JOGPSNBUJPO SFUSJFWBM *O 4*(*3 QBHFT o %0* <> +JOH ;IBOH #JBP -JV +JF 5BOH 5JOH $IFO BOE +VBO[J -J 4PDJBM JOnVFODF MPDBMJUZ GPS NPEFMJOH SFUXFFUJOH CFIBWJPST *O *+$"* QBHFT o <> +JOH ;IBOH +JF 5BOH BOE +VBO[J -J &YQFSU mOEJOH JO B TPDJBM OFUXPSL *O %"4'"" QBHFT o %0* @ <> +VO ;IBOH $IBPLVO 8BOH 1IJMJQ 4 :V BOE +JBONJO 8BOH -FBSOJOH MBUFOU GSJFOETIJQ QSPQBHBUJPO OFUXPSLT XJUI JOUFSFTU BXBSFOFTT GPS MJOL QSFEJDUJPO *O 4*(*3 QBHFT o %0* #*#-*0(3"1): <> +VO ;IV .BYNBSHJO OPOQBSBNFUSJD MBUFOU GFBUVSF NPEFMT GPS MJOL QSFEJDUJPO *O *$.- QBHFT o <> :BPKJB ;IV 9JBPSBO :BO -JTF (FUPPS BOE $SJTUPQIFS .PPSF 4DBMBCMF UFYU BOE MJOL BOBMZTJT XJUI NJYFEUPQJD MJOL NPEFMT *O ,%% QBHFT o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