Musical Influence Network Analysis and Rank of Sample-Based Music

Nicholas J. Bryan and Ge Wang

Stanford University | CCRMA

ISMIR 2011 Introduction

• Influence Network Analysis and Rank • Understand how songs, artist, and genres interact within the musical practice of sample-based music • Sampled-Based Music • A musical work that borrows material from another source, whether it be direct manipulation of a recorded sound or less direct transcribed material as decided from a user community “Amen Break”

“Theme From Lilies of the Field (Amen)” by Jester Hairston A

“We’re a Winner” “Theme From Lilies of the Field (Amen)” by The Impressions by The Impressions B1 B2

C “Amen, Brother” by The Winstons “Amen Break”

“Theme From Lilies of the Field (Amen)” by Jester Hairston A

“We’re a Winner” “Theme From Lilies of the Field (Amen)” by The Impressions by The Impressions B1 B2

C “Amen, Brother” by The Winstons

. . . F D “Straight Outta Compton” by NWA “Rustic Raver” E by Squarepusher “The Perfect Drug” by Nine Inch Nails “Amen Break”

“Theme From Lilies of the Field (Amen)” by Jester Hairston A

“We’re a Winner” “Theme From Lilies of the Field (Amen)” by The Impressions by The Impressions B1 B2

Gospel C “Amen, Brother” by The Winstons Soul / Funk / Disco

Electronic / Dance

Rock / Pop . . . F Hip-Hop / R&B D “Straight Outta Compton” by NWA “Rustic Raver” E by Squarepusher “The Perfect Drug” by Nine Inch Nails Today

• Unique Dataset • User community generated sample-based music data • Initial analysis and trends

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If genre k samplesgj, the only entropy from willa single be zero. other genre If destination genre gk sam- 1 is the probability of source genre gj given the destination manipulation of a recorded sound or lessWithin direct transcribed this work, sample-based material. music is definedgj, the as entropy a musical will work be zero. If destination genre gk sam- that in borrows material from another musical source, whether it be a direct genre gk. If genre gk samples only from a single other genre manipulation of a recorded sound or less direct transcribed material. gj, the entropy will be zero. If destination genre gk sam- Genre & Part-Sampled Trends I

source

destination Genre Visualization

P. Shannon, et al.: “Cytoscape: A Software Environment for Integrated Models of Biomolecular Interaction Networks.” Genome Research 13(11), 2003. Part-Sampled Visualization

P. Shannon, et al.: “Cytoscape: A Software Environment for Integrated Models of Biomolecular Interaction Networks.” Genome Research 13(11), 2003. Time-Based Trends

Source Rise and fall of soul/funk/disco

all samples soul/funk/disco

Destination electronic dance hip-hop/R&B Rise of hip-hop/R&B rock pop Network Analysis

“Theme From Lilies of the Field (Amen)” by Jester Hairston A

“We’re a Winner” “Theme From Lilies of the Field (Amen)” by The Impressions by The Impressions B1 B2

