Analysis of Recommendation Algorithms for E-Commerce
Badrul Sarwar, George Karypis, Joseph Konstan, and John Riedl ¢¡¤£¦¥¨§©£¦¥ £¦¥¡ ¦¦¡¤£¦ ¥ ! #"%$ ¡&(')*&+ ' GroupLens Research Group / Army HPC Research Center Department of Computer Science and Engineering University of Minnesota Minneapolis, MN 55455
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INTRODUCTION T/\=Fj6=>R-M/01 4 :PT23-98.KDEAEAdWi-_T 4AEDEH¤-0AB;I=>1ZT:P-V=>R-[8>-0/91 2323-045 -98 {R -©A(?¨8>L-0:<=CcGNn/012323-98>/0-I:PDB=>-0:Z1¨z¢-98Z23DEA(AEDE1 4 :31Y[@78>1J5 T /9=>: :<;7:<=>-02®?¨L¤?DE4fk,.-0/012323-04657-98:<;7:<=>-023:0j7AEDEH¤-1¨=>R-98:P-F?^8>/\RC:<;7: Yl18b:>?AE- f}e]R1U1:PD(4 L?2314L:P12Z?4U;%1@ =>DE1 4 :3DE:b/!R6?¨AEA(-94L DE4 L =>-023:0j¨R6?FO¤-k=hK1.=h;7@i-0:w1¨Y6/!R6?^8!?/9=>-98>DE:<=>DE/ -98P8>1¨8>:0¯¢°0 ¨9]¢£¤o\¨>j Yl18V/014:PT 23-98>:0f[,.-0/01 2323-9465 -\8p:<;7:<=>-023:yR6?FO¤-M-023-98>L -05uDE4u8>-9N KRDE/!R?¨8>-`@78>1J5 T /9=>:y=>R?¨=[?^8>-_4 1=y8>-0/01 2323-9465 -05j=>R 1 T L Ra=>R- :P@i14:P-3=>1I=>R D(:M@ 8>1WAE-02©fC8>-9/01 2323-045 -98V:<;7:<=>-02Yl18`?4%cdN /014:PT23-\8bK]1 T A+5±AEDEH¤-a=>R-92©j?45%°0 ¨93²7¨¨!lo\¨>jyKR D(/!R³?¨8>- /91 2323-98>/0-V:PDB=>-V8>-0/0-0DEO¤-0:yDE4 Yo1¨8>2Z?¨=>DE1 4aY+8>1 2?Z/91 4:PT 23-98p?Wi1 T7= @ 8>1J57T/9=>:k=>R6?¨= ?¨8>-y8>-9/01 2323-045 -F5¢j¤=>R1TLRb=>R -p/014:PT23-\8 5 1U-9: KR DE/\Ra@78>1J5 T/\=>:y:PR -MDE:.DE4J=>-\8>-0:<=>-F5©DE4#j¢?¨465C8>-9/01 2323-045 : @78>1J57N 41¨=.A(DEH¤-[=>R -02©fgh4C=>R -VcGNn/012323-98>/0-[571 2Z?¨D(4C=>R-[231 :<=DE23@i1¨8PN T /9=>:V=>R6?¨=`?¨8>-ZAEDEH¤-0AB;=>1©x =`R -98_4-0-F57:0fu{¦1J5 ?F;Uj¦8>-0/01 2323-9465 -\8 =!?4U=-98P8>1¨8>:G=>1?^O 1 D(5Q?¨8>- Yo?AE:P-@i1 :PDB=>DEO¤-0:0jU:PDE4/9-=>R-0:P- -98P8>1¨8>:KDEAEA :<;7:<=>-023:.?^8>-V5 -0@ A(1F;U-05C1 4IR7T 465J8>-F5 : 1¨Y5 DBz¢-98>-04U=:PDB=>-0:0j6:P-\8>O7DE4 L AE-F? 5©=>1b?4 L8P;a/91 4:PT 23-98>:0j¢?¨465©:PDE4/0-M=>R-98>-M?^8>-_T :PT6?AEAB;a2Z?¨4J; 23DEAEAEDE1 4:.1Yw/01 4 :PT23-98>:0f @ 8>1J57T/9=>:V14%?4cdNn/01 2323-98>/9-Q:PDB=>-Z=>R?¨=_?I/014:PT 23-98VKD(AEAkA(DEH¤- 4 -k1¨Y=>R -]-F?^8>A(DE-0:<=?¨465V231 :<=¦:PT/0/0-9:P: =>1V@T78>/\R?:P- jJ:P1V=>R-98>-.DE:41[8>-F?¨:P1 4Z=>1[8>D(:PHQ8>-9/01 2323-045 DE4Lp1 4- 4 1 AE1 LDE-0:pDE:M> oE¤><o] \\oUu U j¢¨7j#^ Jj^¡F¢£f e]1A(A(?¨Wi18!?¨N :PR-KDEAEA¦4 1=AEDEH¤- f =>DEO¤-x6AB=>-98>DE4 LVK]18>HJ:]WU;`WTDEA(5 DE4 L_?V5 ?¨=!?W?:P-y1Y@ 8>-9Yl-98>-04 /0-0:]Yl18 gh4V:P123-]K ?0;7:¦=>R-9:P-]=hK]1y/!R6?¨A(AE-04 L -0:?^8>-DE4_/014 ´D(/\=Fj :PDE4/9-]=>R- @78>1J5 T /9=>:pWU;©/91 4:PT 23-98>:0fy¤4-9K¥/01 4 :PT23-98Fji¦y-01 j¢DE:y2Z?¨=>/!R-F5 AE-0:P:V=>D(23-Q?4q?¨AEL 18>DB=>R 2µ:P@i-045 :[:P-F?^8>/\R DE4L©Yo1¨8M4-0DEL RJWi1¨8>:0jw=>R- ?¨L¤?¨D(4 :<=p=>R -V5?¨=!?¨W6?¨:P-M=>1357DE:P/01^O¤-98M¢\(^§ >!¨>jiKRDE/!Ru?¨8>-V1=>R -98 2318>-V:P/F?