C “Amen, Brother” by The Winstons

• Song, artist, and genre-level networks • Focus on song-level network and musical sampling pled source material), showing a rough outline of the rise and fall of soul/funk/disco and the rise of hip-hop/R&B. pled sourceThe general material), shape showing of the a destination rough outline material of the (lower) rise out- and falllines of soul/funk/disco the increased popularity and the rise of sampling of hip-hop/R&B. and/or listener The generaltrends shape within of the the WhoSampled.com destination material user (lower) community. out- In- lines theterestingly, increased there popularity is a sharp of sampling decrease and/or in sample-based listener mu- trends withinsic centered the WhoSampled.com around 2003. While user further community. investigation In- is re- terestingly,quired, there it interestingis a sharp decrease to note that in sample-based this event directly mu- coin- sic centeredcides around with the 2003. Recording While further Industry investigation Association is of re- America quired,(RIAA) it interesting first litigation to note that on Internet this event piracy directly and musiccoin- copy- pled source material), showing a rough outlinecides of the withright rise the infringement Recording Industry [11]. Such Association legal policy of would America have cre- and fall of soul/funk/disco and the rise of(RIAA) hip-hop/R&B. first litigation on Internet piracy and music copy- The general shape of the destination material (lower)ated out- a more conservative and limited view of the musical lines the increased popularity of samplingright and/or listener infringementpractice of sampling, [11]. Such thus legal significantly policy would affecting have cre- the music- trends within the WhoSampled.com user community.ated a moremaking In- conservative process. and limited view of the musical terestingly, there is a sharp decrease in sample-basedpractice mu- of sampling, thus significantly affecting the music- Figure 4. Distribution of Uniquesic centered Samples around 2003. Over While Time. further All investigation is re- quired, it interesting to note that this eventmaking directly coin- process. samples (blue, solid), soul/funk/discocides with the (magenta, Recording Industry triangles), Association of America 3. NETWORK ANALYSIS Figurehip-hop/R&B 4. Distribution (red, of Unique plus), electronic Samples(RIAA) first Over dance litigation Time. (green, on Internet All circle), piracy and music copy- A discussion of network analysis, influence measures, and samplesrock (blue, pop solid), (black, soul/funk/disco x) are shownright across (magenta, infringement time triangles),[11]. for Such source legal mate- policy would have cre- 3. NETWORK ANALYSIS ated a more conservative and limited view of the musicalrank is presented with the motivation of observing how in- hip-hop/R&Brial (upper) (red, and plus), destination electronic materialpractice dance of (lower). sampling, (green, thus circle), significantlyNetwork affecting Analysis the music- II A discussiondividual of songs, network artists, analysis, and influence genres influence measures, one and another. making process. “Theme From Lilies of the Field (Amen)” rock pop (black, x) are shown across time for source mate-by Jester Hairston A rank isComplex presented network with the analysis motivation provides of observing significant how tools in- for such Figure 4. Distributionrial (upper) of Unique and Samples destination Over Time. material All (lower). “We’re a Winner” “Theme Fromdividual Lilies of the Field (Amen)” songs, artists, and genres influence one another. samples (blue, solid), soul/funk/discoples uniformly (magenta, from triangles), each source genre3.g NETWORK, theby The Impressions entropy ANALYSIS willby The Impressions characterization and begins with the formulation of a net- j B1 hip-hop/R&B (red, plus), electronic dance (green, circle), 2 A discussion of networkB analysis, influenceComplex measures,work and network graph. analysis A graph providesG =( significantN,E) is tools defined for such by a set of rock pop (black, x) are shownbe maximized. across time for source The mate- genre entropy for the top five destina- rank is presented with the motivation of observing how in- ples uniformly from each source genre g , the entropy willC “Amen, Brother”characterization nodes N andand begins edges E withor equivalently the formulation an adjacency of a net- matrix rial (upper) and destinationtion material genres (lower). is shown in Table 1. Thej source samples usedby The Winstons in dividual songs, artists, and genres influencework one another. graph.destination A graph G =(N,E) is defined by a set of be maximized. The genre entropy forComplex the network top five analysis destina- provides significant tools forA such.A AB1 weightedB2 C directed edge between node i and j is de- (bits) nodes NA and1 edges E or equivalently an adjacency matrix ples uniformlytion from genres each source is genre showngj, the in entropyGenre Table will 1. Thecharacterization sourceEntropy samples and begins used with in the formulation of afined net- via Aij = wij and 0 otherwise, where wij is the cor- B1 1 be maximized. The genre entropy for the top fiveelectronic destina- dance (E)work2.83 graph. A graph G =(N,E) is definedA. by A a set weighted of directed edge between node i and j is de- respondingB2 1 weight. For unweighted networks, all weights rock pop (P) nodes2.745N and edges E or equivalently an adjacency matrix source tion genres is shown in Table 1. The sourceGenre samples used in Entropy (bits) C hip-hop/R&B (H) A. A2.356 weighted directed edge between nodefinedi and j viaisare de-A eitherij = w zeroij and or one.0 otherwise, where wij is the cor- electronic dance (E) 2.83 Genre Entropy (bits) soul/funk/disco (F) 2.242A = w 0 w rock pop (P) 2.745fined via ij ij and otherwise, whererespondingij is the cor- weight. For unweighted networks, all weights electronic dance (E) 2.83 reggae (R) responding2.129 weight. For unweighted networks, all weights rock pop (P) 2.745hip-hop/R&B (H) 2.356 are either3.1 zero Degree or one. Distributions hip-hop/R&B (H) 2.356soul/funk/disco (F) 2.242are either zero or one. soul/funk/disco (F) 2.242 reggae (R) 2.129reggae (R) 2.129 Table 1. Genre Entropy For3.1 Popular Degree Distributions Destination Genres. 3.1 DegreeFor a Distributions first general measure of how the music sample-based For a first general measure of how the music sample-basednetworks are constructed, degree centrality can be used to Table 1. Genre Entropy For Popular Destination Genres. For a first general measure of how the music sample-based Tablereggae 1. Genre music Entropy are the For most Popular homogeneous,networks Destination are constructed, Genres. while degree electronic centrality can be usedmeasure to the influence from each node (song, artist, or genre) reggae music are the most homogeneous, while electronic measure the influence from each node (song,networks artist, or genre)of are a network. constructed, For degree a given centrality node, the can in- be and used out-degree to dance music is the most heterogeneous.of a network. For A a given closer node, look the in- at and out-degree dance music is the most heterogeneous. A closer look at measurecentrality the influence is defined from each as the node respective (song, artist, in or or out genre) edge counts electronic musicreggae revealselectronic music a near equal are split musicthe of most source reveals homogeneous, ma- a nearcentrality equal while is defined split electronic as of the respective source in ma- or out edge counts normalized by the total number of nodes Nof. The a network. in- and For a given node, the in- and out-degree terial from hip-hop/R&B,dance music electronic is the music, most rock/pop, heterogeneous. and A closer look at | | normalized by the total number of nodes N . The in- and terial from hip-hop/R&B, electronicout-degree distribution music, is rock/pop, then the proportion and of degree k = | | soul/funk/disco with a slight preference towards the latter. centralityout-degree is defined distribution as the respective is then the in or proportion out edge of counts degree k = electronicsoul/funk/disco music reveals with a near a slight equal1 preference, 2, 3 split,...nodes of and source towards can be used ma- the to characterize latter. the network. Such evidence suggests differences in the creative process Power-law distributions f(k) k arenormalized an important1, 2, by3,... thenodes total and number can be of used nodes to characterizeN . The in- the and network. of sampling betweenterial genres. fromSuch hip-hop/R&B, evidence suggests electronic differences music, in rock/pop, the creative and process⇥ | | family of distributions. Such distributions promote the con- out-degreePower-law distribution distributions is then the proportionf(k) k of degreeare ank important= soul/funk/discoof sampling with between a slight genres. preferencecept of towards preferential theattachment latter. and are referred to as scale- 2.2 Time-Based Trends 1, 2, 3,...nodes and can be used to characterize⇥ the network. free. To test the hypothesis that musical sampling followsfamily of distributions. Such distributions promote the con- Such evidence suggests differences in the creative process Initial observations of time-based trends are found when we a power-law, we can construct an unweighted acyclicPower-law songcept of distributions preferential attachmentf(k) k andare are an referred important to as scale- of sampling2.2 Time-Based between genres. Trends ⇥ view the proportion of samples per year within each genre. network using unique songs as nodes and samplingfamily instances offree. distributions. To test the Such hypothesis distributions that musical promote sampling the con- follows The trends can be viewed for both unique source and des- to create directed edges from destination to source. The cept of preferential attachment and are referred to as scale- tination material2.2 normalized Time-BasedInitial by the observations total Trends instances of of sam- time-basedin-degree trends distribution are found can then when be computed we and testeda to power-law, we can construct an unweighted acyclic song pling as shown in Fig. 4.view Plotting the unique proportion instances of source of samplesfollow per a power-law year within distribution each or not.genre. Usingfree. methods Tonetwork de- test the using hypothesis unique that songs musical as nodes sampling and sampling follows instances and destinationInitial material observations indicates general trends of time-based within each trendsscribed are in [12], found we find when that the we network isa consistent power-law, with we can construct an unweighted acyclic song genre and eliminates theThe effect trends of a single can popular be viewed sample forthe both hypothesis unique (p-value source= .16 for andk des-3 and =2.72)to and create directed edges from destination to source. The swaying the proportionsview thetination (as proportion is the case material without of samples uniqueness normalized per yearshow by the the within cumulative total each instances in-degree genre. distribution of sam- innetwork Fig. 5. in-degree using unique distribution songs as can nodes then and be sampling computed instances and tested to enforced). The trendspling can as shown be viewed in Fig. for 4. both Plotting uniqueIn terms unique source of networks instances and based des- on of musical source sampling,to create a scale-follow directed a power-law edges from distribution destination or not. to source. Using methods The de- The general shape of the source material plot (upper) out- free network suggests the idea that very popular samples lines the musicaltination time frameand material of destination each genre normalized (in terms material of sam- by indicates thewill total only general instances continue trends to increase of sam- within in popularity. eachin-degree In addition,scribed if distribution in [12], can we then find that be computed the network and is tested consistent to with pling asgenre shown and in Fig. eliminates 4. Plotting the effect unique of instances a single of popular source samplefollow athe power-law hypothesis distribution (p-value = or.16 not.for Usingk 3 methodsand =2 de-.72) and and destinationswaying material the proportions indicates (as general is the trends case without within each uniquenessscribedshow in [12], the we cumulative find that in-degree the network distribution is consistent in Fig. with 5. genre and eliminates the effect of a single popular sample the hypothesis (p-value = .16 for k 3 and =2.72) and enforced). In terms of networks based on musical sampling, a scale- swaying theThe proportions general shape (as ofis the the source case without material uniqueness plot (upper) out-show thefree cumulative network in-degree suggests the distribution idea that in very Fig. popular 5. samples enforced).lines the musical time frame of each genre (in terms of sam- In termswill of only networks continue based to increase on musical in popularity. sampling, a In scale- addition, if The general shape of the source material plot (upper) out- free network suggests the idea that very popular samples lines the musical time frame of each genre (in terms of sam- will only continue to increase in popularity. In addition, if pled source material), showing a rough outline of the rise and fall of soul/funk/disco and the rise of hip-hop/R&B. The general shape of the destination material (lower) out- lines the increased popularity of sampling and/or listener trends within the WhoSampled.com user community. In- terestingly, there is a sharp decrease in sample-based mu- sic centered around 2003. While further investigation is re- quired, it interesting to note that this event directly coin- cides with the Recording Industry Association of America (RIAA) first litigation on Internet piracy and music copy- right infringement [11]. Such legal policy would have cre- ated a more conservative and limited view of the musical practice of sampling, thus significantly affecting the music- making process. Figure 4. Distribution of Unique Samples Over Time. All samples (blue, solid), soul/funk/disco (magenta, triangles), 3. NETWORK ANALYSIS hip-hop/R&B (red, plus), electronic dance (green, circle), A discussion of network analysis, influence measures, and rock pop (black, x) are shown across time for source mate- rank is presented with the motivation of observing how in- rial (upper) and destination material (lower). dividual songs, artists, and genres influence one another. Complex network analysis provides significant tools for such ples uniformly from each source genre gj, the entropy will characterization and begins with the formulation of a net- be maximized. The genre entropy for the top fiveDegree destina- Centralitywork & Influence graph. A graph G =(N,E) is defined by a set of nodes N and edges E or equivalently an adjacency matrix tion genres is shown in Table 1. The source samples used in destination • Degree Centrality (In/Out) In-Degree A.A AB1 B weighted2 C directed edge between node i and j is de- • In-Degree (# of derived samples) A 1 1 Genre Entropy (bits) • Out-Degree (# of used samples) finedB1 via1 A1 ij = wij and 0 otherwise, where wij is the cor- electronic dance (E) 2.83 B2 1 1 source source rock pop (P) 2.745 respondingC weight. For unweighted networks, all weights hip-hop/R&B (H) 2.356 Out-Degreeare either1 2 zero or one. soul/funk/disco (F) 2.242 reggae (R) 2.129 • Sample chains • Desirable to capture direct and indirect3.1 influence Degree Distributions • Need more!!! Table 1. Genre Entropy For Popular Destination Genres. For a first general measure of how the music sample-based networks are constructed, degree centrality can be used to reggae music are the most homogeneous, while electronic measure the influence from each node (song, artist, or genre) dance music is the most heterogeneous. A closer look at of a network. For a given node, the in- and out-degree electronic music reveals a near equal split of source ma- centrality is defined as the respective in or out edge counts normalized by the total number of nodes N . The in- and terial from hip-hop/R&B, electronic music, rock/pop, and | | soul/funk/disco with a slight preference towards the latter. out-degree distribution is then the proportion of degree k = 1, 2, 3,...nodes and can be used to characterize the network. Such evidence suggests differences in the creative process Power-law distributions f(k) k are an important of sampling between genres. ⇥ family of distributions. Such distributions promote the con- cept of preferential attachment and are referred to as scale- 2.2 Time-Based Trends free. To test the hypothesis that musical sampling follows Initial observations of time-based trends are found when we a power-law, we can construct an unweighted acyclic song view the proportion of samples per year within each genre. network using unique songs as nodes and sampling instances The trends can be viewed for both unique source and des- to create directed edges from destination to source. The tination material normalized by the total instances of sam- in-degree distribution can then be computed and tested to pling as shown in Fig. 4. Plotting unique instances of source follow a power-law distribution or not. Using methods de- and destination material indicates general trends within each scribed in [12], we find that the network is consistent with genre and eliminates the effect of a single popular sample the hypothesis (p-value = .16 for k 3 and =2.72) and swaying the proportions (as is the case without uniqueness show the cumulative in-degree distribution in Fig. 5. enforced). In terms of networks based on musical sampling, a scale- The general shape of the source material plot (upper) out- free network suggests the idea that very popular samples lines the musical time frame of each genre (in terms of sam- will only continue to increase in popularity. In addition, if pled source material), showing a rough outline of the rise and fall of soul/funk/discopled source and material), the rise showing of hip-hop/R&B. a rough outline of the rise The general shapeand of fall the of destination soul/funk/disco material and (lower) the rise out- of hip-hop/R&B. The general shape of the destination material (lower) out- lines thepled increased source material), popularity showing of sampling a rough and/or outline listener of the rise and fall oflines soul/funk/disco the increased and popularity the rise of of hip-hop/R&B. sampling and/or listener trends within the WhoSampled.com user community. In- The generaltrends shape within of the the destination WhoSampled.com material (lower) user community. out- In- terestingly,lines there theterestingly, increased is a sharp popularity there decrease is a of insharp sampling sample-based decrease and/or in mu- listenersample-based mu- sic centeredtrends around withinsic 2003. centered the WhoSampled.com While around further 2003. investigation While user community. further is investigation re- In- is re- quired, itterestingly, interestingquired, there to is it note ainteresting sharp that decrease this to event note in thatsample-based directly this eventcoin- mu- directly coin- cides withsic the centered Recordingcides around with Industry 2003. the Recording While Association further Industry investigation of Association America is re- of America (RIAA)quired, first litigation it(RIAA) interesting on first Internet to litigation note piracy that on this Internet and event music directly piracy copy- and coin- music copy- right infringementcides withright the [11]. Recording infringement Such legal Industry [11]. policypled Association Such source would legal material), have policy of America showing cre- would a rough have outline cre- of the rise ated a more(RIAA) conservative firstated litigation a more and conservativeon limited Internetand view piracyfall and of of limited soul/funk/disco and the music musical view copy- of and the the musical rise of hip-hop/R&B. practiceright of sampling, infringementpractice thus of [11]. significantly sampling, Such legalThe thus affecting general policy significantly shape would the of music- have affecting the destination cre- the music- material (lower) out- lines the increased popularity of sampling and/or listener making process.ated a moremaking conservative process. and limited view of the musical practice of sampling, thus significantlytrends within affecting the WhoSampled.com the music- user community. In- Figure 4. DistributionFigure of Unique 4. Distribution Samples of Over Unique Time. Samples All Over Time. Allmaking process. terestingly, there is a sharp decrease in sample-based mu- sic centered around 2003. While further investigation is re- samples (blue, solid),samples soul/funk/disco (blue, solid), (magenta, soul/funk/disco triangles), (magenta, triangles), 3. NETWORK3. ANALYSIS NETWORK ANALYSIS Figurehip-hop/R&B 4. Distribution (red, of Unique plus), Samples electronic Over dance Time. (green, All circle), quired, it interesting to note that this event directly coin- hip-hop/R&B (red,samples plus), (blue, electronic solid), soul/funk/disco dance (green, (magenta, circle), triangles), A discussion3. NETWORK of networkcides ANALYSIS analysis, with the Recording influence Industry measures, Association and of America rock pop (black, x) are shown across time for sourceA discussion mate- of network analysis, influence(RIAA) first measures, litigation on and Internet piracy and music copy- rock pop (black,hip-hop/R&B x) are shown (red, across plus), time electronic for source dance mate- (green, circle), rank is presented with the motivation of observing how in- rial (upper) and destination material (lower). rank is presentedA discussion with of the network motivation analysis,right of influence observinginfringement measures, how [11]. Such in- and legal policy would have cre- rial (upper) androck destination pop (black, material x) are shown (lower). across time for source mate- dividual songs, artists, and genres influence one another. dividualrank songs, is presented artists, and with genres the motivation influenceated a more of observing one conservative another. how and in- limited view of the musical rial (upper) and destination material (lower). Complex network analysis provides significant tools for such Complexdividual network songs, analysis artists, provides and genres significantpractice influence of sampling, tools one for thus another. such significantly affecting the music- ples uniformly from each source genre gj, the entropy will characterization andmaking begins process. with the formulation of a net- characterizationComplex and networkwork begins graph. analysis with A provides graph the formulationG significant=(N,E oftools) is a defined for net- such by a set of ples uniformly from eachbe maximized. source genre Theg genrej, the entropy entropyFigure for will 4. the Distribution top five of destina- Unique Samples Over Time. All g characterization and begins with the formulation of a net- be maximized.ples The uniformly genretion genres entropy from is each shown for source the in top Table genre five 1.samples The destina-j, the source entropy (blue, samples solid), willwork soul/funk/disco used graph. in A (magenta, graphnodes G triangles),N and=( edgesN,E)Eisor defined equivalently by3. NETWORK a set an adjacency of ANALYSIS matrix work graph. A graph G =(N,E) is defined by a set of be maximized. The genre entropy for thehip-hop/R&B top five destina- (red,nodes plus), electronicN and edgesdanceA. (green,E Aor weighted circle), equivalently directed an edge adjacency between matrix node i and j is de- tion genres is shown in Table 1. The source samples used in A discussion of network analysis, influence measures, and tion genres is shown in Table 1. The sourcerock samples pop (black, used x) are in shownnodes across timeN and for source edges mate-E or equivalently an adjacency matrix Genre Entropy (bits) A. A weighted directedfined via edgeAij = betweenwij rankand node is0 presentedotherwise,i and withj whereis the de- motivationwij is the of observingcor- how in- electronic dance (E) rial2.83 (upper) and destination materialA. A (lower). weighted directed edge between node i and j is de- Genre Entropyrock pop(bits) (P) 2.745 fined via Aij = wrespondingij and 0 otherwise, weight. Fordividual where unweighted songs,wij is artists, the networks, cor- and genres all influenceweights one another. electronic dance (E)Genre2.83 Entropy (bits) fined via Aij = wij and 0 otherwise, where wij is the cor- electronic dancehip-hop/R&B (E) 2.83 (H) 2.356 responding weight.are either For unweighted zero or one.Complex networks, network all analysis weights provides significant tools for such rock pop (P) 2.745soul/funk/disco (F) 2.242 responding weight. For unweighted networks, all weights rock pop (P) 2.745 ples uniformly from each source genre gj, the entropy will characterization and begins with the formulation of a net- hip-hop/R&B (H) hip-hop/R&B2.356reggae (H) (R) 2.356 2.129 are eitherare zero either or zeroone. or one. work graph. A graph G =(N,E) is defined by a set of soul/funk/disco (F) 2.242 be maximized. The genre entropy for the top five destina- soul/funk/disco (F) 2.242 3.1 Degree Distributionsnodes N and edges E or equivalently an adjacency matrix reggae (R) reggae2.129 (R) 2.129 tion genres is shown in Table 1. The source samples used in 3.1 Degree3.1 DistributionsDegreeFor Distributions a first general measureA. A weighted of how directed the music edge sample-based between node i and j is de- Table 1. Genre Entropy For Popular DestinationGenre Genres. Entropy (bits) fined via Aij = wij and 0 otherwise, where wij is the cor- electronic dance (E) 2.83 networks are constructed, degree centrality can be used to rock popFor (P) a firstFor2.745 general a first general measure measure of how of the howresponding music the music sample-based weight. sample-based For unweighted networks, all weights Table 1. GenreTable Entropy 1. Genre For Popular Entropy DestinationFor Popular Destination Genres. Genres. measure the influence from each node (song, artist, or genre) reggae music are the most homogeneous, whilehip-hop/R&B electronic (H) networks2.356 are constructed, degreeare centrality either zero or can one. be used to soul/funk/disconetworks (F) are2.242 constructed,of a network. degree For centrality a given can node, be the used in- to and out-degree dance music is the most heterogeneous. Areggae closer (R) lookmeasure at2.129 the influence from each node (song, artist, or genre) reggae music arereggae the music most homogeneous,are the most homogeneous, while electronic while electronicmeasure the influencecentrality from is each defined node as3.1 (song, the Degree respective artist, Distributions or in genre) or out edge counts dance musicelectronic is the music most reveals heterogeneous. a near equal A closer split look of sourceof at a network. ma-of a network. For a given For a given node, node, the in- the and in- and out-degree out-degree dance music is the most heterogeneous. A closer look at normalized by the totalFor number a first general of nodes measureN of. how The the in- music and sample-based electronicterial music from reveals hip-hop/R&B, a near equal electronic splitTable of music, 1. source Genre rock/pop, Entropy ma-centrality For and Popularcentrality is defined Destination is defined as the Genres. asrespective the respective in or in out or edge out edge counts counts| | electronic music revealssoul/funk/disco a near equal with split a slight of source preference ma- towards the latter.normalizedout-degree by the total distribution numbernetworks of is nodes then are theN constructed, proportion. The in- degree and of degree centralityk = can be used to terial from hip-hop/R&B, electronic music, rock/pop, andnormalized by the total number of nodesmeasureN the.| influence The| in- from and each node (song, artist, or genre) terial from hip-hop/R&B,Such evidence electronic suggests music, differences rock/pop,reggae in and music the creative are the most process homogeneous,out-degree1, while distribution2, 3,... electronicnodes is then and canthe proportion be used to ofcharacterize degree k = the network. soul/funk/disco with a slight preference towards the latter. of a network.| | For a given node, the in- and out-degree dance music is theout-degree most heterogeneous. distributionDegree APower-law closer is look then Distributions at the distributions proportionf( ofk) degree k k are= an important soul/funk/discoSuch with evidenceof a slight sampling suggests preference between differences towardsgenres. in the the latter. creative process 1, 2, 3,...nodes and can be usedcentrality to characterize is defined⇥ the as network. the respective in or out edge counts electronic music reveals1, 2, a3,... nearnodes equal split andfamily of can source of be distributions. used ma- to characterize Such distributions the network. promote the con- Such evidence suggests differences in the creative process Power-law distributions f(knormalized) k byare the an total important number of nodes N . The in- and of sampling between genres. terial from hip-hop/R&B, electronic music, rock/pop, and ⇥ | | •Power-law Power-law distributions distribution,cept of preferential f(k) attachmentout-degreek are distribution an and important are referred is then the to proportion as scale- of degree k = of sampling between2.2 genres. Time-Based Trends soul/funk/disco with a slight preferencefamily of towards distributions. the latter. Such⇥ distributions promote the con- family• ofPreferential distributions. free.attachment To Such test and distributions the scale-free hypothesis1, 2 networks, 3,... promote thatnodes musical and the can con- be sampling used to characterize follows the network. Such evidence suggests differencescept of in thepreferential creative process attachment and are referred to as scale- 2.2 Time-Based Trends Power-law distributions f(k) k are an important Initial observations of time-basedof trends sampling are between foundcept genres. when of• Popular preferentialwefree. To musical testa power-law, attachment the samples hypothesis will we and be can thatpopular are construct musical referred sampling an to unweighted as scale- follows acyclic⇥ song 2.2 Time-Based Trendsview the proportion of samples per year within each genre. network using uniquefamily songs of as distributions. nodes and samplingSuch distributions instances promote the con- Initial observations of time-based trends are found when wefree.• Hypothesis Toa test power-law, the hypothesis we can construct that musicalcept an unweighted of sampling preferential acyclic follows attachment song and are referred to as scale- The trends can be viewed for both2.2 Time-Based unique source Trends and des- to create directed edges from destination to source. The Initial observationsview of the time-based proportion of trends samples are per found year when within we each genre.a power-law,• Buildnetwork unweighted we using can construct unique acyclic songs song-level an as unweighted nodesfree. network To and test sampling acyclic the hypothesis instances song that musical sampling follows The trendstination can material be viewed normalized for both unique byInitial the source total observations instances and des- of time-based of sam-to trends create arein-degree directed found when edges distribution we froma destination power-law, can then be we to source.cancomputed construct The and an unweighted tested to acyclic song view the proportion of samples per year within each genre. network• Maximum using unique likelihood songs fit as[Clauset nodes 2009] and sampling instances tinationpling material as shown normalized in Fig. by 4. thePlotting totalview unique instances the proportion instances of sam- of of samples sourcein-degree per year withinfollow distribution each a power-law genre. can then distributionnetwork be computed using or unique and not. songs tested Using as to nodes methods and sampling de- instances The trends can be viewed for both unique source and des- to create directed edges from destination to source.A Thek have elements representing the number of sample chains pling asand shown destination in Fig. 4. material Plotting indicates uniqueThe instances general trends trendscan of source be viewed within for eachfollow both unique a power-lawscribed source and in distribution [12], des- we findto or create that not. the directed Using network methods edges is from consistent de- destination with to source. The tination material normalized by the total instancestination of sam- material normalizedin-degree by the distribution total instances can of then sam- be computedin-degree distribution and testedof can corresponding to then be computed length andk capturing tested to various levels of indi- and destinationgenre and material eliminates indicates the general effect of trends a single within popular each samplescribed inthe [12], hypothesis we find that (p-value the network= .16 for is consistentk 3 and with =2.72) and pling as shown in Fig. 4. Plotting unique instances ofpling source as shown in Fig. 4. Plotting unique instances of source follow a power-law distributionrect influence. or not. For Using stability, methods1/ must de- be greater than the genre andswaying eliminates the proportions the effect of (as a is single the case popular without samplefollow uniqueness athe power-law hypothesisshow distribution (p-value the cumulative= or.16 not.for in-degreek Using3 and distribution methods =2largest.72 de-) in and eigenvalue Fig. 5. of A and for large networks, (2) becomes and destination material indicates general trends within each scribed in [12], we find that the network is consistent with and destinationswaying materialenforced). the indicates proportions general (as is trends the case withingenre without each and uniqueness eliminatesscribed the effect inshow of [12], a single the we cumulative popular findIn terms that sample in-degree of the networks network distributionthe basedhypothesis is consistent on in musical (p-value Fig. 5.increasingly with= sampling,.16 for k difficult a3 scale-and to invert.=2.72 Typically,) and only the overall in- genre and eliminatesenforced). theThe effect general of a shape single of the popular sourceswaying sample material the proportions plot (upper)the hypothesis (as out- is theIn case terms (p-value withoutfree of networks network uniqueness= .16 based suggestsfor k onshow musical3 theand the idea cumulative sampling,=2 that.72 very in-degree)fluence a and scale- popular rank distribution is samples desired in and Fig. is 5. computed iteratively in a fash- ion to avoid a large memory footprint and matrix inverse enforced). In terms of networks based on musical sampling, a scale- swaying the proportionsThelines general (as the shapeis musical the of case the time source without frame material of uniqueness each plot genre (upper) (in terms out-show of thesam-free cumulative networkwill in-degree suggests only continue the distribution idea to increase that very in Fig. in popular popularity. 5. required samples In for addition,I . if The general shape of the source material plot (upper) out- free network suggests the idea thatK very popular samples enforced). lines the musical time frame of each genre (in terms of sam- In termswill of only networks continue based to increase on musical in popularity. sampling, In a addition, scale-For our if purposes, it is desirable to have both the entire in- lines the musical timeA. Clauset, frame C. ofR. Shalizi, each and genre M. E. J. (in Newman: terms “Power-law of sam- Distributions inwill Empirical only Data.” continue SIAM Review to 51(4), increase 661-703 (2009). in popularity. In addition, if The general shape of the source material plot (upper) out- freeFigure network 5. Cumulative suggests In-degree the idea Distribution that veryP (k) popularof the samplesfluence matrix and overall rank. Given IK , we can view the Sample-Based Song Network (log-log scale). column of a node to find who influenced the node, or view lines the musical time frame of each genre (in terms of sam- will only continue to increase in popularity. In addition,the row if of the node to find who the node influenced [15]. Summing the columns of the influence matrix produces a any of the very popular samples were to be removed, large ranking of the most influential nodes, while summing the portions of sample-based music would cease to exist (or at rows results in a ranking of the most influenced nodes. Such least be altered). analysis is nicely suited for musicological analysis and mo- tivates further improvements discussed below. 