¨A(?WAE-_DE=.KDEAEAdWi- j¢?45I=>R-[K1¨8>:P-`DB=>:ySJT?AEDB=h;Uf.1¨8y=>R DE: /91 4:PT 23-98>:VKR1aR6?FO¤-ZR D(:<=>1¨8>DE/F?AEAB;%R6?5q:PDE23D(A(?^8`=!?:<=>-3=>1a¦y-01 f 8>-F?¨:P1 4#jDB=bDE:ZD(23@i1¨8P=!?4U=3=>1=P8>-F?^=3=>R-©=K1q/!R6?¨A(AE-04 L -0:b:PDE2`T AEN =!?4 -01 T :PAB;s:P1=>R -©:P1 AET7=>D(14:b5 DE:P/01^O¤-\8>-F5±?¨8>-aWi1¨=>RsT :P-9YoT Ap?¨465 @ 8!?¨/9=>DE/F?Af Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are 1.1 Problem Statement not made or distributed for profit or commercial advantage and that copies gh4a=>R D(:y@6?¨@i-98Fj¢K-V8>-0:P-F?¨8>/!R~=>R -0:P-V=hK1b/!R6?AEAE-04 L -0:=>1L -9=>R -98Fj bear this notice and the full citation on the first page. 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RELATED WORK 5 DE:P/01^O¤-\8P;I1¨Y.¨>¨9F9£~ DE:Q=>1x465?:P:P1U/9D+?^=>DE1 4±Wi-9=K-0-94t=K1:P-9=>:31Yy@ 8>1J57T/9=>:QDE4=>R- g4©=>RDE:.:P-0/9=>DE1 4aK-MW 8>DE-9´ ;I8>-0OJDE-9K¥:P1 23-V1YG=>R-[8>-0:P-0?¨8>/!RAEDB=PN =P8!?4 :>?/9=>DE145 ?¨=!?W?:P-_:PT/!Ru=>R?¨=y=>R-M@ 8>-0:P-04 /0-`1¨Y]@78>1J5 T /9=>:pDE4 -\8!?¨=>T 8>-8>-9A+?^=>-F5C=>1Q1T 8K1¨8>Hif 1 4 -[:P-9=yD(23@ AED(-9:=>R -@ 8>-9:P-04/0-V1¨Yw=>R-[@78>1J5 T/\=>:Y+8>1 2®=>R-[1¨=>R-98 :P-9=Ffqy@ 8>DE1¨8>D[ F¢£j «pª|B!,¨¢£j]{#8>-0-IªG8>1+-<-0/\=>D(14±?¨A(L18>DB=>R23:IE\¢ {¦?@i-0:<=P8P;%B9¢DE:p1 4 -`1¨Y=>R -_-0?¨8>AEDBN Recommender Systems. ?45Z=>R -dªdN£=P8>-0-QB ¢w?¨A(L18>DB=>R23:?^8>-:P1 23-p1Y¦=>R -yK]-0AEAENnHJ41FK4 -9:<=_DE23@ A(-923-04U=!?¨=>DE1 4 :p1Y/01 AEA(?Wi1¨8!?¨=>DEO¤-3x6AB=>-98>DE4LCW6?¨:P-F5~8>-0/012QN ?AEL18>DB=>R23: Yo1¨8yx4657D(4 LQ?¨:P:P1U/0D(?¨=>DE1 4a8>TAE-0: Y+8>1 2 5?^=!?W6?¨:P-0:0f 23-9465 -\8]:<;7:<=>-023:0fw{RDE::<;7:<=>-02¤8>-0AEDE-F531 43=>R--97@AEDE/0DB=1@DE4DE14: I18>-[Yl18>2Z?AEAB;Uj Dimensionality Reduction. {R-\8>-CR?^O -bWi-9-04%:PTW :<=!?4U=>D(?A 8>-9:P-F?¨8>/!RIK1¨8>HI571 4 -DE4I=>R-[?^8>-F?`1¨YG5 DE23-04 :PD(146?¨A(DB=;C8>-F57T/9=>DE14#f ©J-0O¤-98!?¨Ap23-9=>R 1J5 :ZR6?FO¤-aWi-9-04}5 -9O7DE:P-F5s=>1q8>-05 T/9-©=>R-u5 DE23-047N 47T 2`Wi-98]1Yd=P8!?¨4:>?/\=>D(14:./01 4U=!?¨D(4 DE4LX1aYb3 :PDE146?AEDB=h;q1Y.5?^=!?©:P-9=>:0f¡ !oi9 ²7 §$y²7¢\ Vi '¨>o¨` ^¢DE: ¥; 4JT2_Wi-98 1Y¦=P8!?4:>?¨/9=>DE1 4 :y/014U=!?DE4DE4L`1 ?uKD(5 -0AB;T:P-05=>-0/!R4 D(SJT -b=>R?¨=3/91 23@T7=>-0:_=>R -C-9D(L-04JO ?¨AET-0:31¨Y =>R -]/0T :<=>1 23-98PNn/0T :<=>1 23-98#18w@ 8>1J5 T /9=PNn@ 8>1J57T/9=¦:PD(23DEA(?¨8>DB=;V2Z?¨=P8>DB ?¨465Q8>-9=>T78>4:£¢3-0DEL-04JO¤-0/9=>1¨8>:/018P8>-9:P@i1 4657DE4LV=>1¤¢3A(?¨8>L-0:<=-0DEL -94 N KRDE/!RvDE:Q4 1=>R D(4 LuWT =_=>R-b/01 45 DB=>DE1 4?A@ 8>1W6?W DEA(DB=;%1Yp:P-0-0DE4L O?AET -0:?¨:y=>R-M@ 8>DE4 /0DE@6?Aw?¨7-0:p1¨Y¥¢a5 DE23-04:PDE146?A¦:P@6?/9- f§¦#\ 3Zj¢L DEO¤-04a=>R6?^=pK]-_R?^O -_:P-0-94]1~f}DB=>Ru?:P:P1U/0D(?^=>D(148>TAE-0:pDE=pDE: ¨9($Q£ao "U©¨oJ ¦ ,7j ¨¢.D(:Z?¨41¨=>R-98Q=;7@i-C1¨Y[5 DE23-047N /0123231 43=>1_x46538>TAE-0: R6?FOJDE4LM:PT@ @i18P=.?45b/91 4 x65 -04 /0-pR DEL R-\8 :PDE146?AEDB=h;8>-F57T/9=>DE1 4=>-0/!R4D(SUT-V=>R6?^=VR6?¨:[Wi-0-04uKD+57-0AB;T:P-F5D(4 =>R6?¨4?bT :P-98PN5 -9x4-F5©23DE4DE2_T2©f.r8>TAE-_=>R?¨=pR6?:?ZR DEL R/01 47N DE47Yo18>2Z?^=>DE1 4±8>-9=P8>DE-0O?A./01 232_T4 DE=;Uf}¤©7gQT :P-0:Z:PD(4 L T A+?^8IO?AET - xi57-04/9-pAE-0O¤-0A¢DE:1Y+=>-04IO¤-\8P;3DE23@i18P=!?4U=Fj7Wi-0/F?¨T:P-DB=@78>1¨OJD(5 -9:?4 57-0/0123@i1 :PDB=>DE1 4I=>1MY?/\=>18.=>R-1¨8>D(LDE46?A#:P@6?¨/0-DE4U=>1`=>R 8>-0-p2Z?¨=P8>DBN ?/9/0T 8!?^=>-I@ 8>-05 DE/9=>DE1 41Y=>R -C1T =>/0123-bDE4tSUT-0:<=>DE14#f~{R-b:PT@7N /9-0:?465V=>R- @78>1U/0-0:P:G1Y¢57DE23-04:PDE1 4?AEDB=h;M8>-F5 T /9=>DE1 4_D(:G@i-98PYl18>23-F5 @i18P=_1Yy?©8>TAE-ZDE:Q?¨A(:P1DE23@i18P=!?¨4J=Fjw:PD(4 /0-Z8>TAE-0:_KDB=>R%O¤-\8P;qAE1FK WU;Z8>-F57T/0DE4L_=>R-:PDE4LTA(?¨8y2Z?¨=P8>DB¢f :PT@ @i18P= dcl!fEj O -98P;ZDE4 Yl8>-0SJT -04U=(¡]?¨8>-[1¨Yl=>-04CT4 D(4U=>-98>-9:<=>D(4 L j7:PDE4/0- =>R-\;35 1V4 1= 57-0:P/98>DEWi-p:PT 3/0DE-04U=>AB;QA(?¨8>L-@i1 @ TA(?¨=>DE14:0j7?4532Z?F; 3. 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EXPERIMENTAL EVALUATION Yl=>-98y/01 23@ T =>DE4LM=>R-V?¨A(ABN 4.1 Data sets Different Neighborhood Types. q-_T:P-F5a=hK]1I57DBz¢-98>-04U=V5?^=!?C:P-9=>:y=>1I-0O?AET6?^=>-_=>R -Q5 DBz¢-98>-94J= =>1¨N?AEA@78>1^7DE23DB=h;[Wi-\=hK-9-04`/0T :<=>1 23-98>:0j=>R-4 -9J=w=!?:PHMDE:d=>1?/\=>T N 8>-0/012323-0465 ?¨=>DE1 4C?AEL18>DB=>R23:.5 DE:P/0T :P:P-F5IDE4I:P-9/9=>DE1 4 f]{R -[5 -\N ?¨AEAE;uYl18>2=>R -`4 -0DEL RJWi18>R 1U1J5fM{R-\8>-3?¨8>-_:P-0O¤-98!?¨A:P/!R-923-0:yYl18 =!?DEAE:.1Yw=>R -V5?¨=!?_:P-9=>:.?¨8>-=>R-yYo1 AEAE1FKDE4L ¯ 4 -0DEL RJWi18>R 1U1J5IYo1¨8>2Z?¨=>DE1 4fk«y-98>-pK]-V5 DE:P/0T:P:=hK]1Q:P/!R-023-0:0f ©+-!#©§ GM "#©+/ :P/!R-023-kYo18>23:k?4-9D(LRJWi18>R1U1J5Q1¨Y¢:PDEm0- $1;¨¡¤© / !##¯kq-[T :P-F5©5?^=!?_Yl8>12 1 T 8I1^OJD(-0#-04 :.8>-0/\N H H!4 ¢ij Yl18p?`@6?^8P=>D(/9TA(?¨8./0T :<=>1 23-98 U¨j6WU;Z:PDE23@AB;b:P-0AE-0/9=>DE4LQ=>R - 1 2323-045 -98k:<;7:<=>-02©j7I1^OJD(-0#-04 :DE: ?VK]-0W NnW?:P-F538>-0:P-F?^8>/\R Xw4-0?¨8>-0:<=.1=>R -98./0T:<=>123-98>:0f 8>-0/01 2323-9465 -\8 :<;7:<=>-02|=>R6?^=p57-0WT7=>-F5ZD(4©6?AEAk , , ¡Jf]ck?¨/\R K-0-0HRJT4578>-F57:31Y[T :P-98>:ZOJD(:PDB=CI1^OJDE-F#-04 :3=>18!?¨=>-u?¨465 ££§©£!#©#"W©+¡¤£¦-ME$§ ¨$I$I/ :P/\R -023-.Yl18>23: ?M4-0DELR N H! 8>-0/0-0DEO¤-8>-9/01 2323-045?^=>D(14:bYo18u231^OJDE-0:0f{R-:PDB=>-q4 1FK Wi18>R 1U1J531Y#:PD(m9- Xj¤Yl18?[/0T :<=>1 23-98¥UjJWU;_x8>:<=@ DE/\HJDE4L=>R - R6?:p1¨O -98 CT:P-\8>:KR1bR6?FO¤-M-97@ 8>-0:P:P-F5u1 @ DE4DE1 4 :[1 4 /0AE1 :P-9:<=4-9D(LRJWi18=>1§UfG{R -04Q=>R-8>-0:<=YX$ I 4-0DELR7Wi1¨8>:]?^8>- <0*5 DBz¢-98>-04U=k231¨OJDE-0:0f#q- 8!?45 1 23AB;_:P-0AE-0/9=>-F53-04 1 T L R :P-0AE-0/9=>-05a?:Yo1 AEAE1FK:0fy#-9=Fj?¨=p?Q/0-98P=!?¨D(4a@i1DE4J==>R -98>-V?¨8>-'? T:P-98>:]=>1V1W =!?DE4u! M8!?