3.2 Influence Measures To analyze and rank influence within each network, four 3.3 Collapse-and-Sum Influence Rank closely related measures are commonly used: degree cen- For the given dataset, we would like to understand and ana- trality, eigenvector centrality, Katz centrality, and PageR- lyze song, artist, and genre influence individually, as well as ank. Degree centrality does not capture any indirect form of how each network relates to one another. To do so, individ- influence (as in the case of sample chains), motivating alter- ual networks can be constructed for song, artist, and genre native methods. Eigenvector centrality extends degree cen- networks with influence matrices and rank computed via (2) trality by weighting the importance of neighboring nodes to or (3). Building separate graphs, however, has several draw- allow for indirect influence, but has limited application for 2 backs. Most notably, there is no straightforward mechanism acyclic networks [13]. Katz centrality and PageRank ap- to relate the influence matrices of each network together ap- propriately modify eigenvector centrality. Both also provide propriately. Furthermore, we would like to model the influ- a mechanism to capture indirect influence between nodes, ence propagation on the song-level topology and then derive compute an overall influence rank among each node, and artist and genre influence measures, as the compositional act observe the influence of one node to another. PageRank, of sampling is presumably based on the musical material it- however, down-weights influence created by a destination self, rather than artist or genre connections. node that samples more than once, or in the case of artist To address this issue, a single influence matrix is con- nodes, down-weights influence from artists with lengthy ca- structed using the song-level network (see Section 3.1) and reers. While this is desirable in numerous other contexts is used to create the artist and genre influence matrices, re- such as web search, we wish to equally weight each instance sulting in the proposed relational collapse-and-sum approach. of sampling and restrict ourselves to Katz centrality. To construct the artist-level influence matrix IA from the I The Katz influence matrix K is defined via song-level network, the song-level network is first used to 1 compute the song influence matrix IS. Given IS, we then IK =(I A) I (2) compute a derived artist influence matrix IA, knowing the Ss Sd where I is an identity matrix, A is the adjacency matrix as source and destination song sets ai and ai belonging to before, and is a decay factor which scales the indirect in- each artist ai. To do so, we take each artist ai in the set of fluence allowed to propagate though the network (larger artists A and implies greater weight on indirect influence). This can be Sum over the destination song sets of each artist Sd , written in equivalent form as • ai collapsing the appropriate columns of IS. 2 2 k k IK = A + A + ... + A + ..., (3) Sum over the source song set of each artist Ss , col- • ai lapsing the appropriate rows of I . where we can see that the influence is a weighted sum of S the powers of the adjacency matrix [14]. When the values The result of the process produces an artist-level influence of A are zero or one, the powers of the adjacency matrix matrix IA which is directly derived from the song-level mu- 2 The song network is exactly acyclic and the artist network is nearly sical material, and is done so via linear combinations of the acyclic. song-level influence matrix. The process can be duplicated Ak have elements representing the number of sample chains of corresponding length k capturing various levels of indi- rect influence. For stability, 1/ must be greater than the largest eigenvalue of A and for large networks, (2) becomes increasingly difficult to invert. Typically, only the overall in- fluence rank is desired and is computed iteratively in a fash- ion to avoid a large memory footprint and matrix inverse required for IK . For our purposes, it is desirable to have both the entire in- Ak have elements representing the number of sample chains Figure 5. Cumulative In-degree Distribution P (k) of the fluence matrix and overall rank. Given IK , we can view the of corresponding length k capturing various levels of indi- Sample-Based Song Network (log-log scale). column of a node to find who influenced the node, or view rect influence. For stability, 1/ must be greater than the the row of the node to find who the node influenced [15]. largest eigenvalue of A and for large networks, (2) becomes Summing the columns of the influence matrix produces a increasingly difficult to invert. Typically, only the overall in- any of the very popular samples were to be removed, large ranking of the most influential nodes, while summing the portions of sample-based music would cease to exist (orfluence at rank is desired and is computed iteratively in a fash- ion to avoidrows a results large memory in a ranking footprint of the and most matrix influenced inverse nodes. Such least be altered). analysis is nicely suited for musicological analysis and mo- required for IK . tivates further improvements discussed below. 3.2 Influence Measures For our purposes, it is desirable to have both the entire in- Figure 5. Cumulative In-degree Distribution P (k) of the fluence matrix and overall rank. Given IK , we can view the Sample-BasedTo analyze Song and Network rank (log-log influence scale). within each network, fourcolumn of3.3 a node Collapse-and-Sum to find who influenced Influence the node, Rank or view closely related measures are commonly used: degree cen-the row ofFor the the node given to dataset, find who we the would node like influenced to understand [15]. and ana- trality, eigenvector centrality, Katz centrality, and PageR-Summing the columns of the influence matrix produces a any of the very popular samples were to be removed, large lyze song, artist, and genre influence individually, as well as ank. Degree centrality does not capture any indirect formranking of of the most influential nodes, while summing the portions of sample-based music would cease to exist (or at how each network relates to one another. To do so, individ- influence (as in the case of sample chains), motivating alter-rows results in a ranking of the most influenced nodes. Such least be altered). ual networks can be constructed for song, artist, and genre native methods. Eigenvector centrality extends degree cen-analysis is nicely suited for musicological analysis and mo- tivates furthernetworks improvements with influence discussed matrices below. and rank computed via (2) 3.2 Influencetralitypled source by Measures weighting material), the importance showing a of rough neighboring outline nodes of the to rise or (3). Building separate graphs, however, has several draw- and fall of soul/funk/disco and the rise of hip-hop/R&B. allow for indirect influence, but has limited application for backs. Most notably, there is no straightforward mechanism To analyzeThe and general rank shape influence of2 within the destination each network, material four (lower)3.3 out- Collapse-and-Sum Influence Rank acyclic networks [13]. Katz centrality and PageRank ap- to relate the influence matrices of each network together ap- closelypropriately relatedlines the measures increased modify are eigenvector commonly popularity centrality. used: of sampling degree Both cen- also and/or provide listenerFor the given dataset, we would like to understand and ana- trality, eigenvector centrality, Katz centrality, and PageR- propriately. Furthermore, we would like to model the influ- atrends mechanism within to the capture WhoSampled.com indirect influence user between community. nodes,lyze In- song, artist, and genre influence individually, as well as ank. Degree centrality does not capture any indirect form of ence propagation on the song-level topology and then derive computeterestingly, an overallthere is influence a sharp decreaserank among in sample-based each node, andhow mu- each network relates to one another. To do so, individ- influence (as in the case of sample chains), motivating alter- artist and genre influence measures, as the compositional act observesic centered the influence around 2003. of one While node further to another. investigation PageRank,ual is re- networks can be constructed for song, artist, and genre native methods.quired, itEigenvector interesting centrality to note extends that this degree event cen- directlynetworks coin- of with sampling influence is matrices presumably and based rank computed on the musical via (2) material it- trality byhowever, weighting down-weights the importance influence of neighboring created nodes by a to destination self, rather than artist or genre connections. nodecides that with samples the Recording more than Industry once, or Association in the case of of America artistor (3). Building separate graphs, however, has several draw- allow for(RIAA) indirect first influence, litigation but has on limited Internet application piracy and for musicbacks. copy- MostTo notably, address there this is no issue, straightforward a single influence mechanism matrix is con- nodes, down-weights2 influence from artists with lengthy ca- acyclic networksright infringement [13]. Katz [11]. centrality Such and legal PageRank policy would ap- haveto cre- relate thestructed influence using matrices the song-level of each network network together (see Section ap- 3.1) and reers. While this is desirable in numerous other contexts propriatelyated modify a more eigenvector conservative centrality. and limitedBoth also view provide of the musicalpropriately.is used Furthermore, to create we the would artist like and to genre model influence the influ- matrices, re- such as web search, we wish to equally weight each instance a mechanismpractice to capture of sampling, indirect thus influence significantly between affecting nodes, the music-ence propagationsulting in on the the proposed song-level relational topologycollapse-and-sum and then derive approach. computeof an sampling overall andinfluence restrict rank ourselves among to each Katz node, centrality. and making process. artist and genreTo construct influence the measures, artist-level as the influence compositional matrix actIA from the observe the influence of one node toI another. PageRank, The Katz influence matrix K is defined via of samplingsong-level is presumably network, based the on song-level the musical network material is it- first used to Figure 4. Distribution of Unique Samples Over Time. Allhowever, down-weights influence created by a destination 1 self, rathercompute than artist the or song genre influence connections. matrix IS. Given IS, we then samples (blue, solid), soul/funk/disco (magenta, triangles),node that samples more3. thanIK NETWORK=( once,I or inA) the ANALYSIS caseI of artist (2) To address this issue, a single influence matrix isI con- hip-hop/R&B (red, plus), electronic dance (green, circle),nodes, down-weights influence from artists with lengthy ca- compute a derived artist influence matrix A, knowing the A discussion of network analysis, influence measures,structed and using the song-level network (see SectionSs 3.1)Sd and rock pop (black, x) are shown across time for source mate- where I is an identity matrix, A is the adjacency matrix as source and destination song sets ai and ai belonging to reers. Whilerank is this presented is desirable with in the numerous motivation other of contexts observing howis used in- to create the artist and genre influence matrices, re- rial (upper) and destination material (lower). before, and is a decay factor which scales the indirect in- each artist ai. To do so, we take each artist ai in the set of such as webdividual search, songs, we wish artists, to equallyKatz and weight genresInfluence each influence instance one another.sulting in the proposed relational collapse-and-sum approach. of samplingfluence and allowed restrict ourselves to propagate to Katz though centrality. the network (larger artists A and Complex network analysis provides significant tools forTo such construct the artist-level influence matrix IA from the The Katzimplies influence greater matrix weightIK onis indirect defined via influence). This can bek ples uniformly from each source genre g , the entropy will characterization• Weighted sum and of begins the powers with theof adjacency formulation matrix of A asong-level net-have elements network,Sum representing the over song-level the destination the network number song is of first sets sample used of each chains to artist Sd , j written in equivalent form as • ai work graph. A graph G 1=(N,E) is defined by aof setcompute corresponding of the song lengthinfluencek capturing matrix IS. various Given I levelsS, we then of indi- be maximized. The genre entropy for the top five destina- I =(I A) I (2) collapsing the appropriate columns of IS. K rect influence. For stability, 1/ must be greater than the tion genres is shown in Table 1. The source samples used in nodes N and edges E 2or equivalently2 k ank adjacency matrixcompute a derived artist influence matrix IA, knowing the IK = A + A + ... + A + ..., (3)largest eigenvalue of A and for largeSs networks,Sd (2) becomesSs where IAis. an A identity weighted matrix, directedA is the edge adjacency between matrix node asi and j sourceis de- and destinationSum over song the sets sourceai and song setai belonging of each artist to ai , col- k k • Genre Entropy (bits) fined• via If A == 0 wor 1,and A 0haveotherwise,A elements have elements where representing representingw representingis the theincreasinglyeach cor- number artist thea numberofi. difficult sample Tolapsing do of so, to chains sample the invert. we appropriate take Typically, chains each artist rows onlya ofi inI the the. overall set of in- before, andwhere is we a decay canij see factor thatij which the influence scales the is indirect a weighted in-ij sum of S electronic dance (E) 2.83 number of sampleof chains correspondingof correspondingof corresponding length lengthk lengthcapturing fluenceartists k capturing variousA rankand is levels various desired of levels and indi- is computedof indi- iteratively in a fash- rock pop (P) 2.745 fluenceresponding allowed to propagate weight. though For unweighted the network networks, (larger all weights the powers [Katz of 1953] the adjacency rect influence. matrix [14]. For When stability, the values1/ion must to avoid beThe greater a result large than of memory the the process footprint produces and an matrix artist-level inverse influence hip-hop/R&B (H) 2.356 impliesare greater either weight zero on or indirect one. influence).rect influence. This can For be stability, 1/ must be greater than the d of A are zero or one, the powers of the adjacency matrixrequiredSum for overIK . the destination song sets of each artist S , soul/funk/disco (F) 2.242 largest eigenvalue of A and forA large networks,matrix (2)IA becomeswhich is directly derived from the song-levelai mu- reggae (R) 2.129 written in equivalent form as largest eigenvalue of and for• large networks, (2) becomes • Captures sampleincreasingly chains in a straightforward difficult to invert. manner Typically, Forcollapsing our only purposes, the the overall appropriate it is desirablein- columns to have of I bothS. the entire in- 3.12 The Degree song network Distributions is exactly acyclicincreasingly and the artist difficult network is to nearly invert. Typically,sical material, only the and overall is done in- so via linear combinations of the Figure 5. Cumulative In-degree2 2 Distributionfluencek rankk P is( desiredk) of the and is computedfluence matrixiteratively and in overall a fash- rank. Given IK , we can view the acyclic.IK = A + A + ... + A + ..., (3) song-level influence matrix. The processs can be duplicated Sample-Based Song Network (log-log scale).fluence rank is desired andcolumn is computedSum of a over node the iteratively to source find who song in a influenced set fash- of each the artist node,Sa , or col- view Table 1. Genre Entropy For Popular Destination Genres. For a first general measureion to of avoid how a the large music memory sample-based footprint• and matrix inverse i L. Katz: “A New Status Index Derived From Sociometricion Analysis,” to avoid Psychometrika a 18, large 1953. memorythe rowlapsing footprint of the the node appropriate and to matrix find rows who inverse of theIS node. influenced [15]. where wenetworks can see are that constructed, the influencerequired degree is a for weightedI centralityK . sum can of be used to required for IK . Summing the columns of the influence matrix produces a any ofthe the powers verymeasure ofpopular the the adjacency samples influence matrix were fromFor to [14]. each be our removed, When node purposes, (song, the valueslarge it isartist, desirable or genre) to have both the entire in- reggae music are the most homogeneous, while electronic For our purposes, it isrankingThe desirable result of toof the have the most process both influential the produces entire nodes, an in- artist-level while summing influence the Figure 5. Cumulative In-degree Distributionof A areof zeroP a( network.k or) of one, the the For powers afluence given of the node, matrix adjacency the and in- overall matrix and rank. out-degree Given IK , we can view the dance music is the most heterogeneous. A closer lookportions at of sample-based music would cease to exist (or at rowsmatrix resultsIA which in a is ranking directly of derived the most from influenced the song-level nodes. mu- Such Sample-BasedFigure 5. Cumulative Song Network In-degree (log-logleast be Distribution scale). altered).centralityP ( isk) definedof the ascolumn the respectivefluence of a node matrix in to or find and out who edge overall influenced counts rank. Given the node,IK , or we view can view the electronic music reveals a near equal split of source ma- 2 analysissical material, is nicely and suited is done for so musicological via linear combinations analysis of and the mo- Sample-Based Song Network (log-logThe scale). songnormalized network is byexactly the acyclic totalthe and number row thecolumn artist of of the network nodes of node a is node nearlyN to find. to The find who in- who the and node influenced influenced the node, [15]. or view terial from hip-hop/R&B, electronic music, rock/pop, andacyclic. | | tivatessong-level further influence improvements matrix. The discussed process canbelow. be duplicated 3.2 Influenceout-degree Measures distributionSumming is thenthe the row the proportion columns of the node of of degree the to influence findk = who matrix the node produces influenced a [15]. soul/funk/disco with aany slight of preference the very popular towards samples the latter. were to be removed, large ranking of the most influential nodes, while summing the portions of sample-based musicTo would analyze cease and1, to2, existrank3,... (ornodes influence at and within can be eachusedSumming to network, characterize the four columns the network. of3.3 the Collapse-and-Sum influence matrix Influence produces Rank a Such evidence suggestsany differences of the very in the popular creative samples process were to be removed, large rows results in a ranking of the most influenced nodes. Such least be altered). Power-law distributions rankingf(k) ofk theare most an important influential nodes, while summing the of sampling between genres.portions of sample-based musicclosely would related cease measures to exist are (or commonly at analysis used: is nicely⇥ degree suited cen- for musicologicalFor the given analysis dataset, and we mo- would like to understand and ana- trality, eigenvectorfamily of centrality, distributions. Katz Suchcentrality,rows distributions results and PageR- in promote a ranking the of con- the most influenced nodes. Such least be altered). tivates further improvements discussedlyze song, below. artist, and genre influence individually, as well as 3.2 Influence Measures ank. Degreecept centrality of preferential does not capture attachment anyanalysis indirect and are is form nicely referred of suited to as for scale- musicological analysis and mo- 2.2 Time-Based Trends how each network relates to one another. To do so, individ- To analyze and rank influenceinfluence within each (asfree. in network, the To case test four of the sample hypothesis chains),3.3 Collapse-and-Sumtivates that motivating musical further alter- sampling improvements Influence followsual Rank networks discussed can below. be constructed for song, artist, and genre Initial observations of time-based3.2 Influence trends Measures are found whennative we methods.a power-law, Eigenvector we centrality can construct extends an unweighted degree cen- acyclic song closely related measures are commonly used: degree cen- For the given dataset, we wouldnetworks like to understand with influence and ana- matrices and rank computed via (2) view the proportion oftrality, samplesTo analyze eigenvector per year and within rank centrality, influence each genre. Katztrality within centrality, by weighting eachnetwork and network, the PageR- using importance unique four songs of neighboring3.3 as nodes Collapse-and-Sum and nodes sampling to instancesor Influence (3). Building Rank separate graphs, however, has several draw- allow for indirect influence, but haslyze limited song, application artist, and genre for influence individually, as well as The trends can be viewedank.closely for Degree both related centrality unique measures source does not and are capture des- commonly any indirectto used: create form degree directed of cen- edges from destination to source.backs. The Most notably, there is no straightforward mechanism acyclic networks [13]. 2 Katz centralityhow eachFor and networkthe PageRank given relates dataset, ap- to one we another. would like To doto understand so, individ- and ana- tination material normalizedinfluencetrality, by eigenvector (asthe in total the instances case centrality, of sample of sam- Katz chains), centrality, motivatingin-degree and alter- distribution PageR- ual can networks then be computedcan be constructed and testedto for relate to song, the artist, influence and matrices genre of each network together ap- pling as shown in Fig. 4.native Plotting methods. unique Eigenvector instances of centrality sourcepropriately extends modifyfollow degree eigenvector a power-law cen- centrality. distributionlyze Both or song, also not. provide artist, Using and methods genrepropriately. influence de- Furthermore, individually, we as would well as like to model the influ- ank. Degree centrality does nota mechanism capture any to indirect capture form indirect of influencenetworks between with influence nodes, matrices and rank computed via (2) and destination materialtrality indicates by weighting general trends the importance within each of neighboringscribed nodes in [12], to we find thathow the eachnetwork network is consistent relatesence with to one propagation another. on To the do song-level so, individ- topology and then derive influence (as in the case of samplecompute chains), an overall motivating influence alter- rankor among (3). Building each node, separate and graphs, however, has several draw- genre and eliminates theallow effect for of indirect a single influence, popular but sample has limitedthe application hypothesis for (p-valuebacks.= .16ual Mostfor networksk notably,3 and can there be=2 is constructed no.72artist straightforward) and and for genre song, influence mechanism artist, measures, and genre as the compositional act native methods. Eigenvector2 observe centrality the extends influence degree of one cen- node to another. PageRank, swaying the proportionsacyclic (as is networks the case without [13]. Katz uniqueness centrality andshow PageRank the cumulative ap- in-degreenetworks distribution with influencein Fig. 5. matricesof sampling and is rank presumably computed based via on (2) the musical material it- trality by weighting the importancehowever, of down-weights neighboring nodes influence to to created relate by the a influence destination matrices of each network together ap- enforced). propriately modify eigenvector centrality. BothIn also terms provide of networkspropriately. basedor on (3). musical Furthermore, Building sampling, separate we would aself, scale- graphs, like rather however, to than model artist the has or influ- several genre connections. draw- aallow mechanism for indirect to capture influence, indirectnode but influence has that limited samples between application more nodes, than for once, or in the case of artist The general shape of the source material plot (upper) out- free network suggestsence the propagation ideabacks. that Most very on notably, the popular song-level there samples isTo topology no address straightforward and this then issue, derive mechanism a single influence matrix is con- computeacyclic an networks overall [13]. influence2 Katz ranknodes, centrality among down-weights each and node, PageRank influence and ap- from artists with lengthy ca- structed using the song-level network (see Section 3.1) and lines the musical time frame of each genre (in terms of sam- will only continue to increaseartist andto relate in genre popularity. the influence influence In measures, addition, matrices as if the of each compositional network together act ap- observepropriately the influence modify eigenvector of one nodereers. centrality. to another.While Boththis PageRank, is also desirable provide in numerous other contexts is used to create the artist and genre influence matrices, re- such as web search, we wish to equallyof sampling weightpropriately. each is presumably instance Furthermore, based on we the would musical like material to model it- the influ- however,a mechanism down-weights to capture influence indirect created influence by a between destination nodes, sulting in the proposed relational collapse-and-sum approach. of sampling and restrict ourselves toself, Katz ratherence centrality. propagationthan artist or ongenre the connections. song-level topology and then derive nodecompute that samples an overall more influence than once, rank or in among the case each of node, artist and To address this issue, a singleTo influence construct matrix the artist-level is con- influence matrix IA from the nodes, down-weights influence fromThe artists Katz with influence lengthy matrix ca- IK is definedartist via and genre influence measures, as the compositional act observe the influence of one node to another. PageRank, structed using the song-level networksong-level (see network, Section 3.1) the and song-level network is first used to reers. While this is desirable in numerous other contexts 1 of sampling is presumablycompute based the on the song musical influence material matrix it-IS. Given IS, we then however, down-weights influence created byI aK destination=(I A)is usedI to create the artist(2) and genre influence matrices, re- such as web search, we wish to equally weight each instance sulting self, in the rather proposed than relational artist orcompute genrecollapse-and-sum connections. a derivedapproach. artist influence matrix IA, knowing the ofnode sampling that samplesand restrict more ourselves than once, to Katz or centrality. in the case of artist source and destination song sets Ss and Sd belonging to where I is an identity matrix, A isTo the construct adjacencyTo address the matrix artist-level this as issue, influence a single matrix influenceIA from matrix the is con-ai ai nodes, down-weights influenceI from artists with lengthy ca- The Katz influence matrix Kbefore,is defined and via is a decay factor whichsong-level scalesstructed the network, indirect using the the in- song-level song-leveleach network artist networkai is. (seeTo first do Section used so, we to 3.1) take eachand artist ai in the set of reers. While this is desirable in numerous other contexts artists A and fluence1 allowed to propagate thoughcompute the network the song (larger influence matrix IS. Given IS, we then I =(I A) I (2) is used to create the artist and genre influence matrices, re- such as web search,K we wishimplies to equally greater weight weight each on instance indirect influence). This can be computesulting a derived in the artist proposed influence relational matrixcollapse-and-sumIA, knowing the approach. Sd s Sum overd the destination song sets of each artist ai , of sampling and restrict ourselveswritten to in Katz equivalent centrality. form as source and destination song sets Sa• and Sa belonging to where I is an identity matrix, A is the adjacency matrix as To construct the artist-leveli influencecollapsingi matrix the appropriateIA from columns the of IS. The Katz influence matrix I is defined via each artist a . To do so, we take each artist a in the set of before, and is a decay factor whichK scales the indirect2 in- 2 k song-levelk i network, the song-level networki is first used to IK = A + A + ... + A + ..., (3) s fluence allowed to propagate though the network (larger artists A and Sum over the source song set of each artist Sa , col- 1 compute the song influence• matrix IS. Given IS, we then i I =(I A) I (2) lapsing the appropriate rows of I . implies greater weightK on indirectwhere influence). we can see This that can the be influence is a weighted sum of d S computeSum over a the derived destination artist song influence sets of matrix each artistIA,S knowingai , the written in equivalent form as • s d the powers of the adjacency matrix [14].collapsing When the the values appropriateThe columns resultS of ofIS the. processS produces an artist-level influence where I is an identity matrix, A is the adjacency matrix as source and destination song sets ai and ai belonging to 2 2 of A arek zerok or one, the powers of the adjacency matrix matrix I which is directly derived from the song-level mu- IK = A + A + ... + A + ..., (3) each artist ai. To do so, we takeA each artistsai in the set of before, and is a decay factor which scales the indirect in- Sum over the source song set of each artist Sa , col- 2 • sical material, and is donei so via linear combinations of the fluence allowed to propagate thoughThe song the network network is exactly (larger acyclic and the artistartistslapsing networkA theand is appropriate nearly rows of I . where we can see that the influenceacyclic. is a weighted sum of song-levelS influence matrix. The process can be duplicated theimplies powers greater of the weightadjacency on matrix indirect [14]. influence). When the This values can be d The result ofSum the process over the produces destination an artist-level song sets of influence each artist Sai , writtenA in equivalent form as • of are zero or one, the powers of the adjacency matrix matrix IA whichcollapsing is directly the derived appropriate from columns the song-level of IS mu-. 2 The song network is exactly acyclic2 2 and the artistk networkk is nearly sical material, and is done so via linear combinations of the IK = A + A + ... + A + ..., (3) s acyclic. song-level influenceSum over matrix. the source The process song set can of be each duplicated artist S , col- • ai lapsing the appropriate rows of I . where we can see that the influence is a weighted sum of S the powers of the adjacency matrix [14]. When the values The result of the process produces an artist-level influence of A are zero or one, the powers of the adjacency matrix matrix IA which is directly derived from the song-level mu- 2 The song network is exactly acyclic and the artist network is nearly sical material, and is done so via linear combinations of the acyclic. song-level influence matrix. The process can be duplicated Ak have elements representing the number of sample chains of corresponding length k capturing various levels of indi- Ak have elements representing the number of sample chains Ak have elementsrect representingA influence.k have elements the For number stability, representing of1 sample/ must the chains number be greater of sample than the chains of corresponding length k capturing various levels of indi- of correspondinglargest lengthof corresponding eigenvaluek capturing of A various lengthand fork levelscapturing large of networks, indi- various (2) levels becomes of indi- rect influence.kkincreasingly Forrect stability, influence. difficult1/ mustk For to invert. stability, be greater Typically,1/ than must only the be the greater overall than in- the Ak have elementsAA havehave representing elements elements the representing representingA numberhave elements of the the sample number number representing chains of of sample sample the chains chains number of sample chains rect influence. 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To do so, individ- closely related measures are commonly used: degree cen- influenceclosely (asinfluence ininfluence the related case (as (as measures of in in sample the the case case areinfluence chains), commonly of of sample sample motivating (as in chains), chains), used: the case alter- degree motivating motivating of sample cen- or alter- alter- chains), (3). 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To doeach so, artist we takeai. each To do artist so,a wei in take the each set of artist ai in thed set of 4 song-levelcomputecompute network, a a derived derived the song-level artist artistcompute influence influence networkI a derived matrix matrix is first artistIIAA used,, influence knowing knowing to matrix the the IA, knowing the nodes, down-weights influenceand song-to-genre from artists influence. with lengthy ca- Marley Marl (0.29) George Clinton (0.25) Fab 5 Freddy (0.23) compute a derived artistSum influence over the matrix destinationA, knowing song sets the of each artist Sai , structed using the song-level network (seewritten Section in equivalent 3.1) form and as artists A and •artists A and s d ss dd s d George Clinton (0.28) Marley Marl (0.25) fluenceGeorge allowed Clinton (0.22) to propagatefluence allowed though to the propagate network1 though (larger the network (largercomputesourcesource the song and and destinationinfluence destinationSsource matrix song song andI setsS setsS. destination GivenSSaa andandIS,SS wea songa belongingbelonging then sets S to toand S belonging to Given the linear relationship from one network to the where I is anwherewhere identityA II isis matrix, an anI identity identity=(A Iiswhere matrix, the matrix,A adjacencyI)isAA anisisI identity the the matrix adjacency adjacency matrix, as matrix(2) matrixA sourceis the as as adjacency and destination matrixcollapsing song as sets theai appropriateand ai belonging columnsii to ofii IS. ai ai reers. 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This can be collapsinglapsing the the appropriate appropriatelapsing rows columns the of appropriateIS. of IS. rows of IS. d AA 1 A 1 where we can seeof thatwhereare the zero we influence can or one, see is thethat a weighted powers the influence of sum the isof adjacency a weighted matrix sum ofSum over theI destination song sets of each artist Sai , Secondly, by solely computing the influence on the acyclic, written in equivalent2 2 form as 22k 22k kk kk 2 2 k k• matrix A which is directly derived from the song-level mu- B1 IIKK ==1AA ++ AAB1 ++I ...... =++AAA+ ++0 A ...,...,… + ... +(3)(3) A + ..., (3) ss s 1 computeTable the 3. Artist song Sample-Based influence Influence matrix RankIISK. for= GivenA=0+ .0IAS,+ we... + then A +K..., (3) collapsingSumSum the over over appropriate the the source source columns song song set set of ofI ofSs. each each artist artist SS ,, col- col- S I =(unweightedI A song-level) I network, we can compute IS from a the powers of the2 adjacencythe powers matrix of the [14]. adjacency When matrix the values [14]. 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[14]. adjacency is values and nearly When When the artist the the matrix network values values [14]. is nearly WhenlapsingTheThe the result result values the appropriate of of the the process processThe rows result produces produces of S of. the an an process artist-level artist-level produces influence influence an artist-level influence ing that the powers of the adjacency matrix A , k =1, 2, 3... ence of an individual artist by looking atwhere the correspond- we can see that the influence is a weighted sum of The result of the process produces an artist-level influence each artist a . To do so, we takeofacyclic.A eachare zeroof artistof orAA one,areareacyclic.a zero the zeroin powers or or the one, one,of set of theA the theare of powers powers adjacency zero of of or the the one, matrix adjacency adjacency the powers matrix matrixsong-level of the adjacency influence matrixsong-level matrix. The influence process matrix. can be The duplicated process can be duplicated before, and is a decaywill factor go to zero which when scalesk is greater the than indirect the maximum in- sample ing row ori column. Table 4, for example,the names powers the of top thei adjacency matrix [14]. When the values matrixTheIA which resultmatrixmatrix is of directly theIIAA whichwhich process derived is is produces directly directlymatrix from derivedI the derived anA which artist-levelsong-level from from is directly the the mu- influence song-level song-level derived mu- mu- from the song-level mu- 2 of A are22 zero or one, the powers2 of the adjacency matrix sicalsical material, material, and and is issical done done material, so so via via linear linear and is combinations combinations done so via of linear of the the combinations of the fluence allowed to propagatechain length though of the the network. network With sparse (larger matrix represen- artistsfiveA influentialand and influenced artistsThe of Jay-Z. song network Finally,TheThe is song song exactly we network network acyclic is is and exactly exactlyThe the artist acyclic acyclicsong network network and and the the is is artist artist nearly exactly network network acyclic is issical and nearly nearly the material,matrix artist networkIA andwhich is is done nearly is directly so via linear derived combinations from the song-level of the mu- tations, this modification can greatly reduced computation, acyclic. acyclic.acyclic. acyclic. song-levelsong-level influence influencesong-level matrix. matrix. The The influence process process matrix. can can be be duplicated duplicated The process can be duplicated 2 The song network is exactly acyclic and the artist network is nearly song-levelsical influence material, matrix.and is done The so process via linear can combinations be duplicated of the implies greater weight on indirect influence). This can be ( =0.2) ( =0.2) increase the allowable in-memory network size, and addi- Influential Influenced acyclic. d song-level influence matrix. The process can be duplicated Sum overThe Notorious the B.I.G. destination (0.97) Girl Talk song (1.0) sets of each artist Sai , written in equivalent formtionally as releases any restriction on , allowing the user to • Dr. Dre (0.91) Lil Wayne (0.80) choose any suitable weighting function. Application of this collapsingPuff Daddy the (0.53) appropriateThe Game columns (0.53) of IS. Nas (0.5) DJ Premier (0.40) approach2 2 is found belowk ink Section 4. James Brown (0.42) Linkin Park (0.39) IK = A + A + ... + A + ..., (3) Sum over the source song set of each artist Ss , col- • ai 4. APPLICATION lapsing the appropriate rows of I . where we can see that the influence is a weighted sum of Table 4. Top Influential and Influenced ArtistsS of Jay-Z . Three levels of influence analysis and rank are computed for the powers of the adjacencysong, artist, matrix and genre [14]. representations, When the providing values a small-to- The resultcan also of compute the process the relative produces proportion of an influence artist-level cre- influence large inspection of the data. Various values of are used to ated by each song within an artist’s overall influence. The of A are zero or one, the powers of the adjacency matrix matrix IA which is directly derived from the song-level mu- compare direct to indirect influence. For this purpose, (3) is top three most influential songs of James Brown, for exam- 1 2 k 1 k 2 The song network is exactlyrescaled acyclic to IK and= A the+ artistA + network... + isA nearly+ ..., allowing sicalple, material, include “Funky and is Drummer” done so (14%), via linear “Think (About combinations It)” of the acyclic. =0to only account for direct sampling, =1to equally song-levelby Lyn Collins influence and produced matrix. by The James process Brown (9%), can and be duplicated account for direct and all indirect sampling, and values be- “Funky President” (7.5%). Similar measures can be com- tween zero and one to preferentially weight direct samples, puted to indicate whether an artist gets more credit as a pro- but also account for indirect sampling. ducer or performer.