^=>D(4 L :]Y+8>1 2=>R-y5?¨=!?¨W6?¨:P- K- Z 4-9D(LRJWi18>:VDE4=>R-Q4 -0DEL RJWi18>R 1U1J5 j#KR-98>- ? 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A@B@CD {R 8>1 T L R 1 T ==>R -@6?¨@i-98K-=>-98>2 =>R DE:y5 ?¨=!?`:P-\=p?¨:HG:¦Gf {R - $¦.©§ *,© /¨!#%g4%? 5 5 DB=>DE1 4q=>1©=>R-Z?¨Wi1^O¤-3231^O7DE- !I Neighborhood Formed in Low-dimensional Space. 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Df - fEj=>1@ N>! ¡\f Dimension sensitivity study (ML data set) Dimension sensitivity study (EC data set) 0.235 0.15 0.225 0.13 0.215 0.11 0.205 0.195 0.09 F1 metric 0.185 0.07 0.175 0.05 0.165 10 20 30 40 50 60 70 80 90 100 50 100 150 200 250 300 350 400 450 500 600 700 Dimension, k Dimension, k ML-train ML-total EC-train EC-total ¢¡¤£¥§© 8# *,!W$&!J© I¥ OME©§ $&\/ ¡ ©+ "J¡¤$¢¡ ¢¡¤£¦¥§©¨§I 8 * ! $& !J©4¨¥ MU©§O$&/ ¡ ©+ "J¡¤$©¡ 4¤£ I /¨!# "#©+!¦¥ / !#."#©! ¥ =>R -98M:P@AEDB=_=>R -`=P8!?DE4 D(4 Lu5?^=!?I:P-9=_D(4U=>1a?b=P8!?DE4%?45O?AED(5?¨=>DE14 Experimental Representation Most frequent item Association rule based data set Center - based Center - based nbrhood ef 8>-0/9N @i1¨8P=>DE1 4q?¨465©=>R-94T :P-_=>R -_=P8!?DE4~5?^=!?Z=>1C@ 8>1J5 T /0-Zn\² nbrhood (F1 metric) (F1 metric) 12323-0465 ?¨=>DE1 4©?465©O?AED(5?^=>DE1 45?^=!?3=>13/91 23@T7=>-V]MO ?¨A(T -0:y=>1 MovieLens data High dimensional 0.21393 0.20711 57-9=>-98>23DE4-y=>R-1@ =>DE2Z?AO ?¨AET-1¨YG4-0DEL RJWi1¨8>:0f Low dimensional 0.22009 0.21479 -[@i-98PYo1¨8>23-F5C=>R -0:P-[-97@i-98>DE23-04U=>:.?465b=>R-8>-0:PT AE=>:y?¨8>-[@78>-9N ( k = 20) :P-94J=>-05QD(4QwD(LT 8>- fe]123@6?^8>D(4 LVwDEL T 8>-y?¨4653wDEL T78>- K]-:P-0- E - commerce dat a High dimensional 0.16654 0.16654 =>R?¨==>R-p:P-04:PDB=>DEOJDE=;I14C=>R -4JT2`Wi-\8 1Yd4 -0DEL RJWi18>:.DE: =>R-:>?¨23- Low dimensional 0.12158 0.13209 -0O¤-94t=>R 1 TLR±57T-C=>1D(4 /98>-F?¨:P-F5sAE-0O¤-0A1¨Y Yl18bWi1=>Rt=>R-©/0?:P-0: ( k = 300) ¡\fGT78PN :P@?¨8>:PDB=h;`=>R-.:P-0/01 453-97@i-98>DE23-04U=kAE-F?5 :]=>1VAE1FK-98 SJT?AEDB=h; =>R -98>2318>-ji=>R-[8!?4 L -`1¨Y]1@ =>DE2Z?A¦47T 2`Wi-98.1¨Y]4 -0DEL RJWi18>:yD(4a=>R - M L¤© 8# *,! $&1§©+*,$-.© /!J¡ $¦ L £$§ ¡¤!J $¦ :P-9/01 45-\ @i-\8>D(23-94J=VDE:M=>R-3:>?23-b?¨:M=>R -Zx 8>:<=Ffe]1 4 :P-FSUT-04U=>AB;Uj §©+*,$-.©+ /¨!J¡¤$ 6¨¥L ¡¤!N23 =>R -C1@ =>DE2Z?A 4JT 2`Wi-98M1Yy4-0?¨8>-0:<=34 -0DEL RJWi18>:`/F?4tWi-C/918P8>-0/9=>AB; AE-F?^8>4U=bY+8>1 2 =>R -©=P8!?DE4DE4L:P-9=b?AE1 4 - f yAE:P1=>R -a@i-98PYo1¨8>2Z?4/9- 57DBz¢-98>-04/9-V8>-92Z?DE4:.SUTDB=>-[:PDE23DEA+?^8p1^O¤-\8p?`KD(57-V8!?¨4L-M1¨YG4-0DELR N =>R-[/!R6?^8P=Yo18.=>R-c]e³5?^=!?`:P-9=Ffk«p-98>-V?¨A(:P1QK]-V1 W:P-\8>O¤-[:PDE23D(A(?^8 Wi1¨8>R1U1J5:PDEm0-0:0f% 18`=>R -38>-0:<=Q1¨Yy=>R -b-\ @i-\8>D(23-94J=>:VK-bT:P-05%? :PR6?¨@i-0:1YGWi1¨=>RC=>R-p@AE1=>:0f 4 -0DEL RJWi18>R 1U1J5a1YG:PDEm0-#, `Yo1¨8p=>R -M©%?465I=>R?¨=.1Y] QYo1¨8y=>R - #1U1HJD(4 L3DE4J=>1Q=>R -8>-0:PTAB=>:.:PR1FK4aDE4uwDEL T 8>- Z?¨465awDEL T78>-` Uj cke³5?¨=!?_:P-9=Ff K-`/F?4~:P-0-Q=>R6?^=V1 T 8[=K1I5?¨=!?b:P-9=>:[-97RDEW DE=V:<=P8>DEHJDE4LAE;~57DEz¢-\8PN 4.3.2 Experiments with number of dimension. -04U=[Wi-0R?FO7DE1¨8FfVgh4a=>R-_/F?:P-Q1¨Y©Gji=>R-_8>-9/01 2323-045 -98pSUT6?¨A(DB=; DE4DB=>D(?AEAB;DE23@ 8>1^O¤-0:M?:MK-bDE4/98>-F?¨:P-C=>R -Z8!?¨4H~1Y=>R-ZAE1FK-98Z57DBN .:p57DE:P/0T:P:P-F5aDE4 ,7j ¨¢d=>R-V4JT2`Wi-\81Yk5 DE23-04 :PD(14aDE:p/98>DB=>DE/F?A 23-04 :PD(146?¨A:P@6?¨/0- jWT7=`DB=3SUT D(/!HJAB;~8>-F?¨/\R -0:QDB=>:`2Z?^7D(2_T2@i-\8PN Yl18V=>R-`-9z¢-0/9=>DEO¤-04 -0:P:[1Yk=>R-QAE1FKX5 DE23-04 :PD(146?¨AG8>-9@ 8>-0:P-04U=!?^=>D(14#f Yo1¨8>2Z?4 /0-[?45C?¨4U;3YoT 8P=>R -98DE4/98>-0?:P-0:DE4b=>R -y8!?¨4H31Y¦=>R-p:P@?/0- -[?¨8>-[DE4U=>-98>-0:<=>-05CDE4©57-9=>-98>23DE4DE4LV=>R-p47T 2`Wi-98]1YG57DE23-04:PDE1 4 : AE-F? 57:=>1bK]18>:P-`8>-9/01 2323-045?^=>D(14a8>-0:PTAB=>:0fM¦p1¨=>-_=>R6?^==>RDE:Wi-\N =>R?¨=DE:kA(?^8>L --041TLR`=>1/F?¨@ =>T 8>-?¨AEA =>R-]A+?^=>-04U=G8>-0A(?¨=>DE1 4 :PRDE@:kD(4 R6?FOJDE18_DE:M/91 4:PDE:<=>-04U=MKDB=>R%-97@i-98>DE23-04U=>:[@i-98PYo1¨8>23-F5WU;gh,X8>-\N =>R -2Z?¨=P8>DB[;U-\=d:P2Z?AEAJ-041TLR_=>1?FO¤1D(5_1^O¤-98PN£x=P=>DE4 Ly-98P8>1¨8>:0f p47N :P-F?^8>/\R -98>:Z ¨¢£fC«y1FK-0O¤-\8Fj¦DE4~=>R -Q/F?¨:P-31Yckeyj¦K]-Q:P-0-Q=>R6?^=[=>R- Yl18P=>T 46?¨=>-9AE;[=>R -98>-D(:#41.5 DB8>-0/\=d?4?AB;J=>DE/F?AJ23-9=>R 1J5p=>1y57-9=>-98>23DE4- 8>-0/012323-0465 ?¨=>DE1 4MSUT6?¨AEDE=;V/01 4U=>DE4JT-0:#=>1pDE23@ 8>1^O¤-k?AEAJ=>R-kK?0;VT@ =>R -GO ?¨A(T -G1Y7=>R-G1 @7=>D(2Z?¨A 4JT2_Wi-98¢1Y 57D(23-94:PDE1 4 :] ,¨¢U:P1 =>R -1@ =>DBN =>1a a5 DE23-04 :PDE1 4:0fZ-QWi-0AEDE-0O¤-Q=>RDE:M5 DE:<=>DE4/\=>AE;5 DBz¢-98>-94J=VWi-\N 2Z?¨AO?AET- R?:G=>1[Wi- -97@i-98>DE23-04U=!?AEAB;`-9O ?¨A(T?¨=>-F5¢fGT78P=>R-98>231¨8>- j R6?FOJDE18[DE:Wi-9/F?T :P- D ¡.=>R-_18>DEL DE4?AG4JT2`Wi-\8p1¨Y57D(23-94:PDE1 4 :pYo1¨8 =>R -31 @7=>D(2Z?¨AkO?AET -31Y =>R-`A(1FK]-98357D(23-94:PDE1 4?A:P@6?/9- D£f - fEjd=>R - =>R-]c]eD(:d2_T/!R[A(?¨8>L -\8d=>R6?4_© ¤ 5 OJ:0f , 5 ¤¡ 1@ =>DE2Z?A 8!?¨4H%1Yy=>R-C/0T:<=>123-98PNn@ 8>1J5 T /9=32Z?^=P8>DE ¡VD(:Z57DBz¢-98>-04U= ?45 D(D ¡pcke DE:p:PDEL4DBx6/F?¨4U=>AE;u:P@?¨8>:P-98 :P@6?¨8>:PDB=;uA(-9O¤-0Aw1¨Y # ,, , Yl18M57DEz¢-\8>-04U=[5?^=!?b:P-\=>:0f -9=>-98>23DE46?^=>D(14u1Y]=>R -_1@ =>DE2Z?AdO?AET - OJ:0f # , , ¡I?¨465±?¨/0/018!57DE4L AB;sR6?:b2`T /\RvAE-0:P:I57-0@i-045 -04 /0DE-0:0f 1¨Y#5 DE23-04:PDE143/F?43Wi-.5 14-WU;`T :PDE4L[:PDE23DEA+?^8]=>-0/!R4 D(SJT - T:P-F5`=>1 {RDE:.K ?:p-0OJD+57-04U=pWU;C1 W :P-98>OJD(4 L3=>R-V2Z?L4DB=>T657-M1¨YG=>R-M:PD(4 L T7N 57-9=>-98>23DE4-V=>R-V1@ =>DE2Z?AdO?AET-M1Yk4-0?¨8>-0:<=p4-0DEL RJWi1¨8>:0fq-M@i-98PN A(?¨8.O?AET-0: KR D(/!Ra57D+5b41¨=y:PT 3/0DE-04U=>AB;C5 -0/98>-0?:P- f Yl18>23-F5I?4©-97@i-98>DE23-04U=KR -98>-K-V57DEO7D(57-F5b=>R -V5?