4.1 Song Influence 4.3 Genre Influence The song-level influence matrix I is computed from the S The song-level influence matrix can further be reduced to a song network described in Section 3.1. The most influential genre-based influence IG. The most influential genres found songs are found in Table 2. We can observe the presence of are: soul/funk/disco, hip-hop/R&B, rock/pop, jazz/blues, and many popular samples including “Change the Beat” by Fab electronic dance, while the top influenced genres are hip- 5 Freddy and the “Amen” break by The Winstons. It is par- hip/R&B, electronic dance, rock/pop, other, and reggae (for ticularly interesting to note that, for the “Amen” break, as all values of ). Alternatively, the top songs and artist for increases, the credit of influence intuitively moves from The each genre can also be computed (omitted due to space con- Winstons to The Impressions, and finally to Jester Hairston. straints). This is a result of a sample chain between material origi- nating from Jester Hairston, that was first sampled by The Impressions, and then massively popularized by The Win- 5. CONCLUSIONS stons. An analysis of music influence and rank of sample-based music is presented using the WhoSampled.com dataset. Gen- 4.2 Artist Influence eral genre and time-based trends are found, identifying where Starting with the song-level influence, we can collapse IS and when the sampling source material is coming from as to form an artist-based influence matrix IA. Table 3 shows well as differences in how various genres are sampling oth- the top influential artists. 3 We can also inspect the influ- ers. Network graphs are employed to both understand gen- 3 Entries with Fab 5 Freddy also include producers Material and Bee- eral trends of sampling behavior, but to also find influence side. All three artists achieved high influence from “Change the Beat”. rank over songs, artists, and genre. A method of influence Ak have elementsAk have representing elementsAk the representinghave number elements of thesample representing number chains of sample the number chains of sample chains of correspondingof corresponding length k capturingof corresponding length variousk capturing levels length various ofk indi-capturing levels of various indi- levels of indi- rect influence.rect For influence. stability, rect1 For/ influence. stability,must be greater1 For/ must stability, than be the greater1/ must than be the greater than the largest eigenvaluelargest of A eigenvalueand forlargest large of A eigenvalue networks,and for large (2) of A becomes networks,and for large (2) becomes networks, (2) becomes increasingly difficultincreasingly to invert. difficultincreasingly Typically, to invert. only difficult Typically, the overall to invert. only in- Typically, the overall only in- the overall in- fluence rank isfluence desired rank and isfluence computeddesired rank and iteratively is is computed desired in and a iteratively fash- is computed in a iterativelyfash- in a fash- ion to avoid aion large to avoid memory aion large footprint to memory avoid and a large footprintmatrix memory inverse and matrix footprint inverse and matrix inverse required for IKrequired. for IKrequired. for IK . 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(0.27) (0.25) Public TableRick Enemy Rubin (0.23) 4, (0.22) forRussell example,Kool Simmons & the (0.19) Gang names (0.19) the top nodes, down-weightsnodes, down-weights influencenodes, from influence down-weights artists with from lengthy influence artists ca- with from lengthy artistsother, ca- with we can lengthy compute the ca- relative proportions of influence Rick Rubin (0.25) Rick Rubin (0.22) Kool & the Gang (0.19) Public Enemy (0.27) Public Enemy (0.23) Russell Simmons (0.19) DJ Premier (0.25) Fab 5 Freddy (0.22) Marley Marl (0.18) other, we can compute the relative proportionschain length of influence of thebetweenstructed network. networks. using Withstructed theAs sparse a song-level result, matrix using we can represen- thestructed network analyze song-level using how (see in- Section networkthefive song-level influentialDJ 3.1) Premier (see and (0.25) Section network and influencedFab 3.1) 5 Freddy (see and (0.22) Section artistsMarley of 3.1)Marl Jay-Z. 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(0.5) to2.(middle), is2 (middle), first network and used and =1 to=1.0 is(right).DJ.0 first Premier(right). used (0.40) to unweighted song-level network, we canapproach compute I isS from found a short, belowshort, finite in finite Section linear linear combination combination 4. of of the the powers powers of of the adja- adja- (left), =0.2 (middle), and =1.0 (right). destination Jamesdestination Brown (0.42) destination Linkin Park (0.39) 1 1 1 computecency matrix the without songcompute any influence iterative the procedure song matrixcompute influence andI byS the. know- Given song matrixI influenceS,IS we. Given then matrixIS,I we. then Given I , we then short, finite linear combination of the powers of the adja- cency matrix without any iterative procedure and by know-A B1 B2 C A B1 B2 C S A B1 B2 C S IK =(I AI)K=(II AI)K =(II (2)A) I (2) (2) kk ing that the powers of the adjacency matrix A , k =1A , 2, 31 ... 0 enceA of an1 individual.5 artistA by1 looking1 at the correspond- cency matrix without any iterative procedure and by know- ingcompute that the powers a derived ofcompute the adjacency artist a influence matrixderivedcomputeA , artistk matrix=1 a, influence2 derived, 3...IA, knowing artistence matrix of influence an theIA individual, knowing matrix artist the byIA looking, knowing at the correspond- the k 4.will APPLICATION go to zero when k is greater than the maximumB1 sample 1 B1 1 B1 1 ing that the powers of the adjacency matrix A , k =1, 2, 3... will goence to ofzero an when individualk is greater artist by than looking the maximum at thes correspond- sample d ingings row row or or column. column.d Tables Table 4, for 4, for example,d example, names names the top the top B2 1Table 4B2 . Top Influential1 B2 and Influenced1 Artists of Jay-Z . source source