¨=!?_:P-9=.D(4U=>1`? =P8!?¨DE4C?¨465Q=>-0:<=k@i18P=>DE1 4Zx8>:<=]?45`YoT78P=>R-985 DEOJD+57- =>R-=P8!?DE4b5?¨=!? «p1FK]-0O¤-98Fjy?4³DE23@i18P=!?¨4U=I1W:P-98>O?¨=>DE1 4³DE:C=>R?¨=b=>R-a8>-0A(?¨=>DEO¤- :P-\= DE4J=>1_?=P8!?DE4C?4653O?AED(5?^=>D(14C@i1¨8P=>DE1 4#fG-.8>-0@i-0?¨=>-F5Q=>R-y-9JN @i-98PYl18>2Z?4 /0-Z5 DBz¢-98>-94/0-0:VK-\8>-ZYo?DB8>AB;q:P2Z?¨A(AGYo1¨8`Wi1¨=>R%cke?¨465 @i-\8>D(23-94J=.Yo1¨8V5 DBz¢-98>-94J=y4JT2_Wi-98.1Y]5 DE23-04:PDE14:y?465a4 1=>-F5I=>R - ©³5?^=!?u:P-\=>:0fq{R D(:`D(:_@6?^8P=>D(/9TA(?¨8>AB;%DE23@i18P=!?¨4U=Q?¨:`AE1FK-98Z57DBN DE23@?/9=p1 4a=>R- `M23-9=P8>DE/`?¨465IYl8>12=>R -_@ A(1¨=K-_5 -\=>-98>23DE4-F5 23-04 :PD(146?¨Ak:P@?/0-0:V/F?¨4qWi-QDE4657-97-F5~T :PDE4L©- Q/0DE-04U=[=>-0/\R 4D(SUT-0: 1@ =>DE2`T 2 4JT 2`Wi-98#1Y65 DE23-04:PDE14:0fd{#1y:PR 1^K%=>R?¨=w=>R DE:d?@ @ 8>1¤?¨/\R - f L fEjEQe >>\¨GL8>-F?^=>AB;3DE4/98>-F?¨:PDE4L[=>R-:P/F?¨A+?¨WDEAEDB=h;Z1Y¢=>R -.4 -F?¨8>-9:<= AE-F?5 :¦=>1 =>R -k/01¨8P8>-0/9=d-9:<=>D(2Z?^=>DE1 4V1Y7=>R-1 @7=>D(2Z?¨A¤O?AET-1Y 5 DE23-047N 4-9D(LRJWi18Q/0?AE/0TA(?^=>D(14:0f 18`=>R -38>-0:<=Q1¨Yy=>R -C-97@i-98>DE23-04U=>:[K- :PDE14#jdK-3/91 4657T/9=>-05?4 1=>R -98M-97@i-98>DE23-04U=[KR-98>-QK]-b:P-9@6?¨8!?^=>- x7-F5u=>R-34JT2_Wi-98[1¨Y.5 DE23-04:PDE14:[=>1u IYl18M=>R-Z©}?¨465 =>R -V-04U=>DE8>-_5?^=!?Q:P-9=DE4U=>1Q=P8!?DE4u?¨465I=>-0:<=5?¨=!?Q14AB;a?¨465a57-9=>-98PN Yo1¨8y=>R -[cke³5 ?¨=!?`:P-\=Ff 23DE4 -`=>R-Q:P-94:PDB=>DEO7DB=;1¨Y.5 DE23-04:PDE14:[1 4q]323-9=P8>DE/ fbwDEL T78>- :PR 1FK:=>R-.@AE1=Yl18=>R -[©5?^=!?V:P-\=?45ZK]-p/F?¨4b1W:P-98>O -y=>R6?^= Wi1¨=>R%/F?:P-9:`@ 8>1^OJD(5 -Z@AE1¨=>:_1¨Yy:PDE23DEA(?¨8`:PR6?@i-fwD(LT 8>-I I:PR1FK: Experimental Representation Most frequent item Most frequent item data set Center - based Aggregate nbrhood Different Recommendation Algorithms nbrhood (F1 metric) (F1 metric) (E-Commerce data set) MovieLens data High dimensional 0.21393 0.18928 0.18 Low dimensional 0.22009 0.20211 0.16 ( k = 20) 0.14 E - commerce data High d imensional 0.16654 0.11726 0.12 0.1 Low dimensional 0.12158 0.08579 0.08 ( k = 300) F1 metric 0.06 0.04 0.02 M L¤© (- /8# *,!$& ©+¡¤£¦-ME$§ ¨$I$I/ &C$§ !#¡¤$¦ §$I*,©+"J" 0 $-.©+ / !J¡¤$¦ 6I¥L ¡¤!N23 $ §© * 1 0.8 0.6 0.4 0.2 Density of data (as % of original) Ctr-MF-Hi Ctr-MF-Lo Rule-non personal Different Recommendation Algorithms ©- ¡1¡¤£ ©+§©+-! E©§ "#$¦L ¡* ©+/6§© * $-.©+ / !J¡¤$¦ (MovieLens data set) ¢¡¤£¦¥§© L £$§ ¡¤!J " ;¨",3 $¦ U©+§ "#$¦¨L ¡*,© / L¤£$§ ¡¤!# ¡ 0.25 I ©§ * © /!# "#©! ¥ 0.2 $- 0.15 0.1 A(?¨8>L-Q?45aRDEL RSUT6?¨A(DB=;©4-9D(LRJWi18>R1U1J57:0fp-`?^8>-_/F?^8>-9YoT AEAE;uDE47N F1 metric O¤-0:<=>DEL ?¨=>DE4LQ=>R D(: 8>-0:PT AB=Ff 0.05 0 4.3.5 Density Sensitivity Analysis 1 0.8 0.6 0.4 0.2 gh4C=>R-[@ 8>-9O7DE1T::P-0/9=>DE1 4 :yK]-M-9O ?