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(0.97) Girl Talk (1.0) fluence allowedfluence to propagate allowedfluence though to propagate allowed the network though to propagate (larger the network though (larger the network Influential (larger( =0.2) Influenced ( =0.2) Dr. Dre (0.91) Lil Wayne (0.80) increase the allowable in-memory networklarge size, inspection and addi- oftionally the data. releases Various any restriction values of on ,are allowing used the to• userView toColumn—“Whoated by each influencedDr. song Drethe (0.91)given within song” an artist’sLil Wayne overall (0.80) influence. The choose any suitableThe Notorious weighting B.I.G. (0.97) function.Girl Talk Application (1.0) of this Puff Daddy (0.53) The Game (0.53) choose any suitable weighting function. 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APPLICATION Table 4 I = A + I A=+A... ++ IA =++...... ,Aaccount++ AA for(3)++ direct...,... + andThreeA all(3) levels indirect+ ..., of influence sampling, analysis and and rank values are computed be- for “FunkyTable President”s 4. Top Influential (7.5%).s and Similar Influenced measures Artistss of Jay-Z can be . com- K K 4. APPLICATIONK Sum over the(3)Sum source over song the set sourceSum of each over song artist the set sourceS of each, col- song artist setS of, each col- artist S , col- tween zero and oneThree tosong, preferentiallyTable levels• artist, 4 of. and Top influence genre Influential weight representations, analysis• and direct andInfluenced rank providing samples, are Artists• computed a small-to- of Jay-Z for .putedcan to alsoa indicatei compute whether the relativeai an proportion artist gets of influence moreai credit cre- as a pro- Three levels of influence analysis and rank are computed for song,large artist, inspection and genre of the representations, data.lapsing Various values providing the appropriate of are a small-to-I used to rows of I . but also account for indirectlapsing sampling. the appropriate rows oflapsingS. theducer appropriateatedcan or by also performer.S each compute song rows within the of relativeI anS artist’s. proportion overall influence. of influence The cre- where we canwhere see thatsong, we the can artist, influencewhere see and genre that we representations, is the can a influence weighted see that providing is sum the a a weighted influence of small-to- large sum iscomparecan a inspection weighted of also direct compute of to the indirect sum thedata. relative of influence. Various proportion values For this of of purpose, influenceare used (3) is to cre- topated three by most each influential song within songs an of artist’s James overall Brown, influence. for exam- The 1 2 k 1 k the powers ofthe the powers adjacencylarge inspection of thethe matrix adjacency powers of the [14]. data. of Various When matrix the adjacency values the [14]. of values are When matrix used to thecompare [14]. valuesrescaledated When direct by to eachIK to the= song indirectAThe values+ within influence. resultA an+ ... artist’s+ of For the overall thisA process purpose,+ influence...., allowing (3) produces Theis ple,top an include three artist-level most “Funky influential Drummer” influence songs (14%), of James “Think Brown, (About for It)” exam- 4.1 Song InfluenceThe =0 resultto only of account the1 for process2 direct sampling, producesk The1 k =1 result anto equally artist-level of the process influence produces an artist-level influence A compare direct to indirect influence. For this purpose, (3) is rescaledtop three to IK most= A influential+ A + songs... + of James A Brown,+ ..., allowing for exam-4.3by Genreple, Lyn include Collins Influence “Funky and produced Drummer” by James (14%), Brown “Think (9%), (About and It)” of A are zeroof or one,are the zero powersof orA one,are of the the1 zero2 powers adjacency or one,k of1 the thek matrix powers adjacency ofmatrix matrixtheaccount adjacencyI forA directwhichmatrix and matrix is all directly indirectIA which sampling, derivedmatrix is and directly from valuesI which the be- derived song-level is directly“Funky from President” the mu- derived song-level (7.5%). from Similar mu- the song-level measures can bemu- com- rescaled to IK = A + A + ... + The A song-level+ ..., allowing influence =0ple,to includeonly matrix account “FunkyI foris Drummer” direct computed sampling, (14%), from “Think=1 theto (AboutA equally It)” by Lyn Collins and produced by James Brown (9%), and =0to only account for direct sampling, =1to equally accounttween for zero direct and one andS to all preferentially indirect sampling, weight direct and values samples, be- Theputed song-level to indicate influence whether an matrix artist gets can more further credit as be a pro- reduced to a 2 The song network2 The is exactly song network acyclic2 The is and exactly song the artist network acyclic network isand exactly the is nearly artist acyclic network and thesical is nearlyby artist Lyn material, network Collinssical and and is nearly produced is material, done by so James andsical via Brown is linear material, done (9%), combinations so and and via linear is“Funky done of combinations President” so the via linear (7.5%). of combinations the Similar measures of can the be com- account for direct and all indirect sampling,song network and values described be- tweenbut zero also in Section account and one for to 3.1. indirect preferentially The sampling. most weight influential direct samples, ducer or performer. acyclic. acyclic. “Funky President” (7.5%). Similar measures can be com-genre-basedputed to indicate influence whetherIG. an The artist most gets influential more credit as genres a pro- found tween zeroacyclic. and one to preferentially weightsongs direct are found samples, inbut Tablesong-level also account 2. We influence for can indirectsong-level observe sampling. matrix. the influence presencesong-level The process matrix. of influence can The be process duplicated matrix. can The be process duplicated can be duplicated 4.1puted Song to Influenceindicate whether an artist gets more credit as a pro-are: soul/funk/disco,ducer or performer. hip-hop/R&B, rock/pop, jazz/blues, and but also account for indirect sampling.many popular samplesducer including or performer. “Change the Beat” by Fab 4.3 Genre Influence The song-level influence matrix I is computed from the electronic dance, while the top influenced genres are hip- 5 Freddy and the “Amen”4.1 Song break Influence by The Winstons.S It is par- The4.3 song-level Genre Influence influence matrix can further be reduced to a 4.1 Song Influence song network described in Section 3.1. The most influential hip/R&B, electronic dance, rock/pop, other, and reggae (for 4.3 Genre Influence genre-based influence IG. The most influential genres found ticularly interestingThe tosongs song-level note are that, found influence for in Table the matrix “Amen” 2. We canIS observeis break, computed the as presence from the of all valuesare:The soul/funk/disco, song-level of ). influenceAlternatively, hip-hop/R&B, matrix rock/pop, can the further top jazz/blues, songs be reduced and and to artist a for The song-level influence matrix IS is computed from the songmany network popular described samples in including Section “Change 3.1. The the most Beat” influential by Fab increases, the credit ofThe influence song-level intuitively influence matrix moves can from further The be reduced to a electronicgenre-based dance, influence while theIG. top The influenced most influential genres genres are hip- found song network described in Section 3.1. The most influential songs5 Freddy are found and the in Table “Amen” 2. breakWe can by observe The Winstons. the presence It is par- of each genre can also be computed (omitted due to space con- Winstons to The Impressions,genre-based and influence finallyIG. to The Jester most influential Hairston. genres found hip/R&B,are: soul/funk/disco, electronic dance, hip-hop/R&B, rock/pop, other, rock/pop, and reggae jazz/blues, (for and songs are found in Table 2. We can observe the presence of manyticularly popular interesting samples to including note that, “Change for the “Amen” the Beat” break, by as Fab are: soul/funk/disco, hip-hop/R&B, rock/pop, jazz/blues, andstraints).allelectronic values of dance,). Alternatively, while the top the top influenced songs and genres artist are for hip- many popular samples including “ChangeThis the is Beat” a result by Fab of5 a Freddyincreases, sample and the chain the credit “Amen” between of influence break by material intuitively The Winstons. moves origi- from It is The par- electronic dance, while the top influenced genres are hip- eachhip/R&B, genre can electronic also be computed dance, rock/pop, (omitted other, due to and space reggae con- (for 5 Freddy and the “Amen” break by The Winstons. It is par- ticularlyWinstons interesting to The Impressions, to note that, and for finally the “Amen” to Jester break, Hairston. as nating from Jester Hairston,hip/R&B, that electronic was dance, first sampled rock/pop, other, by The and reggae (for straints).all values of ). Alternatively, the top songs and artist for ticularly interesting to note that, for the “Amen” break, as increases,This is the a result credit of of a influence sample chain intuitively between moves material from origi- The Impressions, and thenall massively values of ). popularized Alternatively, by the top The songs Win- and artist for each genre can also5. be CONCLUSIONS computed (omitted due to space con- increases, the credit of influence intuitively moves from The Winstonsnating tofrom The Jester Impressions, Hairston, and that finally was first to sampled Jester Hairston. by The stons. each genre can also be computed (omitted due to space con- straints). Winstons to The Impressions, and finally to Jester Hairston. Impressions, and then massively popularized by The Win- 5. CONCLUSIONS Thisstraints). is a result of a sample chain between material origi- An analysis of music influence and rank of sample-based stons. This is a result of a sample chain between material origi- nating from Jester Hairston, that was first sampled by The musicAn is analysis presented of music using influence the WhoSampled.com and rank of sample-based dataset. Gen- nating from Jester Hairston, that was4.2 first sampled Artist by Influence The Impressions, and then massively popularized by The Win- music is presented using5. the CONCLUSIONS WhoSampled.com dataset. Gen- 4.2 Artist Influence eral genre and time-based trends are found, identifying where Impressions, and then massively popularized by The Win- stons. 5. CONCLUSIONS eral genre and time-based trends are found, identifying where Starting with the song-level influence, we can collapse IS and whenAn analysis the sampling of music influence source and material rank of is sample-based coming from as stons. Starting with the song-level influence, we can collapse IS and when the sampling source material is coming from as An analysis of music influence and rank of sample-based music is presented using the WhoSampled.com dataset. Gen- to form an artist-based4.2to Artist form influence an Influence artist-based matrix influenceIA. Table matrix 3IA shows. Table 3 shows wellwell as differences as differences in in how how various various genres genres are sampling are sampling oth- oth- music is presented using the WhoSampled.com dataset. Gen- eral genre and time-based trends are found, identifying where 4.2 Artist Influence the top influential artists.the top3 influentialWe can artists. also3 inspectWe can also the inspect influ- the influ- ers.ers. Network Network graphs graphs are are employed employed to both to understand both understand gen- gen- Startingeral with genre the and song-level time-based influence, trends are found, we can identifying collapse whereIS and when the sampling source material is coming from as 3 Entries with Fab 5 Freddy also include producers Material and Bee- eral trends of sampling behavior, but to also find influence Starting with the song-level influence, we3 can collapse IS to formand an when artist-based the sampling influence source matrix materialI . is Table coming 3 shows from aseral trends of sampling behavior, but to also find influence Entries with Fab 5 Freddyside. All also three include artists achieved producers high influence Material from “ChangeA and Bee- the Beat”. well as differences in how various genres are sampling oth- 3 rank over songs, artists, and genre. A method of influence to form an artist-based influence matrixside.IA All. Table three 3 artists shows achievedthe topwell highinfluential as differences influence artists. from in how “ChangeWe various can also the genres Beat”. inspect are sampling the influ- oth-rankers. over Network songs, graphs artists, are and employed genre. to both A method understand of gen- influence the top influential artists. 3 We can also inspect the influ- 3 Entriesers. Network with Fab 5 graphs Freddy are also employed include producers to both Material understand and Bee- gen- eral trends of sampling behavior, but to also find influence 3 Entries with Fab 5 Freddy also include producers Material and Bee- side. Alleral three trends artists of achieved sampling high behavior, influence from but “Change to also thefind Beat”. influence rank over songs, artists, and genre. A method of influence side. All three artists achieved high influence from “Change the Beat”. rank over songs, artists, and genre. A method of influence or further reduced for other relations, such as artist-to-genre James Brown (1.0) James Brown (1.0) James Brown (1.0) or further reduced for other relations, such as artist-to-genre Dr. DreJames (0.34) Brown (1.0) Dr.James Dre Brown (0.28) (1.0) JamesRun-DMC Brown (1.0) (0.25) Dr. Dre (0.34) Dr. Dre (0.28) Run-DMC (0.25) and song-to-genre influence. Marley Marl (0.29) George Clinton (0.25) Fab 5 Freddy (0.23)4 and song-to-genre influence. Marley Marl (0.29) George Clinton (0.25) Fab 5 Freddy (0.23)4 George Clinton (0.28) Marley Marl (0.25) George Clinton (0.22) Given the linearGiven relationship the linear relationship from one from network one network to the to the George Clinton (0.28) Marley Marl (0.25) George Clinton (0.22) PublicPublic Enemy Enemy (0.27) (0.27) PublicPublic Enemy Enemy (0.23) (0.23) RussellRussell Simmons Simmons (0.19) (0.19) other, we can computeother, we thecan compute relative the proportions relative proportions of influence of influence Rick RubinRick Rubin (0.25) (0.25) RickRick Rubin Rubin (0.22) (0.22) KoolKool & the & Gang the Gang (0.19) (0.19) between networks.between As networks. a result, As we a result, can analyze we can analyze how in- how in- DJ PremierDJ Premier (0.25) (0.25) FabFab 5 5 Freddy Freddy (0.22) (0.22) MarleyMarley Marl Marl (0.18) (0.18) MaterialMaterial (0.24) (0.24) MaterialMaterial (0.21) (0.21) RickRick Rubin Rubin (0.17) (0.17) fluential a given song is to an overall artist’s influence or Fab 5 Freddy (0.24) Run-DMC (0.21) Public Enemy (0.17) fluential a given song is to an overall artist’s influence or Fab 5 Freddy (0.24) Run-DMC (0.21) Public Enemy (0.17) how influential an artist is to a genre by taking ratios be- Hank Shocklee (0.23) DJ Premier (0.21) Larry Smith (0.16) Hank Shocklee (0.23) DJ Premier (0.21) Larry Smith (0.16) how influentialtween an artist the respective is to a genre influence by graphs, taking among ratios other be- tasks. or furthertween reduced the for respective other relations, influence such as artist-to-genre graphs, among otherJames Brown tasks. (1.0) James Brown (1.0) James Brown (1.0) Secondly, by solely computing the influenceDr. Dre on (0.34) the acyclic,Dr. Dre (0.28) Run-DMC (0.25) James Brown (1.0) James Brown (1.0)Table 3James. Artist Brown Sample-Based (1.0) Influence Rank for =0.0 orand further song-to-genre reduced for influence. other relations, such as artist-to-genre Marley Marl (0.29) George Clinton (0.25) Fab 5 Freddy (0.23)4 Secondly, by solelyunweighted computing song-level the network, influence we on can theDr. compute Dre acyclic, (0.34) IS fromDr. a Dre (0.28) Run-DMC (0.25) GeorgeJames Brown Clinton (1.0) (0.28) MarleyJames Brown Marl (0.25) (1.0)(left),. ArtistGeorgeJames=0 Brown. Clinton2 Sample-Based(middle), (1.0) (0.22) and =1 Influence.0 (right). Rank for =0.0 orand furtherGiven song-to-genre reducedthe linear for influence. relationship other relations, from such one as network artist-to-genre to the Marley Marl (0.29) GeorgeTable Clinton (0.25) 3 Fab 5 Freddy (0.23)4 unweighted song-levelshort, finite network, linear combination we can compute of the powersPublicDr.I Dre Enemyfrom (0.34) of (0.27) the a adja-PublicDr. Dre Enemy (0.28) (0.23) RussellRun-DMC Simmons (0.25) (0.19) GeorgeS Clinton (0.28) Marley Marl (0.25) George Clinton (0.22) andother,Given song-to-genre we canthe linearcompute influence. relationship the relative from proportions one network of influence to the RickMarley Rubin Marl (0.25) (0.29) RickGeorge Rubin(left), Clinton (0.22) (0.25) =0KoolFab.2 5 & Freddy(middle), the Gang (0.23) (0.19)4 and =1.0 (right). cency matrix without any iterative procedurePublic Enemy and (0.27) by know-Public Enemy (0.23) Russell Simmons (0.19) short, finite linear combination of the powers ofDJGeorge the Premier Clinton adja- (0.25) (0.28) FabMarley 5 Freddy Marl (0.25) (0.22) MarleyGeorge Marl Clinton (0.18) (0.22) other,betweenGiven we networks. canthe linearcompute relationship As the a result, relative from we proportions can one analyze network of influence how to the in- Rick Rubink (0.25) Rick Rubin (0.22) Kool & the Gang (0.19) ing that the powers of the adjacency matrixMaterialPublicA Enemy, (0.24)k =1 (0.27), 2, 3MaterialPublic... Enemy (0.21) (0.23) RickRussell Rubin Simmons (0.17) (0.19) DJ Premier (0.25) Fab 5 Freddy (0.22)ence ofMarley an individual Marl (0.18) artist by looking at the correspond- other,betweenfluential wecency a networks. can given compute matrix song As is the without a to result, relative an overall we anyproportions can artist’s iterative analyze influence of influence how procedure in- or andFabRick by 5 Rubin Freddy know- (0.25) (0.24) Run-DMCRick Rubin (0.21) (0.22) PublicKool & Enemy the Gang (0.17) (0.19) will go to zero when k is greater than theMaterial maximum (0.24) sampleMaterial (0.21) Rick Rubin (0.17) k HankDJ Premier Shocklee (0.25) (0.23) DJFab Premier 5 Freddy (0.21) (0.22)ing rowLarryMarley or Smith column. Marl (0.16) (0.18) Table 4, for example, names the top betweenfluentialhow influential a networks. given an song artist As is a is to result, to an a overall genre we can by artist’s taking analyze influence ratios how be- in- or A k Fab=1 5 Freddy, 2, 3 (0.24)... Run-DMC (0.21) Public Enemy (0.17) ing that the powerschain of length the adjacency of the network. matrix With sparse, Material matrix (0.24) represen-Materialence (0.21) of anRick individual Rubin (0.17) artist by looking at the correspond- fluentialhowtween influential the a respective given an song artist influence is is to to an a graphs, overall genre by artist’s among taking influence other ratios tasks. be- or Hank Shocklee (0.23) DJ Premier (0.21)five influentialLarry Smith and (0.16) influenced artists of Jay-Z. Finally, we will go to zerotations, when k thisis greater modification than can the greatly maximum reducedFab 5 Freddy sample computation, (0.24) Run-DMC (0.21) Public Enemy (0.17) howtweenSecondly, influential the by respective solely an artist computing influence is to a the graphs, genre influence by among taking on other the ratios acyclic, tasks. be- Hank Shocklee (0.23) DJ Premiering (0.21) row orLarry column. Smith (0.16) Table 4, for example, names the top increase the allowable in-memory networkTable 3 size,. Artist and Sample-Based addi- Influence RankInfluential for (=0=0.20) Influenced ( =0.2) tweenSecondly,unweighted thechain by respective song-level solely length computing influence network, of the the graphs, wenetwork. influence can among compute on With other theIS acyclic,from sparse tasks. a matrix represen- five influential and influenced artists of Jay-Z. Finally, we Table(left), 3.=0 Artist.2 (middle), Sample-Based and Influence=1.0 (right). RankThe Notorious for =0 B.I.G..0 (0.97) Girl Talk (1.0) Secondly,unweightedshort, finitetations, by song-level linear solely this combination computing modification network,tionally the of we influence thereleases can powers can compute onany greatly of theI restriction theS acyclic,from adja- reduced a on computation,, allowing the user to Dr. Dre (0.91) Lil Wayne (0.80) Table(left), 3.=0 Artist.2 (middle), Sample-Based and Influence=1.0 (right). RankPuff Daddy for (0.53)=0.0 The Game (0.53) unweightedshort,cency matrix finite song-level linear without combination any network, iterativechoose of we any procedure the can suitable powers compute and of weightingI by theS from know- adja- a function. Application of this Influential ( =0.2) Influenced ( =0.2) increase the allowable in-memoryk network size,(left), and =0 addi-.2 (middle), and =1.0 (right).Nas (0.5) DJ Premier (0.40) short,cencying that matrix finite the powers linear without of combination the any adjacency iterativeapproach of procedure matrixthe is found powersA and, belowk of=1 by the, know- in2 adja-, Section3... 4.ence of an individual artist by lookingThe atJames Notorious the correspond- Brown B.I.G. (0.42) (0.97) LinkinGirl Talk Park (0.39)(1.0) tionally releases any restrictionk on , allowing the user to cencyingwill that go matrix to the zero powers without when ofk the anyis adjacency greater iterative than procedure matrix the maximumA and, k =1 by sample, know-2, 3... enceing row of an or individualcolumn. Table artist 4, by for looking example,Dr. at Dre the names (0.91) correspond- the top Lil Wayne (0.80) choose any suitable weightingk function. Application of this Puff Daddy (0.53) The Game (0.53) ingwillchain that go length to the zero powers of when the of network.k theis adjacency greater With than matrix sparse the maximumA matrix, k4.=1 represen- APPLICATION sample, 2, 3... enceingfive row influential of an or individualcolumn. and influenced Table artist 4, by for artists looking example, of at Jay-Z. the names correspond- Finally, the top we willchaintations, go length to this zero modification of when the network.k is greater can greatly With than sparse reduced the maximum matrix computation, represen- sample TableNas 4. Top (0.5) Influential and InfluencedDJ Premier Artists (0.40) of Jay-Z . approach is found below in Section 4. ingfive row influential or column. and influenced Table 4, for artists example, ofJames Jay-Z. namesBrown Finally, (0.42) the top we Linkin Park (0.39) chaintations,increase length this the modification allowable of the network. in-memory canThree greatly With levels network sparse reduced of influencematrix size, computation, and represen- analysis addi- and rank are computedInfluential ( for=0.2) Influenced ( =0.2) five influentialThe Notorious and influenced B.I.G. (0.97) artistsGirl Talk of (1.0) Jay-Z. Finally, we Influential ( =0.2) Influenced ( =0.2) tations,increasetionally this releases the modification allowable any restriction in-memory cansong,Katz greatly on artist, Influence network, reduced allowing and genre size, computation, theComputation and representations, user addi- to providingDr. a Dre small-to- (0.91) canLil Wayne also (0.80) compute the relative proportion of influence cre- The Notorious B.I.G. (0.97) Girl Talk (1.0) InfluentialPuff Daddy( (0.53) =0.2) InfluencedThe Game (0.53)( =0.2) increasetionallychoose any releases the suitable allowable any weighting restriction in-memorylarge function.4. inspection on network APPLICATION, allowing Application of size, the the and data. user of addi- this Various to values of Dr.are Dre used (0.91) to Lil Wayne (0.80) NasThe (0.5)Notorious B.I.G. (0.97) atedDJGirl Premier Talk by (1.0) each (0.40) song within an artist’s overall influence. The Puff Daddy (0.53) TableThe 4 Game. Top (0.53) Influential and Influenced Artists of Jay-Z . tionallychooseapproach any releases is suitable found• any belowCompute weighting restriction incompare Section using function. on 4. directexpanded, allowing Application to indirect form the user of influence. this to For this purpose,JamesDr. Dre Brown (0.91) (3) (0.42) is LinkinLil Wayne Park (0.80) (0.39) Nas (0.5) topDJ Premier three (0.40) most influential songs of James Brown, for exam- approachThree is found levels below of in influence Section 4. analysis and1 rank2 are computedk 1 k Puff for Daddy (0.53) The Game (0.53) choose any suitable weighting• Eliminatesrescaled function. any to restrictionsIK Application= A on+ ofA this+ ... + A +James..., allowing Brown (0.42) ple,Linkin include Park (0.39) “Funky Drummer” (14%), “Think (About It)” approach is found below in Section 4. Nas (0.5) DJ Premier (0.40) song, artist,4.• Song-level and APPLICATION genre=0 networkto representations, only is account very sparse for direct providing sampling, a small-to- =1Jamesto Brown equally (0.42) can alsoLinkin compute Park (0.39) the relative proportion of influence cre- Table 4. Top Influential and Influencedby Lyn Collins Artists of and Jay-Z produced . by James Brown (9%), and 4.• Sample-chains APPLICATIONaccount for are direct limited and length all indirect sampling, and values be- Three levelslarge of inspection influence analysis of the and data. rank are Various computed values for of Tableare used 4. Top to Influentialated and Influenced“Funky by each President” Artists song of within Jay-Z (7.5%). . an Similar artist’s measures overall can influence. be com- The • 4.Rescale APPLICATIONtween zero and one to preferentially weight direct samples, Threesong, artist, levelscompare and of influence genre direct representations, analysis to indirect and rank providing influence. are computed a small-to- For for this purpose,canTable also 4. compute (3) Top is Influential the relativetop and Influenced three proportionputed most to indicate Artists of influential influence of whether Jay-Z cre- . songs an artist of gets James more Brown, credit as fora pro- exam- Threesong,large inspection artist, levels and of influence genre of the representations, data. analysisbut Various also and account values rank1 providing2 are of for computed indirectare a small-to- usedk for sampling. to1 k ducer or performer. rescaled to IK = A + A + ... + A +canated..., also by allowing each compute song the within relativeple, an artist’s proportion include overall “Funky of influence. influence Drummer” Thecre- (14%), “Think (About It)” song,largecompare inspection artist, direct and to genre of indirect the representations, data. influence. Various values For providing this of purpose, are a small-to- used (3) to is canatedtop three also by each compute most song influential the within relative songs an artist’s proportion of James overall Brown, of influence. influence for exam- Thecre- =0to only1 account2 fork 1 directk sampling, =1to equally by Lyn Collins and produced by James Brown (9%), and largecomparerescaled inspection to directIK = to of A indirect the•+ data. =A influence.4.10, Various +only... Song +direct values For Influence influence thisA of purpose,+...are , allowing used (3) to is atedtopple, three include by each most “Funky song influential within Drummer” songs an artist’s4.3 of (14%), James Genre overall “Think Brown, Influence influence. (About for exam- The It)” 1 2 k 1 k comparerescaled =0toaccount to direct onlyIK account= toA forindirect+• directfor >A direct influence.0, +direct and... sampling,+ + all Forindirect indirect thisA influence=1 purpose,+ ...,to allowing sampling, equally (3) is andple,by valuesLyn include Collins be- “Funky and producedDrummer”“Funky by (14%), James President” “Think Brown (About (9%), (7.5%). and It)” Similar measures can be com- The song-level influence matrix IS istop computed three most from influential the songs of James Brown, for exam- account=0to for onlyI direct account= A and+ for all1A indirect direct2 + ... sampling,+ sampling,k 1Ak and=1+ ... valuesto equally be- The song-level influence matrix can further be reduced to a rescaledtween to K zero• and = song1, one equal network to weighting preferentially described of direct, allowing in and weight Section indirect direct3.1. influenceple,by“Funky The Lyn include samples, most CollinsPresident” “Funky influential and (7.5%). producedDrummer”puted Similar by (14%), to James measuresindicate “Think Brown can whether (About (9%), be com- and It)” an artist gets more credit as a pro- accounttween=0 zeroto for only and direct account one and to for preferentiallyall indirect direct sampling, sampling, weight direct and=1 valuesto samples, equally be- puted to indicate whether an artistgenre-based gets more credit influence as a pro-IG. The most influential genres found but also accountsongs for indirect are found sampling. in Table 2. We can observeby“Funky Lyn the CollinsPresident” presence and (7.5%). produced of ducer Similar by or James measures performer. Brown can (9%), be com- and accounttweenbut also zero accountfor and direct one for and to indirect preferentiallyall indirect sampling. sampling, weight direct and values samples, be- “Funkyputedducer toor President” indicate performer. whether (7.5%). an Similar artistare: gets soul/funk/disco, measures more credit can as be a hip-hop/R&B, com- pro- rock/pop, jazz/blues, and many popular samples including “Change the Beat” by Fab tweenbut also zero account and one for to indirect preferentially sampling. weight direct samples, putedducer toor indicate performer. whether an artistelectronic gets more dance, credit as while a pro- the top influenced genres are hip- 5 Freddy and the “Amen” break by The Winstons. It is par- but4.1 also Song4.1 account Influence Song for indirect Influence sampling. 