¨A(T?¨=>-F5b=>R-[@i-98PYl18>2Z?4 /0-V1Y Density of data (as % of original) 5 DBz¢-98>-94J=y?¨A(L18>DB=>R23DE/M/\R 1 DE/0-0:Yo1¨8-F?¨/\Ra1¨Yd=>R-[=>R 8>-9-[:PTW N£=!?¨:PH7: Ctr-MF-Hi Ctr-MF-Lo Rule-non personal DE4JO¤1 AEO¤-F5MDE4Ze¦NnW6?:P-05_8>-0/012323-04657-98G:<;7:<=>-023:0fwg4_=>RDE:G:P-0/9=>DE14#j K-©Yl1U/0T:b1 4v-0O?AET6?^=>D(4 L=>R-I@i-98PYo1¨8>2Z?4/9-a1YMe¦NnW6?¨:P-F5±?¨465 =P8!? 57DB=>D(146?¨A?¨:P:P1U/0D(?¨=>DE1 438>TAE-9NnW?:P-F5[8>-0/012323-04657-98d:<;7:<=>-023:d?¨465 ¢¡¤£¥§© ¢¡W¡¤£ ©§© -! U©§ "#$L ¡ * ©+/ §©+*,$-.© /!J¡ $¦ ?AE:P1-9O ?¨A(T?¨=>-=>R -0DB8G:P-04:PDB=>DEOJDE=;M1 4_=>R - 5 -94:PDB=h;V1¨Y6=>R-]5?¨=!?y:P-9=>:0f L¤£$§ ¡¤!# "!;",3 ¨$¦ U©§ "#$¦L¤¡* ©+/ L¤£$§ ¡¤!J ¡ $1;¨¡¤© 4 wDEL T78>- `?45IwDEL T78>-M¡M:PR 1^K: =>R -p8>-0/012323-0465 ?¨=>DE1 4b@i-98PYo1¨8PN /¨!# "#©+!¦¥ 2Z?4 /0- ?¨:23-F?:PT78>-F5bWU;b][23-\=P8>D(/!¡k1Yw=K1Qe¦NW?:P-F5Z8>-0/012QN 23-045?¨=>DE14?¨A(L18>DB=>R23:M?¨465a=>R-`=P8!?5 DB=>DE1 46?¨A]?¨:P:P1U/0D(?¨=>DE1 4%8>T A(-\N W6?¨:P-F5b?AEL 1¨8>DE=>R 23: 5 DE:P/0T :P:P-F53DE4 ©J-0/9=>DE1 4 fEyYo18 5 DBz¢-98>-04U=AE-0O -0AE: 4.3.3 Experiments with the recommendation genera- 1Y[5 -04 :PDE=;Uf}{R -I=hK]1e¦NnW6?:P-05s?AEL18>DB=>R23:ZT:P-C=>R-©/0-94J=>-\8PN tion process. 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CONCLUSION =>R -3AE1^K]-98357DE23-04:PDE1 4?AG8>-0@ 8>-9:P-04U=!?¨=>DE1 4fuy:[K-Z/F?¨4q:P-0-3Yl8>12 ,.-0/01 2323-9465 -\8:<;7:<=>-023: ?^8>-[?_@i1FK-\8PYoTA4-\K}=>-0/\R 41A(1L;bYo1¨8 =>R DE:Q=!?WAE- j]=>R-©/0-94J=>-\8PNW?:P-F5t4-0DELR7Wi1¨8>R1U1J5Yo18>2Z?^=>DE1 4}?¨A(L1N -9J=P8!?/\=>D(4 LQ?55 DB=>DE1 4?AO ?¨AET-yYl18y?_W T:PDE4-9:P:Yl8>1 2®DB=>: /0T :<=>1 23-98 8>DB=>R 2 1T =>@i-98PYl18>23:M=>R-Z?LL8>-0L ?¨=>-9NnW?:P-F523-9=>R1J5¢jd-0:P@i-0/9D+?¨AEAE; 5?^=!?W?:P-0:0f{R -0:P-]:<;7:<=>-023:wR -0AE@_/9T:<=>1 23-\8>:¦x645V@78>1J5 T /9=>:¦=>R-\; Yl18C=>R-c]e 5?^=!?q:P-9=Ff{RDE:bK ?:I?q:PT 8>@78>D(:PDE4 L8>-9:PTAB=©?¨:bK]- K ?¨4U=M=>1IWT ;uY+8>1 2 ?IW T:PDE4-0:P:0fC,.-0/01 2323-9465 -\8:<;7:<=>-023:[Wi-047N K]-98>-`-\ @i-9/9=>DE4LQ=>R6?^=p=>R -MO -98P;©:P@?¨8>:P-`4?¨=>T78>-M1¨Yk=>R DE:5?^=!?3:P-9= -9x =p/0T :<=>1 23-98>:.WU;©-04?W A(DE4 LZ=>R -02®=>1Qx645I@ 8>1J57T/9=>:.=>R-9;CAED(H - f KDEAEA@78>-0O¤-04U=#=>R-/0-94J=>-\8PNW?:P-F5V:P/!R-023-Yo18W TDEA(5 DE4Ly:PT 3/0DE-04U=>AB; e]1 4JO¤-\8>:P-0AB;Uj¤=>R-9;MR -0AE@`=>R- W T:PDE4-0:P:WU;ML -04 -98!?¨=>DE4LV231¨8>- :>?AE-0:0f ¡F¢ k8>-0-0:P- j f ©¢fEj«y-0/!H¤-98>2Z?4j fEj6?¨465 ?5 DE- j6eyf , , ¡\f ,.-0/012323-04657-98:<;7:<=>-023:V?^8>-`8!?@ D(5 AB;Wi-0/01 23DE4 L©?I/98>T /0D(?AG=>1U1 A c23@ DE8>DE/F?¨A¦.46?¨AE;7:PDE:1YGªd8>-F57D(/\=>D(O -VyAEL 1¨8>DE=>R 23: Yo18 DE4acdNn/01 2323-\8>/0-1 4C=>R-q-9W#f,y-9/01 2323-045 -98:<; :<=>-923:y?^8>-[Wi-9N e]1 AEA(?Wi18!?^=>DEO¤-`wDEAB=>-98>DE4L7f6g4 PF!