4.3ducer Genre or performer. Influence 4.3hip/R&B, Genre Influence electronic dance, rock/pop, other, and reggae (for 4.1 Song Influence ticularly interesting to note that, for the “Amen” break, as The song-level influence matrix IS is computed from the 4.3 Genre Influence all values of ). Alternatively, the top songs and artist for 4.1 SongThe Influence song-levelincreases, influence the matrix credit ofI influenceS is computed intuitivelyThe song-level from moves the from influence The matrix can further be reduced to a Thesong song-level network described influence in matrix SectionIS 3.1.is The computed most influential from the 4.3 Genre Influence The song-leveleach genre can influence also be computed matrix can(omitted further due to be space reduced con- to a song network describedWinstons to in The Section Impressions, 3.1. The and most finallyThegenre-based influential to song-level Jester influence Hairston. influenceIG. matrix The most can influential further be genres reduced found to a Thesongsongs song-level network are found described influence in Table in 2. matrix Section We canIS 3.1. observeis The computed most the presence influential from the of straints). I Thegenre-basedare: soul/funk/disco, song-level influence influence hip-hop/R&B,IG. matrixgenre-based The most can rock/pop, influential further influence be jazz/blues, genres reduced foundG to and. a The most influential genres found songsongsmany network popular aresongs found described samples are in Table found including in 2.This Section We in Table can is “Change 3.1.a observe result 2.The the We most of the Beat” a can presence influential sample by observe Fab of chain the between presence material of origi- genre-basedare:electronic soul/funk/disco, dance, influence while hip-hop/R&B,IG the.are: The top most soul/funk/disco, influenced rock/pop, influential genres jazz/blues, genres are hip-hop/R&B, found hip- and rock/pop, jazz/blues, and songsmany5 Freddy popular are and found the samples in “Amen” Table including 2. breaknating We can by “Change from The observe JesterWinstons. the the Beat” Hairston, presence It by is par- Fab of that was first sampled by The many popular samples including “Change the Beat”are:electronichip/R&B, soul/funk/disco, by electronic dance, Fab while dance, hip-hop/R&B, the rock/pop, top influenced rock/pop, other, genres and jazz/blues, reggae are hip- (for and many5ticularly Freddy popular interesting and the samples “Amen” to note including breakImpressions, that, forby “Change The the “Amen” Winstons. and the then Beat” break, It massively by is as par- Fab popularized by The Win- electronic dance, while5. CONCLUSIONS the top influenced genres are hip- 5 Freddy and the “Amen” break by The Winstons.electronichip/R&B,all values It is electronicof dance, par-). Alternatively, while dance, the rock/pop, top the influenced top other, songs genres and and reggae artist are hip- (for for 5ticularlyincreases, Freddy interesting and the thecredit “Amen” to of note influence breakstons. that, intuitivelyforby The the “Amen” Winstons. moves break, from It is as par- The hip/R&B, electronic dance, rock/pop, other, and reggae (for hip/R&B,alleach values genre electronicof can). also Alternatively, be dance, computed rock/pop,An the (omitted analysis top other, songs due and of andto reggae music space artist con- (for influence for and rank of sample-based ticularlyincreases,Winstonsticularly interesting to the The credit Impressions, interesting to of note influence that, and intuitivelyfor to finally thenote “Amen” to that, moves Jester break, for fromHairston. the as The “Amen” break, as alleachstraints). values genre of can). also Alternatively, be computedall valuesmusic the (omitted top is of songs presented due). andto Alternatively, space artist using con- for the WhoSampled.com the top songs dataset. and artist Gen- for increases,WinstonsThis isincreases, a resultto the The credit of Impressions, a of the sample influence credit4.2 chain and Artist intuitively of finally between influence Influence to moves Jester material intuitively fromHairston. origi- The moves from The eachstraints). genre can also be computedeacheral genre (omitted genre can due and also to time-based space be computed con- trends are (omitted found, identifying due to space where con- WinstonsThisnating is from a resultto The Jester of Impressions, Hairston, a sample thatchain and was finally between first to sampled Jester material Hairston. by origi- The Winstons to TheStarting Impressions, with the song-leveland finally influence, to Jesterstraints). we Hairston. can collapse IS and when the sampling source material is coming from as ThisnatingImpressions, is from a result Jester and of then Hairston, a sample massively thatchain popularizedwas between first sampled material by The by origi- Win- The 5. CONCLUSIONSstraints). to form an artist-based influence matrix I . Table 3 shows Impressions,stons. This and is a then result massively of a popularized sample chain by The between Win- materialA origi- 5. CONCLUSIONSwell as differences in how various genres are sampling oth- nating from Jester Hairston, that was first sampled by3 The An analysis of music influence and rank of sample-based stons. nating from Jesterthe top Hairston, influential that artists. was firstWe can sampled also inspect by The the influ-5. CONCLUSIONSers. Network graphs are employed to both understand gen- Impressions, and then massively popularized by The Win- Anmusic analysis is presented of music using influence the WhoSampled.com and rank of sample-based dataset. Gen- stons.4.2 Artist Influence 3 eral trends of sampling behavior, but to also find influence Impressions, and thenEntries massively with Fab 5 Freddy popularized also include producers byAnmusiceral analysisThe genre is Material presented Win- and of time-based and music using Bee- influence the trends WhoSampled.com are and found, rank identifying of sample-based dataset.5. CONCLUSIONSwhere Gen- 4.2 Artist Influence side. All three artists achieved high influence from “Change the Beat”. rank over songs, artists, and genre. A method of influence Startingstons. with the song-level influence, we can collapse IS musiceraland genre when is presented and the time-based sampling using thesource trends WhoSampled.com material are found, is identifying coming dataset. from where Gen- as 4.2 Artist Influence An analysis of music influence and rank of sample-based Startingto form an with artist-based the song-level influence influence, matrix weIA. can Table collapse 3 showsIS eralandwell genre when as differences and the time-based sampling in how source trends various material are genres found, is are identifying coming sampling from where oth- as 3 Startingtothe form top influential an with artist-based the song-level artists. influenceWe influence, can matrix also weIA inspect. can Table collapse the 3 shows influ-IS andwellers. when Network as differences the graphs sampling in are how source employedmusic various material is genres to presented both is are understandcoming sampling using from gen- oth- the as WhoSampled.com dataset. Gen- 4.2 Artist Influence3 tothe3 formEntries top influential an with artist-based Fab 5 artists. Freddy influence alsoWe include can matrix producers alsoIA inspect. Material Table the 3 and shows influ- Bee- wellers.eral trendsNetwork as differences of graphs sampling in are how behavior, employederal various genre but genres to to both and also are understand time-based samplingfind influence gen- oth- trends are found, identifying where 3 theside.3 top All three influential artists achieved artists. high influenceWe can from also “Change inspect the the Beat”. influ- rank over songs, artists, and genre. A method of influence EntriesStarting with Fab 5 with Freddy the also include song-level producers influence, Material and Bee- we caners.eral collapse trendsNetwork ofI graphs samplingS are behavior, employedand when but to to both the also understand sampling find influence gen- source material is coming from as side.3 All three artists achieved high influence from “Change the Beat”. eralrank trends over songs, of sampling artists, behavior, and genre. but A to method also find of influence Entriesto with form Fab an5 Freddy artist-based also include producers influence Material matrix and Bee-IA. Table 3 shows well as differences in how various genres are sampling oth- side. All three artists achieved high influence from “Change the Beat”. rank over songs, artists, and genre. A method of influence the top influential artists. 3 We can also inspect the influ- ers. Network graphs are employed to both understand gen- 3 Entries with Fab 5 Freddy also include producers Material and Bee- eral trends of sampling behavior, but to also find influence side. All three artists achieved high influence from “Change the Beat”. rank over songs, artists, and genre. A method of influence Ak have elements representing the number of sample chains k A have elements representingof the corresponding number of sample length chainsk capturing various levels of indi- of corresponding length k capturingrect influence. various levels For stability, of indi-1/ must be greater than the Ak have elements representing the number of sample chains rect influence. For stability, 1largest/ must eigenvalue be greater of A thanand the for large networks, (2) becomes largestof eigenvalue corresponding of lengthA andk forcapturing large networks, various levels (2) becomes of indi- increasingly difficult to invert. 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Typically, only the overall in- ion to avoid a large memoryion footprint to avoid and a matrix large memory inverse footprint and matrix inverse or further reduced for other relations, such as artist-to-genre James Brown (1.0) James Brown (1.0) James Brown (1.0) fluence rank is desired and is computedDr. Dre (0.34) iterativelyI Dr. in Dre a fash- (0.28) Run-DMC (0.25) required for IK . required for K . or furtherand reduced song-to-genre for other influence. relations, such as artist-to-genreion to avoid a large memoryJames BrownMarley footprint (1.0) Marl (0.29) andJames matrix BrownGeorge (1.0) inverse Clinton (0.25)James BrownFab 5 (1.0) Freddy (0.23)4 For our purposes, it is desirableDr. Dre (0.34)GeorgeFor to haveour Clinton purposes, both (0.28)Dr. Dre the (0.28)Marley entire it is Marl desirable in- (0.25)Run-DMC to haveGeorge (0.25) both Clinton the (0.22) entire in- Given the linear relationship from onerequired network for I to. the 4 and song-to-genre influence. K Marley MarlPublic (0.29) Enemy (0.27)George ClintonPublic (0.25) Enemy (0.23)Fab 5 FreddyRussell (0.23) Simmons (0.19) . Cumulative In-degree Distribution P (k) of the fluence matrix and overall rank. Given IK , we can view the Figure 5. Cumulative In-degreeGivenFigureother, Distribution the 5 we linear can relationshipcomputeP (k) of the the from relative one proportionsfluence networkFor matrix to of our the influence purposes, and overall itGeorge is rank. desirable ClintonRick Given Rubin (0.28)to haveI (0.25)K ,Marley both we can the MarlRick entire view (0.25) Rubin in- the (0.22)George ClintonKool & (0.22) the Gang (0.19) Public Enemy (0.27) Public Enemy (0.23) Russell Simmons (0.19) Sample-Based Song NetworkSample-Based (log-logbetween scale). networks. 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(0.21) whoMarley the MarlPublic node (0.18) Enemy influenced (0.17) [15]. how influential an artist is to a genre by taking ratios be- Material (0.24)Hank Shocklee (0.23)Material (0.21)DJ Premier (0.21)Rick RubinLarry (0.17) Smith (0.16) fluential a given song is to an overall artist’sSumming influencethe row the of or columns the node toofFab find the 5 FreddySumming who influence (0.24) the node the matrixRun-DMC influenced columns produces (0.21) of [15]. the a Public influence Enemy (0.17) matrix produces a any of the very popular samplestween were the to be respective removed, influence large graphs, among other tasks. howany influential of the very an artist popular is to samples a genre by were takingranking toSumming be ratios removed, of the be- the most large columns influentialHank of the Shockleeranking nodes, influence (0.23) of while the matrixDJ Premier most summing produces (0.21) influential the a Larry nodes, Smith (0.16) while summing the portions ofany sample-based of the very populartween musicSecondly, the wouldsamples respective cease were by solely to influence be exist removed,computing (or graphs, at large the among influence other on tasks. the acyclic, portions of sample-based music wouldrows ceaseranking results to exist inof a the ranking (or most at influential of theTablerows most nodes, 3 results influenced. 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Artist most =0 influenced Sample-Based.2 analysis(middle), nodes. and Influence and Such mo- =1 Rank.0 (right). for =0.0 least be altered).unweightedshort, song-level finite linear network, combination we can of compute the powersI from of the a adja- analysis is nicely suited for musicological analysis and mo- tivatesanalysis furtherS is improvements nicely suited(left), for discussed musicological=0.2 (middle), below. analysis and and=1 mo-.0 (right). short, finitecency linear matrix combination without any of iterative the powers procedure of the and adja- by know- tivates further improvements discussed below. 3.2 Influence Measures tivatesk further improvements discussed below. 3.2 Influence Measurescency3.2 matrixing Influence that without the powers Measures any of iterative the adjacency procedure matrix andA by, know-k =1, 2, 3... ence of an individual artist by looking at the correspond- To analyze and rank influencewill within go to each zero network, when k is four greater than3.3k the Collapse-and-Sum maximum sample Influence Rank To analyze anding rank that influence the powers within of the each adjacency network, matrix four A , k3.3=1 Collapse-and-Sum, 2, 3... ence Influence ofing3.3 an row individual Collapse-and-Sum Rank or column. artist Table by looking Influence 4, for at example, the Rank correspond- names the top closely related measures are commonlyTochain analyze length used: and of rank the degree network. influence cen- With within sparse each matrix network, represen- four closely related measureswill go to are zero commonly when k is used: greater degree than cen- the maximumFor the given sample dataset, weing would rowfive or like influential column. to understand Table and influenced 4, and for ana- example, artists of names Jay-Z. the Finally, top we closelytations, related this modification measures are can commonly greatly reduced used:For the computation, degree given dataset, cen- we would like to understand and ana- trality, eigenvectortrality, eigenvector centrality,chain centrality, Katz length centrality, of Katz the centrality, network. and PageR- and With PageR- sparse matrixlyze song, represen- artist, and genrefive influential influenceFor the individually, and given influenced dataset, as we artists well would as of Jay-Z. like to Finally, understand we and ana- trality,increase eigenvector the allowable centrality, in-memory Katz network centrality,lyze size, song, and and artist, PageR- addi- and genre influence individually,Influential ( =0 as. well2) as Influenced ( =0.2) ank. Degree centrality doestations, not capture this modification any indirect can form greatly of reduced computation, lyze song,The artist, Notorious and B.I.G. genre (0.97) influenceGirl Talk individually, (1.0) as well as ank. Degree centrality does not capture any indirect form of how each network relates to one another. To do so, individ- influence (as in the case ofincrease sampleank.tionally the chains), Degree allowable releases centrality motivating in-memory any restriction does alter- not network capture on , size, allowing anyhow and indirect each addi- the network form user to of relates to oneInfluential another.Dr.( Dre=0 To (0.91). do2) so, individ-InfluencedLil( Wayne=0.2 (0.80)) influence (as in the case of sample chains), motivating alter- howThe each Notorious network B.I.G. (0.97) relatesGirl to Talk one (1.0) another. To do so, individ- tionallychoose releases any any suitable restriction weighting on , function. allowingual networks Applicationual the networks user can to of can be this beconstructed constructed for for song, song,Puff Daddy artist, artist, (0.53) and and genre genre The Game (0.53) native methods.native methods. Eigenvector Eigenvector centralityinfluence centrality extends (as in the extends degree case ofdegree cen- sample cen- chains), motivating alter- Dr. Dre (0.91)Nas (0.5) Lil WayneDJ (0.80) Premier (0.40) chooseapproach any suitable is found weighting below function. in Section Application 4.networksnetworks of with this with influence influence matrices matricesualPuff and networks and Daddy rank rank (0.53) computed computed can be constructed via viaThe (2) (2) Game (0.53) for song, artist, and genre trality by weightingtrality by weighting the importance thenative importance of methods. neighboring of neighboring Eigenvector nodes nodes to centrality to extends degree cen- James Brown (0.42) Linkin Park (0.39) approach is found below in Section 4. or (3).or Building (3). Building separate separate graphs, graphs,networksNas however, however, (0.5) with has has influence several several draw- draw-DJ matrices Premier (0.40) and rank computed via (2) allow for indirectallow for influence, indirect influence, buttrality has by limited but weighting has limited application the application importance for for of neighboring nodes to James Brown (0.42) Linkin Park (0.39) 4. APPLICATIONbacks.backs. Most Most notably, notably, there there is nois no straightforward straightforward mechanism mechanism acyclic networks2 [13]. 2 Katz centrality and PageRank ap- or (3). Building separate graphs, however, has several draw- acyclic networks [13]. Katzallow centrality for indirect and PageRank influence, ap- but hasto limited relateto relate application the influence the influence for matrices matricesTable of of each each 4. network Top network Influential together together and ap- ap- Influenced Artists of Jay-Z . Three levels of4. influence APPLICATION analysis and rank are computed for backs. Most notably, there is no straightforward mechanism propriatelypropriately modify eigenvector modify eigenvectoracyclic centrality. networks centrality. Both also [13]. Both provide2 alsoKatz provide centrality andpropriately. PageRank Furthermore, ap- Table we 4. would Top Influential like to model and the Influenced influ- Artists of Jay-Z . song, artist, and genre representations,propriately. providing a Furthermore, small-to- we wouldto relate like the to influence model the matrices influ- of each network together ap- a mechanisma mechanism to capture to indirectThree capture levels indirect influence of influence influence between analysis between nodes, and nodes, rank are computedence propagation for on the song-levelcan also topology compute and the then relative derive proportion of influence cre- propriatelylarge inspection modify of eigenvector the data. Various centrality.ence values propagation Both of alsoare provideused on to the song-level topology and then derive compute ancompute overall an influence overallsong, influence rank artist, among and rank genre among each representations, node, each node, and and providingartist a small-to- and genre influencecan also measures,atedpropriately. compute by each as the the song Furthermore, compositional relative within proportion an we act artist’s would of overall influence like to influence. model cre- the The influ- observe the influencelargea inspection ofcompare mechanism one node direct of to the to another. to capture data. indirect Various PageRank, indirect influence. values influenceartist For of thisare and between purpose, used genre to influence nodes, (3) is measures,top three as most the compositional influential songs act of James Brown, for exam- observe the influence of one node to another. PageRank,1 2 k 1ofk sampling is presumablyated by basedence each on propagation song the within musical on an material the artist’s song-level it- overall topology influence. and The then derive computerescaled an to I overallK = A influence+ A + rank... + amongof samplingA each+ ... is, node, allowing presumably and basedple, include on the musical “Funky material Drummer” it- (14%), “Think (About It)” however, down-weightscompare influence direct to created indirect by influence. a destination For this purpose,self, rather (3) is than artisttop or three genreartist most connections. and influential genre influence songs of measures, James Brown, as the for compositional exam- act however, down-weights influence =0 created by a1 destination2 k 1 k =1 node that samplesrescaled moreobserve than to IK once,to the= onlyA influence or+ account in theA of case+ for... one direct of+ artist node sampling,A toself,+ another.... rather, allowing than PageRank,to equally artist or genreby connections. Lyn Collins and produced by James Brown (9%), and node that samples more than once, or in the case of artist To address this issue,ple, include aof single sampling “Funky influence is Drummer” presumably matrix is (14%), con- based “Think on the (About musical It)” material it- =0account for direct and all indirect sampling, =1To address and values this be- issue, a single“Funky influence President” matrix (7.5%). is con- Similar measures can be com- nodes, down-weightshowever, influenceto only accountfrom down-weights artists for with direct lengthy influence sampling, ca- createdstructedto by equally a destination using the song-levelby Lyn Collins network and (see produced Section 3.1) by Jamesand Brown (9%), and nodes, down-weights influenceaccount fromtween for artists direct zero and and with one all lengthy indirect to preferentially ca- sampling, weight and values direct be- samples, putedself, torather indicate than whether artist or an genre artist connections. gets more credit as a pro- reers. While this isnode desirable that in samples numerous more other than contexts once, orstructed inis the used using case to create the of artist song-level the“Funky artist and network President” genre (see influence (7.5%). Section matrices, Similar 3.1) and re- measures can be com- reers. While this is desirabletween in zerobut numerous also and account one to other preferentially for contexts indirect sampling. weight direct samples, ducerTo or address performer. this issue, a single influence matrix is con- such as web search, we wish to equally weight each instance is usedsulting to create in the proposed the artistputed relational and to genreindicatecollapse-and-sum influence whether matrices, an artistapproach. gets re- more credit as a pro- such as web search, we wishbut to alsonodes, equally account down-weights weight for indirect each instance influence sampling. from artists with lengthy ca- of sampling and restrict ourselves to Katz centrality. sulting in the proposedducer relational orstructed performer.collapse-and-sum using theI song-levelapproach. network (see Section 3.1) and of sampling and restrict ourselvesreers.4.1 to Song Katz While Influence centrality. this is desirable in numerousTo construct other contexts the artist-level influenceCollapse-and-Sum matrix A from the Influence I The Katz influence matrix IK is defined via To construct the artist-level4.3 influenceis used Genre to matrix Influence createI thefrom artist andthe genre influence matrices, re- 4.1 Song Influence song-level network, the song-level network is firstA used to The Katz influence matrix IsuchKTheis as defined song-level web search, via influence we wish matrix to equallyIS is weight computed each from instance the 4.3 Genre• Influence Derived artist- and genre-level influence from song-level 1 song-levelcompute network, the song the influence song-levelThesulting matrix song-level network inIS the. Given proposed influence is firstIS, we used relational matrix then to cancollapse-and-sum further be reducedapproach. to a IK =(I A) I (2) Theof song-levelsong sampling network influence and described restrict matrix ourselves in SectionIS is computed to 3.1. Katz The centrality. frommost influential the 1 computecompute the asong derived influence artistThe song-level influence matrixgenre-basedTo constructI matrixS influence. Given influenceI theA, matrix knowingI artist-levelS,IG we. can The then the further most influence influential be reduced matrix genres toIA a foundfrom the IK =(I Asongs) areI found in Table 2.(2) We can observe the presence of song networkThe Katz described influence in Section matrix 3.1.IK Theis defined most influential via are: soul/funk/disco,Ss Sd hip-hop/R&B, rock/pop, jazz/blues, and where I is an identity matrix,A is the adjacency matrix as computesource a andderived destination artistgenre-based influence song sets influence matrixai andIIAaG,i. knowingbelonging The most the influential to genres found songs aremany found popular in Table samples 2. We including can observe “Change the presence the Beat” of by Fab song-level network, the song-level network is first used to before, and is a decay factor which scales the indirect in- sourceeach and artist destinationai. To doare: song so, soul/funk/disco, weelectronic sets takeS eachs and dance, artistS hip-hop/R&B,da whileibelongingin the the set top rock/pop, of to influenced jazz/blues, genres and are hip- where I is an identity matrix, A5is Freddy the adjacency and the “Amen” matrix break as by1 The Winstons. It is par- compute• aCollapse-and-sumi the songai the influence rows and columns matrix of IS. Given IS, we then many popular samples includingIK =(I “ChangeA) the Beat”Iartists byA Faband (2) hip/R&B, electronic dance, rock/pop, other, and reggae (for fluence allowed to propagate though the network (larger each artist ai. To do so,electronic we take dance, each based artist whileon song-artistai thein and top the song-genre influenced set of relations genres are hip- before, and is a decay factor5 Freddy whichticularly and scales the interesting “Amen” the indirect break to note by in- that, The for Winstons. the “Amen” It is break, par- as compute a derived artist influence matrix IA, knowing the hip/R&B,all values electronic– e.g. of sum all dance,). song-level Alternatively, rock/pop, influence of an other, the artist top together and songs reggae and (for artist for implies greater weightincreases, on indirect the influence). credit of influence This can be intuitivelyartists movesA and from The d s d fluence allowed to propagateticularly though interesting the network to note (larger that, for the “Amen” break,Sum as over the destinationeachsource song genre– e.g. and sets sum can destination all of also song-level each be artist computedinfluence songSa of ,a sets genre (omitted togetherS and dueS to spacebelonging con- to written in equivalent formwhereWinstons asI is an to The identity Impressions, matrix, A andis finally the adjacency to Jester• Hairston. matrix asall values of ). Alternatively, the topi songsai and artistai for implies greater weight onincreases, indirect the influence). credit of influence This can intuitively be moves fromcollapsing The the appropriatestraints).each columns artist a of. ToIS. do so, wed take each artist a in the set of before, and is a decay factor which scalesSum the over indirect the in- destinationeach genre song can also sets be ofi computed each artist (omittedSa , due to space con-i WinstonsThis2 to2 is The a result Impressions,k ofk a sample and finally chain to between Jester Hairston. material origi- i written in equivalentI form= asA + A + ... + A + ..., (3) • straints). s K fluencenating allowed from Jester to propagate Hairston, that though was the first networkcollapsing sampledSum (larger byover the The the appropriate source songartists columns setA ofand each of I artistS. S , col- This is a result of a sample chain between material• origi- ai 2nating2 impliesImpressions, from Jester greaterk k Hairston, and weight then that on massively indirect was first popularized influence). sampled by bylapsing This The The can Win- the be appropriate rows of IS. 5. CONCLUSIONS IwhereK = weA can+ seeA that+ ... the+ influence A + is..., a weighted(3) sum of Sum over the source song setSum of each over artist the destinationSs , col- song sets of each artist Sd , Impressions,stons. and then massively popularized by The Win- 5. CONCLUSIONSai ai the powers of the adjacencywritten matrix in equivalent [14]. When form the as values •The result of the process producesAn analysis• an artist-level of music influence influence and rank of sample-based stons. lapsing the appropriate rows ofcollapsingIS. the appropriate columns of IS. where weof canA seeare that zero the or one, influence the powers is a weighted of the adjacency sum of matrix An analysismusic of is presented music influence using the and WhoSampled.com rank of sample-based dataset. Gen- 4.2 Artist Influence 2 2 k matrixk IA which is directly derived from the song-level mu- the powers of the adjacency matrix [14].IK When= A the+ valuesA + ... + A + ..., (3)music iseral presented genre and using time-based the WhoSampled.com trends are found, dataset. identifying Gen- wheres 2 The song network is exactly acyclic and the artist network is nearly The resultsical material, of the process and is done produces so via linear anSum artist-level combinations over the influence source of the song set of each artist S , col- 4.2 ArtistStarting Influence with the song-level influence, we can collapse IS and when the sampling source material is coming fromai as of A are zeroacyclic. or one, the powers of the adjacency matrix matrixsong-levelI which influence is directlyeral matrix. genre derived The and• process from time-based the can song-level be trends duplicated are mu- found, identifying where to form an artist-based influence matrix I .A Table 3 shows lapsing the appropriate rows of IS. Startingwhere with we the can song-level see that influence, the influence we can is a collapseA weightedIS sum ofand whenwell the as differences sampling source in how material various is genres coming are from sampling as oth- 2 The song network is exactly acyclic and the artist network is nearly3 sical material, and is done so via linear combinations of the to formthe an top artist-based influential influence artists. matrixWe canIA. also Table inspect 3 shows the influ- well asers. differences Network in graphs how various are employed genres are to both sampling understand oth- gen- acyclic. the powers of the adjacency3 matrix [14].song-level When influence the values matrix. TheThe process result of can the be process duplicated produces an artist-level influence the top influential3 Entries with artists. Fab 5 FreddyWe also can include also inspect producers the Material influ- and Bee- ers. Networkeral trends graphs of sampling are employed behavior, to both but understand to also find gen- influence ofside.A are All three zero artists or one, achieved the high powers influence of from the “Change adjacency the Beat”. matrix rankmatrix overIA songs,which artists, is directly and genre. derived A from method the of song-level influence mu- 3 Entries with Fab 5 Freddy also include producers Material and Bee- eral trends of sampling behavior, but to also find influence side. All2 threeThe artists song network achieved ishigh exactly influence acyclic from and “Change the artist the Beat”. network is nearlyrank oversical songs, material, artists, and and is genre. done so A via method linear of combinations influence of the acyclic. song-level influence matrix. The process can be duplicated Ak have elements representing the number of sample chains of corresponding length k capturing various levels of indi- k rect influence.A have elements For stability, representing1/ themust number be greater of sample than chains the largestof eigenvalue corresponding of lengthA andk forcapturing large networks, various levels (2) becomes of indi- increasinglyrect influence. difficult For to stability, invert. Typically,1/ must only be greater the overall than the in- A fluencelargest rank eigenvalue is desired of andand is computed for large networks, iteratively (2) in becomes a fash- increasingly difficult to invert. Typically, only the overall in- ion to avoid a large memory footprint and matrix inverse fluence rank is desired and is computed iteratively in a fash- I requiredion to for avoidK . a large memory footprint and matrix inverse For our purposes, it is desirable to have both the entire in- required for IK . Figure 5. Cumulative In-degree Distribution P (k) of the fluenceFor matrix our purposes, and overall it is rank. desirable Given to haveIK , both we can the entire view in- the Sample-BasedFigure Song 5. Network Cumulative (log-log In-degree scale). Distribution P (k) of the columnfluence of a matrix node and to find overall who rank. influenced Given IK the, we node, can view or view the Sample-Based Song Network (log-log scale). the rowcolumn of the of a node node to to find who who influenced the node the influenced node, or view [15]. Summingthe row the of columns the node toof find the who influence the node matrix influenced produces [15]. a any of the very popular samples were to be removed, large rankingSumming of the the most columns influential of the nodes, influence while matrix summing produces the a any of the very popular samples were to be removed, large portions of sample-based music would cease to exist (or at rowsranking results inof a the ranking most influential of the most nodes, influenced while summing nodes. Such the portions of sample-based music would cease to exist (or at least be altered). analysisrows is results nicely in suited a ranking for of musicological the most influenced analysis nodes. and Such mo- least be altered). tivatesanalysis further is improvements nicely suited for discussed musicological below. analysis and mo- 3.2 Influence Measures tivates further improvements discussed below. 