> "¨oJ¨_<°l§ $ l§ DE4 L[:<=P8>-0:P:P-F5`WU;V=>R- RJTL-O¤1A(T 23-1Y¢/9T:<=>1 23-\85?¨=!?yD(4`-97D(:<=>DE4 L §F°F\P\i!`&%i!\!no 'Zo'.! k9£ ! 9o (U\6\ /918>@i18!?^=>-`5 ?¨=!?¨W6?:P-9:0j?465bKD(AEAwWi-V:<=P8>-0:P:P-05©-0O¤-04©231¨8>-[WU;C=>R - @@#f Nh Uf DE4 /98>-F?:PDE4 L~O¤1AET23-31Y./0T :<=>1 23-98`5?^=!?a?FO ?¨D(A(?¨WAE-C14q=>R-3q-9W#f ¦y-9K±=>-0/!R4 1 AE1 LDE-0:?¨8>-4 -0-F57-F5Q=>R6?¨=]/F?4C578!?¨2Z?¨=>DE/F?¨A(AB;ZDE23@ 8>1^O¤- ^¢_e]T 8>-9=>14#jcfcfEj6?465 P yL1 :<=>DE417j6,Vf .f !, ¡\fi6?¨/9=>18 =>R -[:P/F?A(?¨WDEAEDE=;©1¨Yw8>-0/012323-04657-98 :<;7:<=>-023:0f y46?¨AB; :PDE:0¯ky4Iy@ @AEDE-F5I.@@ 8>1 ?/!R#fF¦¦GP\i! 9E>¥¦$ g4%=>RDE:`@?@i-98QK]-C@78>-0:P-04U=>-F5?45%-97@i-98>DE23-04U=!?AEAB;%-0O?AET6?^=>- ¨>¨9F9\¨² ¥ 9¨$c«yDEA(AE:>5 ?AE- j6¦ f O?¨8>DE1T:y?AEL 1¨8>DE=>R 23DE/M/!R1DE/0-0:Yo18pe¦NnW6?¨:P-F5I8>-0/012323-04657-98 :<;7: ,^¢ -0-98PK]-0:<=>-98Fj ©ifEj T 2Z?DE:0j ©¢f {pfEjiT78>46?¨:0j _f7rfEj =>-923:0f T78 8>-0:PTAB=>::PR1FK*=>R6?^=.5 DE23-04:PDE146?AEDB=h;b8>-F57T/9=>DE1 4C=>-0/\R7N ¦?45?¨T-98Fj{pf fEj?45I«?^8>:PR2Z?4jJ,Mf !,, ¡\f6gh45 -97DE4L 4 D(SJT -0:R 1 A(5Q=>R-p@78>1 23DE:P-.1Y¦?AEAE1^KDE4 LZe¦NnW6?:P-05C?¨A(L18>DB=>R23:=>1 WJ;C#?¨=>-04U= ©7-92Z?4U=>DE/[y4?AB;7:PD(:0f( J¥J!i ¦<°Vl§ ¥ $Z\!£> :P/0?AE-[=>1`A(?¨8>L-_5 ?¨=!?M:P-9=>:.?465C?¨==>R-p:>?23-p=>DE23-p@78>1J5 T /0-RDELR N iF9n\ 'y°0[!F°0 $3¨£¡ i9n\6!) +*k^j@@f ,7\N ¤¡Uf SUT?AEDB=h;%8>-0/012323-0465 ?¨=>DE1 4 :0fT7=>T 8>-ZK18>H%DE:`8>-0SJT DB8>-F5=>1T47N B! ^¢M6?0;7;U? 5j Mf6~fEj6ªD(?¨=>-\=>:PHJ;JN ©7R?@ DE8>17j _fEj ©72M;7=>Rj7ªwf(j?45 57-98>:<=!?45C-9 ?¨/9=>AB;3KRJ;ZAE1FK 5 DE23-04 :PD(146?¨A68>-0@ 8>-0:P-94J=!?^=>DE1 4CK]18>HJ: y=>RJT 8>T :>?2_;Uj¤,MfEjck57:0f , , ¡\fiy5 O?4/9-0: DE4 41FKAE-F57L - K]-0AEA Yo18Z:P123-b8>-9/01 2323-045 -98`?@ @AEDE/F?¨=>DE14:0j ?¨465AE-0:P:`K-9A(A Yl18 DE:P/01^O¤-98P;C?45 ?¨=!?QID(4 DE4L f,-.[²>\¨>¨0/7G- ²6P\¨>¨!f 1¨=>R-98>:0f B \¢#p1 A(5 Wi-98>L7j fEj ¦pDE/!R1 AE:0j fEj HJDj yfi~fEj6?465C{¦-98P8P;Uj f !, , ¡\f p:PDE4LZe]1AEA+?¨Wi18!?^=>D(O -`wDEAB=>-98>DE4LQ=>1`-F?FO¤-[?¨4 §$¨$#¥7 £>£ ¨V<°l§! §2Gaf 6. ACKNOWLEDGMENTS gh4 Yl18>2Z?^=>D(14©{w?¨@i-0:<=P8P;Uf -0/0-02_Wi-98Ff T4657DE4L%Yo1¨8a=>RDE:I8>-0:P-F?^8>/\R*K ?¨:a@ 8>1^OJD+57-F5}DE4 @?¨8P=aWU;±=>R - B^F¢#p1U1J5j6¦MfEj ©J/\R?¨Yo-\8Fj yfEj 1 4:<=!?¨4#j1 fEj k18>/!R-98>:0j6MfEj ¦p?¨=>DE1 4?A ©J/0DE-04/9-`1T45?¨=>DE14aT4657-98.L8!?¨4J=>:ygPg ©,7 , 7j#gPg © © ?¨8PK?¨8Fj yfEj«y-98>AE1U/\H¤-\8Fj, fEj?465C,yDE-F57A£j1 f !,, , ¡\f , ¡ ¤Jj?¨465%gPg © ,,¤¡ ¡JF¡KDB=>Rv?557DE=>DE146?AYlT45 DE4LuWU;q¦y-9= e]1 2`W DE4DE4LQe]1 AEA(?Wi18!?^=>DEO¤-`wDEAB=>-98>DE4LQ±DE=>RIªw-98>:P1 4?A ªw-\8>/0-0@ =>DE14:agh4 / f{RDE:©K1¨8>H}K ?:u?¨AE:P1s:PT@ @i18P=>-F5³WU;}¦ ©7 yL -94J=>:Yl18 ]-9=P=>-\8,y-0/91 2323-045?¨=>DE14:0fJgh4- <F!! 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