3.2 Influence Measures To analyze and rank influence within each network, four 3.3 Collapse-and-Sum Influence Rank To analyze and rank influence within each network, four 3.3 Collapse-and-Sum Influence Rank closely related measures are commonly used: degree cen- For the given dataset, we would like to understand and ana- closely related measures are commonly used: degree cen- For the given dataset, we would like to understand and ana- trality, eigenvectortrality, eigenvector centrality, centrality, Katz centrality, Katz centrality, and PageR- and PageR- lyze song, artist, and genre influence individually, as well as ank. Degree centrality does not capture any indirect form of lyze song, artist, and genre influence individually, as well as ank. Degree centrality does not capture any indirect form of howhow each each network network relates relates to to one one another. another. To To do do so, so, individ- individ- influence (as in the case of sample chains),or motivating further reduced alter- for other relations, such as artist-to-genre James Brown (1.0) James Brown (1.0) James Brown (1.0) influence (as in the case of sample chains), motivating alter- ual networksual networks can can be beconstructed constructed for for song, song,Dr. artist, Dre artist, (0.34) and and genre genreDr. Dre (0.28) Run-DMC (0.25) native methods. Eigenvector centrality extendsand song-to-genre degree cen- influence. Marley Marl (0.29) George Clinton (0.25) Fab 5 Freddy (0.23)4 native methods. Eigenvector centrality extends degree cen- networksnetworks with with influence influence matrices matrices and and rank rank computed computed via via (2) (2) trality by weighting the importance of neighboringGiven nodes the linear to relationship from one network to the George Clinton (0.28) Marley Marl (0.25) George Clinton (0.22) trality by weighting the importance of neighboring nodes to or (3).or Building (3). Building separate separate graphs, graphs, however, however,Public has has Enemy several several (0.27) draw- draw-Public Enemy (0.23) Russell Simmons (0.19) allow for indirectallow for influence, indirect influence, but has limited but hasother, limited application we can application compute for for the relative proportions of influence Rick Rubin (0.25) Rick Rubin (0.22) Kool & the Gang (0.19) 2 2 between networks. As abacks. result,backs. Most we Most can notably, analyze notably, there how there is in- nois no straightforward straightforwardDJ Premier mechanism mechanism(0.25) Fab 5 Freddy (0.22) Marley Marl (0.18) acyclic networksacyclic [13]. networksKatz [13]. centralityKatz centrality and PageRank and PageRank ap- ap- Material (0.24) Material (0.21) Rick Rubin (0.17) fluential a given song is toto an relateto overall relate the influence artist’sthe influence influence matrices matrices or of of each each network network together together ap- ap- propriatelypropriately modify eigenvector modify eigenvector centrality. centrality. Both also Both provide also provide Fab 5 Freddy (0.24) Run-DMC (0.21) Public Enemy (0.17) how influential an artist ispropriately. to apropriately. genre by Furthermore, taking Furthermore, ratios we be- we would would like likeHank to to model model Shocklee the the (0.23) influ- influ-DJ Premier (0.21) Larry Smith (0.16) a mechanism to capture indirect influence between nodes, a mechanism to capture indirect influencetween between the respective nodes, influenceenceence propagationgraphs, propagation among on other the on the song-level tasks. song-level topology topology and and then then derive derive compute ancompute overall an influence overall influence rank among rankSecondly, among each node, each by solely node, and computing and artist the influence and genre on influence the acyclic, measures, as the compositional act artist and genre influence measures, asTable the compositional 3. Artist Sample-Based act Influence Rank for =0.0 observe the influence of one nodeunweighted to another. song-level PageRank, network, we can compute I from a observe the influence of one node to another. PageRank, of samplingof sampling is presumably is presumablyS based based on on the the(left), musical musical =0 material material.2 (middle), it- it- and =1.0 (right). however, down-weightshowever, down-weights influence influence createdshort, created by a finite destination by a linear destination combinationself, of the rather powers than artist of the or adja- genre connections. node that samples more than once, or in the case ofor artist further reducedself, rather for other than relations, artist such or genre as artist-to-genre connections. James Brown (1.0) James Brown (1.0) James Brown (1.0) cency matrix without any iterativeTo procedure address and this by issue, know- a single influenceDr. matrix Dre (0.34) is con-Dr. Dre (0.28) Run-DMC (0.25) node that samples more than once, or in the case of artistand song-to-genre influence. 4 nodes, down-weights influence froming artists that the with powers lengthy of ca- the adjacencyTo address matrix thisAk, k issue,=1, 2 a, single3... influenceence ofMarley matrix an individualMarl (0.29) is con-George artist Clinton by (0.25) lookingFab 5 Freddy at the (0.23) correspond- nodes, down-weights influence from artists with lengthy ca- Given the linearstructed relationship using from the song-level one network network to the (see SectionGeorge Clinton 3.1) (0.28) andMarley Marl (0.25) George Clinton (0.22) reers. While this is desirable inwill numerous go to zero other when contextsk is greaterstructed than using the maximum the song-level sample networking (see row SectionPublic or Enemy column. 3.1) (0.27) and TablePublic Enemy 4, (0.23) for example,Russell Simmons names (0.19) the top reers. While this is desirable in numerous other contextsother, we can computeis used the to relative create proportions the artist of and influence genre influenceRick matrices, Rubin (0.25) re-Rick Rubin (0.22) Kool & the Gang (0.19) such as web search, we wish to equallychain weight length each of the instancebetween network. networks.is used Withsulting to As sparse create a in result, the matrix proposed the we artist can represen- analyze relational and genre howcollapse-and-sum in- influencefive influentialDJ Premier matrices,approach. (0.25) and influencedre-Fab 5 Freddy (0.22) artistsMarley of Jay-Z. Marl (0.18) Finally, we such as web search, we wish to equally weighttations, each this instance modificationfluential a can given greatly song is reduced to an overall computation, artist’s influence or Material (0.24) Material (0.21) Rick Rubin (0.17) of sampling and restrict ourselves to Katz centrality. sultingTo in construct the proposed the artist-level relational influencecollapse-and-sum matrixFab 5I Freddyfromapproach. (0.24) theRun-DMC (0.21) Public Enemy (0.17) how influential an artist is to a genre by taking ratios be- HankInfluential ShockleeA (0.23)( =0DJ. Premier2) (0.21) InfluencedLarry Smith( =0 (0.16).2) of sampling andThe restrict Katz influence ourselves matrix to KatzIK isincrease centrality. defined thevia allowable in-memory network size, and addi- tween theTo respective constructsong-level influence the network, graphs, artist-level among the song-level other influence tasks. network matrix isIThe firstA from Notorious used the to B.I.G. (0.97) Girl Talk (1.0) tionally releases any restriction on , allowing the user to The Katz influence matrix IK is defined via Secondly, by solely computing the influence onCollapse-and-Sum the acyclic, InfluenceDr. Dre (0.91) II Lil Wayne (0.80) 1 song-levelcompute network, the song the influence song-level matrix networkIS. GivenTable is first 3I.S Artist, we used thenSample-Based to Influence Rank for =0.0 IK =(I A)choose I any suitableunweighted weighting(2) song-level function. network, Application we can compute of thisI from a Puff Daddy (0.53) The Game (0.53) • Song-to-Artist,S (left), I , Nas=0 (0.5).2 (middle), and =1DJ.0 Premier(right). (0.40) 1 approach is foundshort, below finite incompute Section linearcompute combination 4. the asong derived of influence the powers artist influence of matrix the adja-I matrixS. GivenA, knowingIS, we then the IK =(I A) I (2) s d James Brown (0.42) Linkin Park (0.39) destination S destinationS destination where I is an identity matrix,A is the adjacency matrixcency as matrixcompute withoutsource any a andderived iterative destination procedure artist influence song and by sets know- matrixai andIAa,i knowingbelonging the to Ak B1 B2 C A B C A B C A k =1, 2, 3s... d A) Jester Hairston ing that the powerseach of the artist adjacencyai. To matrix do so,, we take each artistenceai ofin an the individual1 set.5 of artist by looking at the correspond- before, and is a decay factor which scales the indirect in- source and destination songA 1 sets.5 Sa A and1 S.5 a belongingA to where I is an identity matrix, A is the adjacency matrix as 4. APPLICATIONk i i B) The Impressions will go to zero when is greater than theB maximum1 1 sample B1 1ing rowB or column.2 Table 4, for example, names the top artists A and Table 4. Top InfluentialC) The Winstons and Influenced Artists of Jay-Z . fluence allowed to propagate though the network (larger each artist a . To do so, we take each artist1 a source in the set of i 2 1 B2 i C chain length of the network. With sparseB matrix represen- source before, and is a decay factor which scalesThree the levels indirect of influence in- analysis and rank are computed source for five influential and influenced artists of Jay-Z. Finally, we implies greater weight on indirect influence). This cantations, be this modification can greatly reducedC computation,C fluence allowed to propagate though the network (larger artists A andSum over the destination song sets of each artist Sd , song, artist, and genreincrease representations, the allowable in-memory providing network a small-to- size, and addi- can also computeInfluential thea(i =0 relative.2) proportionInfluenced ( =0 of.2) influence cre- written in equivalent form as • • Rank—sum rows or columns The Notorious B.I.G. (0.97) Girl Talk (1.0) implies greater weight on indirect influence).large inspection This can be oftionally the data. releases Various any restriction valuescollapsing of on the,are allowing appropriate used the to user columns to ated by of I eachS. Dr. song Dre (0.91) withind an artist’sLil Wayne overall (0.80) influence. The Sum over the destination song sets of each artist Sa , written in equivalent form as 2 2 comparek k direct to indirectchoose any influence. suitable weighting For this function. purpose,• ApplicationView (3) Column—“Who is of this top influenced three most the givenPuff influential Daddy artist” (0.53)i songsThe of Game James (0.53) Brown, for exam- I = A + A + ... + A + ..., (3) • Nass (0.5) DJ Premier (0.40) K approach1 is2 foundcollapsing belowSumk in1 Section overk the 4. the appropriate• sourceView Row—”Who song columns set the of given each of artistI artistS. influenced”S , col- rescaled to IK = A + A + ... +• A + ..., allowing ple, include “FunkyJamesai Brown Drummer” (0.42) Linkin (14%), Park (0.39) “Think (About It)” 2 2 k k lapsing the appropriate rows of I . IwhereK = weA can+ seeA that+ ... the+ influence A =0+ is..., ato weighted only account(3) sum of for direct sampling, =1to equally byS Lyn Collinss and produced by James Brown (9%), and Sum4. APPLICATION over the source song set of each artist Sa , col- account for direct and all indirect• sampling, and values be- “FunkyTable President” 4. Topi Influential (7.5%). and Similar Influenced measures Artists of Jay-Z can be . com- the powers of the adjacency matrix [14]. When the values Thelapsing result the of the appropriate process produces rows of anI artist-level. influence where we can see that the influence is atween weighted zero sum and one ofThree to preferentially levels of influence weight analysis direct and rank samples, are computed for putedS to indicate whether an artist gets more credit as a pro- of A are zero or one, the powers of the adjacency matrixsong, artist, and genrematrix representations,I which is providing directly a derived small-to- from the song-level mu- but also account for indirect sampling. A ducercan or also performer. compute the relative proportion of influence cre- the powers of the adjacency matrix [14]. When the valueslarge inspection of the data. Various values of are used to ated by each song within an artist’s overall influence. The 2 The song network is exactly acyclic and the artist network is nearly The resultsical material, of the process and is done produces so via linear an artist-level combinations influence of the of A are zero or one, the powers of the adjacency matrixcompare direct to indirect influence. For this purpose, (3) is top three most influential songs of James Brown, for exam- acyclic. 4.1 Song Influence matrixsong-levelIA which1 2 influence is directlyk 1 matrix.k derived The process from the can song-level be duplicated mu- rescaled to IK = A + A + ... + A + ..., allowing 4.3 Genreple, include Influence “Funky Drummer” (14%), “Think (About It)” 2 =0to onlysical account material, for direct and sampling, is done =1 so viato equally linear combinationsby Lyn Collins of and the produced by James Brown (9%), and The song network is exactly acyclic and the artistThe network song-level is nearly influence matrix IS is computed from the account for direct and all indirect sampling, and values be- The song-level“Funky President” influence (7.5%). matrix Similar can measures further can be be reduced com- to a acyclic. song network described insong-level Section 3.1. influence The most matrix. influential The process can be duplicated tween zero and one to preferentially weight direct samples, genre-basedputed to indicate influence whetherIG. an The artist most gets influential more credit as genres a pro- found songs are found in Table 2. We can observe the presence of but also account for indirect sampling. are: soul/funk/disco,ducer or performer. hip-hop/R&B, rock/pop, jazz/blues, and many popular samples including “Change the Beat” by Fab electronic dance, while the top influenced genres are hip- 5 Freddy and the “Amen”4.1 Song break Influence by The Winstons. It is par- 4.3 Genre Influence hip/R&B, electronic dance, rock/pop, other, and reggae (for The song-level influence matrix I is computed from the ticularly interesting to note that, for the “Amen”S break, as The song-level influence matrix can further be reduced to a song network described in Section 3.1. The most influential all values of ). Alternatively, the top songs and artist for increases, the credit of influence intuitively moves from The genre-based influence IG. The most influential genres found songs are found in Table 2. We can observe the presence of each genre can also be computed (omitted due to space con- are: soul/funk/disco, hip-hop/R&B, rock/pop, jazz/blues, and Winstons to The Impressions,many popular samples and finally including to Jester “Change Hairston. the Beat” by Fab straints).electronic dance, while the top influenced genres are hip- This is a result of5 a Freddy sample and chain the “Amen” between break by material The Winstons. origi- It is par- hip/R&B, electronic dance, rock/pop, other, and reggae (for ticularly interesting to note that, for the “Amen” break, as nating from Jester Hairston, that was first sampled by The all values of ). Alternatively, the top songs and artist for increases, the credit of influence intuitively moves from The Impressions, and then massively popularized by The Win- each genre can also5. be CONCLUSIONS computed (omitted due to space con- Winstons to The Impressions, and finally to Jester Hairston. stons. straints). This is a result of a sample chain between material origi- An analysis of music influence and rank of sample-based nating from Jester Hairston, that was first sampled by The music is presented using the WhoSampled.com dataset. Gen- 4.2 Artist Influence Impressions, and then massively popularized by The Win- eral genre and time-based5. CONCLUSIONS trends are found, identifying where stons. Starting with the song-level influence, we can collapse IS and whenAn analysis the sampling of music influence source and material rank of is sample-based coming from as music is presented using the WhoSampled.com dataset. Gen- to form an artist-based4.2 Artist influence Influence matrix IA. Table 3 shows well as differences in how various genres are sampling oth- eral genre and time-based trends are found, identifying where the top influential artists. 3 We can also inspect the influ- ers. Network graphs are employed to both understand gen- Starting with the song-level influence, we can collapse IS and when the sampling source material is coming from as 3 Entries with Fab 5to Freddy form an also artist-based include producers influence Material matrix IA and. Table Bee- 3 shows eral trendswell as differencesof sampling in how behavior, various genres but to are also sampling find oth- influence side. All three artists achievedthe top highinfluential influence artists. from3 “ChangeWe can also the Beat”. inspect the influ- rankers. over Network songs, graphs artists, are and employed genre. to both A method understand of gen- influence 3 Entries with Fab 5 Freddy also include producers Material and Bee- eral trends of sampling behavior, but to also find influence side. All three artists achieved high influence from “Change the Beat”. rank over songs, artists, and genre. A method of influence Ak have elements representing the number of sample chains of corresponding length k capturing various levels of indi- k rect influence.A have elements For stability, representing1/ themust number be greater of sample than chains the largestof eigenvalue corresponding of lengthA andk forcapturing large networks, various levels (2) becomes of indi- increasinglyrect influence. difficult For to stability, invert. Typically,1/ must only be greater the overall than the in- A fluencelargest rank eigenvalue is desired of andand is computed for large networks, iteratively (2) in becomes a fash- increasingly difficult to invert. Typically, only the overall in- ion to avoid a large memory footprint and matrix inverse fluence rank is desired and is computed iteratively in a fash- I requiredion to for avoidK . a large memory footprint and matrix inverse For our purposes, it is desirable to have both the entire in- required for IK . Figure 5. Cumulative In-degree Distribution P (k) of the fluenceFor matrix our purposes, and overall it is rank. desirable Given to haveIK , both we can the entire view in- the Sample-BasedFigure Song 5. Network Cumulative (log-log In-degree scale). Distribution P (k) of the columnfluence of a matrix node and to find overall who rank. influenced Given IK the, we node, can view or view the Sample-Based Song Network (log-log scale). the rowcolumn of the of a node node to to find who who influenced the node the influenced node, or view [15]. Summingthe row the of columns the node toof find the who influence the node matrix influenced produces [15]. a any of the very popular samples were to be removed, large rankingSumming of the the most columns influential of the nodes, influence while matrix summing produces the a any of the very popular samples were to be removed, large portions of sample-based music would cease to exist (or at rowsranking results inof a the ranking most influential of the most nodes, influenced while summing nodes. Such the portions of sample-based music would cease to exist (or at least be altered). analysisrows is results nicely in suited a ranking for of musicological the most influenced analysis nodes. and Such mo- least be altered). tivatesanalysis further is improvements nicely suited for discussed musicological below. analysis and mo- 3.2 Influence Measures tivates further improvements discussed below. 3.2 Influence Measures To analyze and rank influence within each network, four 3.3 Collapse-and-Sum Influence Rank To analyze and rank influence within each network, four 3.3 Collapse-and-Sum Influence Rank closely related measures are commonly used: degree cen- For the given dataset, we would like to understand and ana- closely related measures are commonly used: degree cen- For the given dataset, we would like to understand and ana- trality, eigenvectortrality, eigenvector centrality, centrality, Katz centrality, Katz centrality, and PageR- and PageR- lyze song, artist, and genre influence individually, as well as ank. Degree centrality does not capture any indirect form of lyze song, artist, and genre influence individually, as well as ank. Degree centrality does not capture any indirect form of howhow each each network network relates relates to to one one another. another. To To do do so, so, individ- individ- influence (asinfluence in the case (as in of the sample case of chains), sample chains), motivating motivating alter- alter- ual networks can be constructed for song, artist, and genre native methods. Eigenvector centrality extends degree cen- ual networks can be constructed for song, artist, and genre native methods. Eigenvector centrality extends degree cen- networksnetworks with with influence influence matrices matrices and and rank rank computed computed via via (2) (2) trality by weighting the importance of neighboring nodes to trality by weighting the importance of neighboring nodes to or (3).or Building (3). Building separate separate graphs, graphs, however, however, has has several several draw- draw- allow for indirectallow for influence, indirect influence, but has limited but has limited application application for for backs.backs. Most Most notably, notably, there there is nois no straightforward straightforward mechanism mechanism acyclic networks2 [13]. 2 Katz centrality and PageRank ap- acyclic networks [13]. Katz centrality and PageRank ap- to relateto relate the influence the influence matrices matrices of of each each network network together together ap- ap- propriately modify eigenvector centrality. Both also provide propriately modify eigenvector centrality. Both also provide propriately.propriately. Furthermore, Furthermore, we we would would like like to to model model the the influ- influ- a mechanism to capture indirect influence between nodes, a mechanism to capture indirect influence between nodes, enceence propagation propagation on the on the song-level song-level topology topology and and then then derive derive compute ancompute overall an influence overall influence rank among rank among each node, each node, and and artist and genre influence measures, as the compositional act observe the influence of one node to another. PageRank, artist and genre influence measures, as the compositional act observe the influence of one node to another. PageRank, of samplingof sampling is presumably is presumably based based on on the the musical musical material material it- it- however, down-weights influence created by a destination self, rather than artist or genre connections. however, down-weights influence created by a destination self, rather than artist or genre connections. node that samples more than once, or in the case of artist To address this issue, a single influence matrix is con- node that samples more than once, or in the case of artist To address this issue, a single influence matrix is con- nodes, down-weights influence from artists with lengthy ca- structed using the song-level network (see Section 3.1) and nodes, down-weightsreers. While influence this is desirable from artists in numerous with lengthy other ca- contexts structed using the song-level network (see Section 3.1) and reers. While this is desirable in numerous other contexts is used to create the artist and genre influence matrices, re- such as web search, we wish to equally weight each instance is usedsulting to create in the proposed the artist relational and genrecollapse-and-sum influence matrices,approach. re- such as webof search, sampling we and wish restrict to equally ourselves weight to Katz each centrality. instance sultingTo in construct the proposed the artist-level relational influencecollapse-and-sum matrix IA fromapproach. the of sampling andThe restrict Katz influence ourselves matrix to KatzI is centrality. defined via K To constructsong-level the network, artist-level the song-level influence network matrix isI firstA from used the to The Katz influence matrix IK is defined via Relating Influence Levels 1 song-levelcompute network, the song the influence song-level matrix networkIS. Given is firstIS, we used then to IK =(I A) I (2) 1 computecompute the asong derived influence artist influence matrix• I matrix S . vs. Given IA, knowingIS, we then the I =(I A) I (2) K Ss Sd where I is an identity matrix,A is the adjacency matrix as computesource a andderived destination artist influence song sets matrixai andIAdestinationa,i knowingbelonging the todestination A B1 B2 C a s da A B C each artist i. To do so, we takeS each artistA S 1 i in.5 the set of where I isbefore, an identity and matrix,is a decayA factoris the which adjacency scales matrix the indirect as in- source and destination song sets ai and ai belongingA to 1 .5 B1 1 fluence allowed to propagate though the network (larger eachartists artist Aa and. To do so, we take each artist a in the setB of 2 i B2 i 1 source before, and is a decay factor which scales the indirect in- source C implies greater weight on indirect influence). This can be C fluence allowed to propagate though the network (larger artists A andSum over the destination song sets of each artist Sd , written in equivalent form as • ai implies greater weight on indirect influence). This can be collapsing the appropriate• columnsCompute influence of IS. of song for artistd Sum over the destination song sets of each artist Sa , written in equivalent form as 2 2 k k • i.e. B1 / B = 50% influence from songi B1 IK = A + A + ... + A + ..., (3) • s collapsingSum over the the appropriate source song columns set• i.e. ofB2 / eachB of = 50%I artistS influence. S from, col- song B2 • ai 2 2 k k lapsing the appropriate rows of IS. IwhereK = weA can+ seeA that+ ... the+ influence A + is..., a weighted(3) sum of Sum over the source song set of each artist Ss , col- • ai the powers of the adjacency matrix [14]. When the values Thelapsing result the of the appropriate process produces rows of anI artist-level. influence where we can see that the influence is a weighted sum of S of A are zero or one, the powers of the adjacency matrix matrix IA which is directly derived from the song-level mu- the powers of the adjacency matrix [14]. When the values 2 The song network is exactly acyclic and the artist network is nearly The resultsical material, of the process and is done produces so via linear an artist-level combinations influence of the of A are zeroacyclic. or one, the powers of the adjacency matrix matrixsong-levelIA which influence is directly matrix. derived The process from the can song-level be duplicated mu- 2 The song network is exactly acyclic and the artist network is nearly sical material, and is done so via linear combinations of the acyclic. song-level influence matrix. The process can be duplicated or further reduced for other relations, such as artist-to-genre James Brown (1.0)or furtherJames reduced Brown (1.0) for otherJames relations, Brown (1.0)such as artist-to-genre James Brown (1.0) James Brown (1.0) James Brown (1.0) Dr. Dre (0.34) Dr. Dre (0.28) Run-DMC (0.25) Dr. Dre (0.34) Dr. Dre (0.28) Run-DMC (0.25) and song-to-genre influence. Marley Marl (0.29)and song-to-genreGeorge Clinton influence.(0.25) Fab 5 Freddy (0.23)4 Marley Marl (0.29) George Clinton (0.25) Fab 5 Freddy (0.23)4 Given the linear relationship from one network to the George Clinton (0.28)GivenMarley the Marl linear (0.25) relationshipGeorge Clinton from (0.22) one network to the George Clinton (0.28) Marley Marl (0.25) George Clinton (0.22) Public Enemy (0.27) Public Enemy (0.23) Russell Simmons (0.19) Public Enemy (0.27) Public Enemy (0.23) Russell Simmons (0.19) other, we can compute the relative proportions of influence Rick Rubin (0.25) Rick Rubin (0.22) Kool & the Gang (0.19) other, we can compute the relative proportions of influence Rick Rubin (0.25) Rick Rubin (0.22) Kool & the Gang (0.19) between networks. As a result, we can analyze how in- DJ Premier (0.25) Fab 5 Freddy (0.22) Marley Marl (0.18) between networks. As a result, we can analyze how in- DJ Premier (0.25) Fab 5 Freddy (0.22) Marley Marl (0.18) Material (0.24) Material (0.21) Rick Rubin (0.17) Material (0.24) fluentialMaterial a given (0.21) song is toRick an Rubin overall (0.17) artist’s influence or fluential a given song is to an overall artist’sor further influence reduced or for other relations, such as artist-to-genre James Brown (1.0) James Brown (1.0) JamesFab 5 Brown Freddy (0.24) (1.0) Run-DMC (0.21) Public Enemy (0.17) Fab 5 Freddy (0.24)how influentialRun-DMC (0.21) an artist isPublic toDr. a Dre Enemy genre (0.34) (0.17) by takingDr. ratios Dre (0.28) be- Run-DMCHank Shocklee (0.25) (0.23) DJ Premier (0.21) Larry Smith (0.16) how influential an artist is to a genre byand taking song-to-genre ratios be- influence. Hank Shocklee (0.23)tweenDJ the Premier respective (0.21) influenceLarryMarley Smith graphs, Marl (0.16) (0.29) among otherGeorge tasks. Clinton (0.25) Fab 5 Freddy (0.23)4 George Clinton (0.28) Marley Marl (0.25) George Clinton (0.22) tween the respective influence graphs, amongGiven other the tasks. linear relationship from oneSecondly, network by to solely the computing the influence on theSong acyclic, Influence Public Enemy (0.27) Public Enemy (0.23) TableRussell 3. Simmons Artist (0.19) Sample-Based Influence Rank for =0.0 Secondly, by solely computing the influenceother, on we the can acyclic, compute the relative proportionsunweighted of influence song-level network,Rick we Rubin can (0.25) computeRickIS from Rubin (0.22) a Kool & the Gang (0.19) Table 3. Artist Sample-Based Influence RankDJ Premier for (0.25) =0.0 Fab 5 Freddy (0.22) (left),Marley Marl=0 (0.18).2 (middle), and =1.0 (right). unweighted song-level network, we canbetween compute networks.IS from a As a result, we canshort, analyze finite how linear in- combinationChange ofChange the the Beat the (Female powers Beat (Female Version) Version) byof Fab the 5 by Freddy Fab adja- 5 (1.0) Freddy (1.0)Change theChange Beat the (Female Beat (Female Version) Version) by Fab 5 by Freddy Fab 5 (1.0) Freddy (1.0)Change theChange Beat (Femalethe Beat Version) (Female byVersion) Fab 5 byFreddy Fab 5 (1.0) Freddy (1.0) (left), =0.2 (middle), and =1.0 (right).MaterialAmen, BrotherAmen, (0.24) Brother by The Winstons by The Winstons (0.82)Material (0.82) (0.21)Amen, BrotherAmen, by BrotherRick The Winstons by RubinThe Winstons (0.74) (0.17) (0.74) Funky DrummerFunky Drummer by James by Brown James (0.84) Brown (0.84) short, finite linear combination of the powersfluential of a the given adja- song is to an overall artist’scency influence matrix without or any iterativeFabFunky 5 Freddy DrummerFunky procedure Drummer by (0.24) James by Brown James and (0.63) BrownRun-DMC by (0.63) know- (0.21)Funky DrummerFunky Drummer byPublic James by Brown James Enemy (0.71) Brown (0.17) (0.71) ImpeachImpeach the President the President by The Honey by The Drippers Honey Drippers(0.62) (0.62) La Di DaLa Di Di by Da Doug Di by E. Doug Freshk E. (0.53) Fresh (0.53) La Di DaLa Di Di by Da Doug Di by E. Doug Fresh E. (0.51) Fresh (0.51) SyntheticSynthetic Substitution Substitution by Melvin by Bliss Melvin (0.55) Bliss (0.55) how influential an artist is to a genre by takinging that ratios the powers be- of the adjacencyHankThink Shocklee (AboutThink matrix It) (About by Lyn (0.23) It)A Collins by Lyn, (0.49) Collinsk DJ=1 (0.49) Premier, 2, 3... (0.21)ImpeachImpeach the President theLarry President by The Smith Honey by The Drippers (0.16)Honey Drippers (0.49) (0.49)Get Up, GetGet Into Up, It,Get Get Into Involved It, Get Involved by James by Brown James (0.54) Brown (0.54) cency matrix without any iterative procedure and by know- ImpeachImpeach the President the President by The Honey by The Drippers Honey Drippers (0.44) (0.44)Think (AboutThink It)ence (About by Lyn It) Collins byof Lyn an (0.45) Collins individual (0.45) The artist Big BeatThe Big by Billy Beat looking Squier by Billy (0.51) Squier (0.51) at the correspond- k Funky PresidentFunky President by James by Brown James (0.35) Brown (0.35) Funky PresidentFunky President by James by Brown James (0.37) Brown (0.37) Scratchin’Scratchin’ by The Magic by The Disco Magic Machine Disco Machine (0.50) (0.50) tweenk the respective influence graphs, amongwill go other to zero tasks. when is greaterHere than WeHere Go (Live We the Go at (Live the maximum Funhouse) at the Funhouse) by Run-DMC by sample Run-DMC (0.34) (0.34)SyntheticSynthetic Substitutioning Substitution by row Melvin by or Bliss Melvin (0.36)column. Bliss (0.36) TableWe’re a WinnerWe’re 4, a by Winner for The Impressions by example, The Impressions (0.46) (0.46) names the top ing that the powers of the adjacency matrix A , k =1, 2, 3... ence of an individual artist by looking at theBring theBring correspond- Noise the by Noise Public by Enemy Public (0.33) Enemy (0.33) Here WeHere Go (Live We Go at the(Live Funhouse) at the Funhouse) by Run-DMC by Run-DMC (0.34) (0.34)AssemblyAssembly Line by Commodores Line by Commodores (0.46) (0.46) Secondly, by solely computing the influencechain on the length acyclic, of the network. WithSynthetic Substitution sparse by matrix Melvin Bliss (0.32) represen- Bring the Noisefive by Public influential Enemy (0.32) and influencedAmen by Jester Hairston artists (0.46) of Jay-Z. Finally, we will go to zero when k is greater than the maximum sample Table 3.Synthetic Artist Substitution Sample-Based by Melvin Bliss (0.32) InfluenceBring the Noise Rank by Public Enemy for (0.32) =0.0 Amen by Jester Hairston (0.46) unweighted song-level network,ing row we or can column. computetations, TableI thisfrom modification 4, a for example, can greatly names reduced the top computation, S (left), =0.2 (middle), and =1.0 (right). chain length of the network. With sparse matrix represen- five influential and influenced artists of Jay-Z. Finally,TableTable 2. Song we 2. SongSample-Based Sample-Based Influence Influence Rank forRank =0 for .0=0Influential(left),.0 (left), =0(.2 =0(middle),=0.2.2(middle),) and and=1Influenced.0 =1(right)..0 (right).( =0.2) short, finite linear combinationChange of the Beatthe (Female powers Version)increase by of Fab 5 the Freddy the (1.0) adja- allowableChange the Beat in-memory (Female Version) by network Fab 5 Freddy (1.0) size,Change and the Beat addi- (Female Version) by Fab 5 Freddy (1.0) tations, this modification can greatly reduced computation, Amen, Brother by The Winstons (0.82) Amen, Brother by The Winstons (0.74) Funky Drummer by James Brown (0.84) The Notorious B.I.G. (0.97) Girl Talk (1.0) cency matrix without any iterativeFunky Drummer procedure by James Browntionally and (0.63) by releases know-Funky any Drummer restriction by James Brown on (0.71) , allowingImpeach the the user President to by The Honey Drippers (0.62) Dr. Dre (0.91) Lil Wayne (0.80) increase the allowable in-memory network size, and addi- La Di Da Di by DougInfluential E. Freshchoose (0.53)k ( =0 any.2) suitableLa DiInfluenced Daweighting Di by Doug E.( Freshrank function.=0 (0.51) isrank. proposed,2) is proposed, Application in an effort in anSynthetic effort to unify Substitution of to unifyhigher-level this by higher-level Melvin artist Bliss (0.55) and artist and PuffSignal DaddySignal Processing,” (0.53) Processing,”In ProceedingsIn ProceedingsThe of Game the ofInternational (0.53) the International ing that the powers of the adjacencyThink (About matrix It) by Lyn CollinsA (0.49), k =1, 2, 3...Impeach the President by The Honey Drippers (0.49) Get Up, Get Into It, Get Involved by James Brown (0.54) Conference on Computer Music Impeach the PresidentThe by Notorious The Honey Drippers B.I.G. (0.44) (0.97) ThinkGirl (About Talk It) byence (1.0) Lyn Collinsgenre of (0.45)genre influence an influence individual measures measures asThe appropriate Big artist as Beat appropriate by Billy bylinear Squier looking linear combinations (0.51) combinations at theNas correspond- (0.5)Conference on Computer, MusicDJ 2008. Premier, 2008. (0.40) tionally releases any restriction on , allowing the user to Funky President by James Brownapproach (0.35) is foundFunky below President in by James Sectionof Brown song-levelof (0.37) song-level 4. network network influence.Scratchin’ influence. Empirical by The Empirical Magic results Disco Machine results suggest (0.50) suggest James Brown (0.42) Linkin Park (0.39) will go to zero when k is greater thanDr. the Dre maximum (0.91) sample Lil Wayne (0.80) [6] B.[6] Fields, B. Fields, C. Rhodes, C. Rhodes, M. Casey, M. Casey, and K. and Jacobson: K. Jacobson: “So- “So- Here We Go (Live at the Funhouse) by Run-DMC (0.34) Synthetic Substitutioning bysample-based Melvin rowsample-based Bliss or (0.36) column. musical musical networksWe’re networks Table a Winner follow byfollow 4, a The power-law for Impressions a power-law example, degree (0.46) degree names the top Bring the NoisePuff by Public Daddy Enemy (0.33) (0.53) HereThe We Go Game (Live at the(0.53) Funhouse) by Run-DMC (0.34) Assembly Line by Commodores (0.46) cial Playlistscial Playlists and Bottleneck and Bottleneck Measurements: Measurements: Exploiting Exploiting choose any suitable weighting function.chain Application length of of this the network. With sparse matrix represen- distribution;distribution; heavy heavy influence influence of funk, of funk,soul, and soul, disco and discomusic music Synthetic SubstitutionNas by (0.5) Melvin Bliss (0.32) BringDJ the Premier Noise byfive Public (0.40) Enemy influential (0.32) and influencedAmen by Jester Hairston artists (0.46) of Jay-Z.Musician Finally,Musician Social we Social Graphs Graphs Using Using Content-Based Content-Based Dissimi- Dissimi- 4. APPLICATIONon modernon modern hip-hop, hip-hop, R&B, R&B, and electronic and electronic music; music; and other and other approach is found below in Section 4. tations, this modification can greatly reduced computation, larity andlarity Pairwise and Pairwise Maximum Maximum Flow Values,” Flow Values,”In Proceed-In Proceed- James Brown (0.42) Linkin Park (0.39)musicologicalmusicological results. results. Table 4. Top Influential and Influenced Artists of Jay-Z . ings of the International Symposium on Music Informa- increase the allowable in-memory networkTable 2.Three Song size, Sample-Based levels and addi- of Influence influence Rank analysis for =0. and0 (left),Influential rank =0 are.2 ((middle), computed =0.2 and) for=1.0Influenced(right). ( =0.2) ings of the International Symposium on Music Informa- The Notorious B.I.G. (0.97) Girl Talk (1.0) tion Retrievaltion Retrieval, pp. 559–564,, pp. 559–564, 2008. 2008. tionally releases any restriction on , allowingsong, artist, the user and to genre representations, providing6. ACKNOWLEDGEMENTS6. ACKNOWLEDGEMENTS a small-to- 4. APPLICATION Dr. Dre (0.91) Lil Waynecan (0.80) also[7] compute N.[7] Collins: N. Collins: the “Computational relative “Computational Analysis proportion Analysis of Musical of of Musical Influ- influence Influ- cre- rank is proposed, in an effort to unify higher-level artist and This workSignal was made Processing,” possible fromIn Proceedings a generous collaboration of the International choose any suitable weightingTable function. 4. Top Application Influentiallarge inspection of and this Influenced of the data. Artists VariousThis of values workPuff Jay-Z Daddy was of made . (0.53) possibleare used from to a generousThe Game collaboration (0.53) ence:ence: A Musicological A Musicological Case Study Case Study Using Using MIR Tools,” MIR Tools,” genre influence measures as appropriate linear combinations with founderConference of WhoSampled.com, on Computer MusicNadav, Poraz, 2008. whoated pro- by each song within an artist’s overall influence. The Three levels of influence analysis and rank are computed for withNas founder (0.5) of WhoSampled.com, NadavDJ Poraz, Premier who (0.40) pro- In ProceedingsIn Proceedings of the of International the International Symposium Symposium on Mu- on Mu- approach is found below in Sectionof song-level 4. networkcompare influence. direct Empirical to results indirect suggest influence.videdvided access For access to the this to rich the purpose, and rich unique and unique dataset. (3) is dataset. Additional Additionaltop help three help most influential songs of James Brown, for exam- [6] B.James Fields, Brown C. Rhodes, (0.42) M. Casey, andLinkin K. Jacobson: Park (0.39) “So- sic Informationsic Information Retrieval Retrieval, pp. 177–182,, pp. 177–182, 2010. 2010. sample-based musical networks follow a power-law degree1 2 was providedwas providedk by1 National byk National Science Science Foundation Foundation Creative Creative IT IT song, artist, and genre representations, providing a small-to- can also computerescaled the relative to IK = proportionA + A + of... influence+cial PlaylistsA cre-+ and... Bottleneck, allowing Measurements:ple, Exploiting include “Funky Drummer” (14%), “Think (About It)” distribution; heavy influence of funk, soul, and disco music grantgrant No. IIS-0855758. No. IIS-0855758. [8] WhoSampled.com,[8] WhoSampled.com, Exploring Exploring and Discussing and Discussing the DNA the DNA =0to only account for direct sampling,Musician Social=1 Graphsto equally Using Content-Based Dissimi- large inspection of the data. Various values of are used to atedon modern by each hip-hop, song R&B, within and electronic an artist’s music; and overall other influence. The by Lyn Collinsof Music,of and Music, 2011. produced 2011.www.whosampled.comwww.whosampled.com by James. Brown. (9%), and 4. APPLICATION larity and Pairwise Maximum Flow Values,” In Proceed- musicological results.account for direct and all indirectTable 4sampling,. Top Influential7. and REFERENCES values and be- Influenced“Funky Artists[9] President” P. of Shannon, Jay-Z (7.5%). A. . Markiel, Similar O. Ozier, N. measures S. Baliga, J. can T. be com- compare direct to indirect influence. For this purpose, (3) is top three most influential songs of James Brown,ings for of the exam- International7. REFERENCES Symposium on Music Informa- [9] P. Shannon, A. Markiel, O. Ozier, N. S. Baliga, J. T. Wang,Wang, D. Ramage, D. Ramage, N. Amin, N. Amin, B. Schwikowski, B. Schwikowski, and T. and T. 1 2 k Three1 k levels of influence analysis and rank aretween computed zero and for one to preferentially[1] P.[1] Canotion P. weight Cano and Retrieval M. and direct Koppenberger:, M. pp. Koppenberger: 559–564, samples, “The 2008. “The Emergence Emergenceputed of toof indicate whether an artist gets more credit as a pro- rescaled to IK = A + A + ... + A + ..., allowing ple, include “Funky Drummer” (14%), “Think (About It)” Ideker:Ideker: “Cytoscape: “Cytoscape: A Software A Software Environment Environment for Inte- for Inte- song, artist, and genre representations,6. providing ACKNOWLEDGEMENTSbut also a small-to-account for indirect sampling.ComplexComplex Network Network Patterns Patterns in Music in Music Artist Artist Networks,” Networks,”ducer or performer. =0to only account for direct sampling, =1to equally can alsoIn[7] Proceedings N. compute Collins: of “Computational the the International relative Analysis Symposium proportion of on Musical Mu- of Influ- influencegratedgrated Models cre- Models of Biomolecular of Biomolecular Interaction Interaction Networks.” Networks.” byThis Lyn work Collins was made possible and produced from a generous by collaboration James BrownIn (9%), Proceedings and of the International Symposium on Mu- Genome Research, 13(11), pp. 2498-2504, 2003. large inspection of the data. Various values of are used to sic Informationence: A Musicological Retrieval, pp. 466–469, Case Study 2004. Using MIR Tools,” Genome Research, 13(11), pp. 2498-2504, 2003. account for direct and all indirect sampling, and values be- with founder of WhoSampled.com, Nadav Poraz, who pro-ated by eachsic Information song within Retrieval, pp.an 466–469, artist’s 2004. overall influence. The “Funky President”4.1 (7.5%). Song Influence Similar measures canIn Proceedings be com- of the International Symposium on Mu-[10] R. Lambiotte and M. Ausloos: “On the Genre-fication of compare direct to indirect influence.vided access For to the this rich and purpose, unique dataset. (3) is Additional help [2] P. Cano, O. Celma, M. Koppenberger, and J. Martin-4.3 Genre[10] Influence R. Lambiotte and M. Ausloos: “On the Genre-fication of top three[2]sic most P. Cano, Information influential O. Celma, Retrieval M. Koppenberger, songs, pp. 177–182, of James and 2010. J. Martin- Brown,Music: for Aexam- Percolation Approach (Long Version).” The tween zero and one to preferentially weight direct samples, 1 puted2 was provided to indicatek by1 Nationalk whether Science Foundation an artist Creative gets more IT creditBuldu:´ “Topology as a pro- of Music Recommendation Net- Music: A Percolation Approach (Long Version).” The rescaled to IK = A + A + ... + AThe+ song-level..., allowing influence matrix I Buldisu:´ computed “Topology fromof Music the Recommendation Net- European Physical Journal B, 50 (1-2), pp. 183-188, ple, includeworks,”[8]S WhoSampled.com,Chaos “Funky An Interdisciplinary Drummer” Exploring Journal and (14%),Discussing of Nonlin- “Think the DNA (AboutEuropean It)” Physical Journal B, 50 (1-2), pp. 183-188, but also account for indirect sampling. ducergrant No. or IIS-0855758. performer. works,” Chaos An Interdisciplinary JournalThe of Nonlin- song-level2006. influence matrix can further be reduced to a =0 =1 ear Science www.whosampled.com 2006. to only account for direct sampling, song networkto equally described inby Section Lyn Collins 3.1.ofear Music, Science The, 2006. 2011. and most, 2006. produced influential by James. Brown (9%), andI genre-based[11] P. influence R. La Monica:G. “Music The most Industry influential Sues Swappers: genres found account for direct and all indirect sampling,7.songs REFERENCES and are values found be- in Table 2. We can observe the presence of [11] P. R. La Monica: “Music Industry Sues Swappers: “Funky[3] K.[9][3] Jacobson, President” P. K. Shannon, Jacobson, M. Sandler, A. M. (7.5%). Markiel, Sandler, and B. and O. Fields: Similar Ozier, B. Fields: “Using N. S.“Using measures Audioare: Baliga, Audio soul/funk/disco, J. T. canRIAA be Says com- 261 hip-hop/R&B, Cases Pursued for Illegal rock/pop, Distribution jazz/blues, of and 4.1 Song Influence AnalysisWang, and D. Network Ramage, Structure N. Amin, to Identify B. Schwikowski, Communi- and T. RIAA Says 261 Cases Pursued for Illegal Distribution of tween zero and one to preferentially4.3[1] P. Genre Cano weight and Influence M.many Koppenberger: direct popular samples, “The samples Emergence includingputed of to “Change indicateAnalysis the and whether Network Beat” Structure by an Fab artist to Identify gets Communi- more creditCopyrighted asCopyrighted a pro- Music; Music; Amnesty Amnesty Program Program Offered.” Offered.”CNN CNN ties inIdeker: On-line “Cytoscape: Social Networks A Software of Artists,” EnvironmentIn Proceed-electronic for Inte- dance, while the top influenced genres are hip- Complex Network5 Patterns Freddy in and Music the Artist “Amen” Networks,” break by Theties in Winstons. On-line Social It Networks is par- of Artists,” In Proceed- Money,Money, Technology Technology News, News September, September 8, 2003. 8, 2003. The song-level influence matrix I is computedbut also account from the for indirect sampling. ducerings or performer. ofgrated the International Models of Biomolecular Symposium on Interaction Music Informa- Networks.” S TheIn song-level Proceedings of influence the International matrix Symposium can on further Mu- be reducedings of the International to a Symposium on Musichip/R&B, Informa- electronic dance, rock/pop, other, and reggae (for ticularly interesting to note that,tion for RetrievalGenome thetion Retrieval “Amen”, Research pp. 269–274,, pp. break,, 269–274, 13(11), 2008. as pp. 2008. 2498-2504, 2003. [12] A.[12] Clauset, A. Clauset, C. R. Shalizi, C. R. Shalizi, and M. and E. J. M. Newman: E. J. Newman: “Power- “Power- song network described in Section 3.1. The most influential sic Information Retrieval, pp. 466–469, 2004. all values oflaw Distributions). Alternatively, in Empirical the Data.” top SIAM songs Review and artist for genre-based influence IG. The most influential genres found law Distributions in Empirical Data.” SIAM Review 4.1 Song Influence increases, the credit of influence[4][10] K.intuitively[4] Jacobson R. K. Lambiotte Jacobson and moves M. and Sandler: M. M. from Ausloos: Sandler: “Musically The “On “Musically the Meaningful Genre-fication Meaningful of 51(4), 661-703 (2009). songs are found in Table 2. We can observe the presence of [2] P. Cano, O. Celma, M. Koppenberger, and J. Martin-4.3 Genre Influence each genre can51(4), also 661-703 be computed (2009). (omitted due to space con- Winstons to The Impressions, andor finally JustMusic:or Noise? Just to A Noise? Percolation Jester An Analysis An Hairston. Analysis Approach of On-line of (Long On-line Artist Version).” Artist Net- Net-The are:Buld soul/funk/disco,u:´ “Topology of Music hip-hop/R&B, Recommendation rock/pop, Net- jazz/blues, and [13] M. E. J. Newman: Networks: An Introduction, Oxford many popular samples including “Change the Beat” by Fab I works,”Europeanworks,”ComputerComputer Physical Music Music Modeling Journal Modeling Band, 50 Retrieval. and (1-2), Retrieval. pp.straints). Gen- 183-188, Gen- [13] M. E. J. Newman: Networks: An Introduction, Oxford The song-level influence matrixworks,”S Chaosis computed AnThis Interdisciplinary is a from result Journal the of a of sample Nonlin- chain between material origi- University Press, New York, 2010. electronic dance, while the top influencedThe song-level genresesis of2006.esis Meaning ofare Meaning influence hip- in Sound in Sound and matrix Music and Music, eds. can, S. eds. further Ystad, S. Ystad, be reducedUniversity to a Press, New York, 2010. 5 Freddy and the “Amen” break by The Winstons.song network It is described par- in Sectionear Science 3.1., The 2006. most influential R Kronland-Martinet, and K. Jension. Springer-Verlag, hip/R&B, electronicnating dance, from Jester rock/pop, Hairston, other,genre-based that and wasR reggae Kronland-Martinet, first influence sampled (for IG and by. The K. The Jension. most Springer-Verlag, influential[14] genres L.[14] Katz: L. Katz:found “A New “A Status New Status Index IndexDerived Derived From Sociomet- From Sociomet- songs are found in Table 2. We can observe the presence of [11]Berlin, P.Berlin, pp. R. 107–118, La pp. Monica: 107–118, 2009. 2009. “Music Industry Sues Swappers: ric Analysis,”5.Psychometrika CONCLUSIONS18, 1953. ticularly interesting to note that, for the “Amen” break, as [3] K. Jacobson, M.Impressions, Sandler, and B. Fields: and “Using then massively Audio popularizedRIAA Says 261 by Cases The Pursued Win- for Illegal Distribution of ric Analysis,” Psychometrika 18, 1953. all values of ). Alternatively, the topare: songs[5] soul/funk/disco, B. and Fields, artist K. Jacobson, for hip-hop/R&B, M. Casey, and M. Sandler: rock/pop, “Do jazz/blues, and many popular samples includingAnalysis “Change and Network thestons. Beat” Structure by to Identify Fab Communi- [5]Copyrighted B. Fields, K. Jacobson,Music; Amnesty M. Casey, Program and M. Offered.” Sandler: “DoCNN[15] C. H. Hubbel: “An Input-Output Approach to Clique increases, the credit of influence intuitively moves from The You Sound Like Your Friends? Exploring Artist Simi- [15] C. H. Hubbel: “An Input-Output Approach to Clique eachties genre in On-line can Social also Networks be computed of Artists,” In (omitted Proceed-electronic due toMoney,You space dance, Sound Technology con- Like while Your News Friends? the, September top Exploring influenced 8, 2003. ArtistAn Simi- analysis genresIdentification,” of are music hip-Sociometry influence28 (4), and pp. 377–399, rank of 1965. sample-based 5 Freddy and the “Amen” break by The Winstons. It is par- larity via Artist Social Network Relationships and Audio Identification,” Sociometry 28 (4), pp. 377–399, 1965. Winstons to The Impressions, and finally to Jester Hairston. ings of the International Symposium on Music Informa-hip/R&B,larity electronic via Artist Social dance, Network rock/pop, Relationshipsmusic other, and Audio is and presented reggae using (for the WhoSampled.com dataset. Gen- ticularly interesting to notestraints). that,tion for Retrieval the “Amen”, pp.4.2 269–274, Artist break, 2008. Influence as [12] A. Clauset, C. R. Shalizi, and M. E. J. Newman: “Power- This is a result of a sample chain between material origi- all valueslaw of Distributions). Alternatively, in Empirical Data.” the top SIAMeral songs Review genre and and artist time-based for trends are found, identifying where increases, the credit of influence[4] K. intuitively Jacobson and moves M. Sandler: from “Musically The Meaningful nating from Jester Hairston, that was first sampled by The Starting with the song-leveleach influence, genre51(4), can we 661-703 also can (2009). be collapse computedIS (omittedand when due to the space sampling con- source material is coming from as Winstons to The Impressions, andor Just finally Noise? to An Jester Analysis Hairston. of On-line Artist Net- Impressions, and then massively popularized by The Win- works,” Computerto Music form5. Modeling CONCLUSIONS an artist-based and Retrieval. influence Gen-straints).[13] matrix M. E. J.IA Newman:. TableNetworks: 3 shows An Introductionwell, Oxford as differences in how various genres are sampling oth- 3 stons. This is a result of a sample chainesis of between Meaningthe in material Sound top influential and Music origi-, eds. artists. S. Ystad, We canUniversity also inspect Press, New the York, influ- 2010. ers. Network graphs are employed to both understand gen- An analysisR Kronland-Martinet, of music and K. influence Jension. Springer-Verlag, and rank of[14] sample-based L. Katz: “A New Status Index Derived From Sociomet- nating from Jester Hairston, that was first sampled3 Entries with by The Fab 5 Freddy also include producers Material and Bee- eral trends of sampling behavior, but to also find influence musicBerlin, is presented pp. 107–118, 2009. using the WhoSampled.com dataset.ric Analysis,” Gen-Psychometrika5. CONCLUSIONS18, 1953. 4.2 Artist Influence Impressions, and then massively popularizedside. by All three The artists Win- achieved high influence from “Change the Beat”. rank over songs, artists, and genre. A method of influence stons. eral[5] genre B. Fields, and K. Jacobson, time-based M. Casey, trends and M. Sandler: are found, “Do identifying[15] C. H. Hubbel: where “An Input-Output Approach to Clique You Sound Like Your Friends? Exploring Artist Simi-An analysisIdentification,” of musicSociometry influence28 (4), pp. and 377–399, rank 1965. of sample-based Starting with the song-level influence, we can collapse I larity via Artist Social Network Relationships and Audio S and when the sampling source materialmusic is coming is presented from using as the WhoSampled.com dataset. Gen- 4.2 Artist Influence to form an artist-based influence matrix IA. Table 3 shows well as differences in how various genreseral are genre sampling and time-based oth- trends are found, identifying where the top influential artists. 3 We can also inspect the influ- Starting with the song-levelers. influence, Network we graphs can collapse are employedIS to bothand whenunderstand the sampling gen- source material is coming from as 3 Entries with Fab 5 Freddy also include producersto form Material an artist-based and Bee- influenceeral trends matrix ofI samplingA. Table 3 behavior, shows but towell also as find differences influence in how various genres are sampling oth- side. All three artists achieved high influence fromthe “Change top influential the Beat”. artists. 3rankWe over can also songs, inspect artists, the and influ- genre. Aers. method Network of influence graphs are employed to both understand gen- 3 Entries with Fab 5 Freddy also include producers Material and Bee- eral trends of sampling behavior, but to also find influence side. All three artists achieved high influence from “Change the Beat”. rank over songs, artists, and genre. A method of influence or further reduced for other relations, such as artist-to-genre James Brown (1.0) James Brown (1.0) James Brown (1.0) Dr. Dre (0.34) Dr. Dre (0.28) Run-DMC (0.25) and song-to-genre influence. Marley Marl (0.29) George Clinton (0.25) Fab 5 Freddy (0.23)4 Given the linear relationship from one network to the George Clinton (0.28) Marley Marl (0.25) George Clinton (0.22) Public Enemy (0.27) Public Enemy (0.23) Russell Simmons (0.19) other, we can compute the relative proportions of influence Rick Rubin (0.25) Rick Rubin (0.22) Kool & the Gang (0.19) between networks. As a result, we can analyze how in- DJ Premier (0.25) Fab 5 Freddy (0.22) Marley Marl (0.18) Material (0.24) Material (0.21) Rick Rubin (0.17) fluential a given song is to an overall artist’s influence or Fab 5 Freddy (0.24) Run-DMC (0.21) Public Enemy (0.17) how influential an artist is to a genre by taking ratios be- Hank Shocklee (0.23) DJ Premier (0.21) Larry Smith (0.16) tween the respective influence graphs, among other tasks. Secondly, by solely computing the influence on the acyclic, Table 3. Artist Sample-Based Influence Rank for =0.0 unweighted song-level network, we can compute I from a S (left), =0.2 (middle), and =1.0 (right). short, finite linear combination of the powers of the adja- or further reducedcency for matrix other without relations, any iterativesuch as artist-to-genreprocedure and by know- James Brown (1.0) James Brown (1.0) James Brown (1.0) ing that the powers of the adjacency matrix Ak, k =1, 2, 3... Dr. Dre (0.34) Dr. Dre (0.28) Run-DMC (0.25) and song-to-genre influence. Marleyence Marl (0.29)of an individualGeorge Clinton artist (0.25) by lookingFab 5 Freddyat the (0.23) correspond-4 Givenor the furtherwill linear go reduced to relationship zero when for otherk fromis greater relations, one than network such the maximum as to artist-to-genre the sample Georgeing Clinton rowJames (0.28) or column. BrownMarley (1.0) Marl Table (0.25)James 4, for Brown example,George (1.0) Clinton names (0.22)James the Brown top (1.0) Public Enemy (0.27)Dr. Dre (0.34)Public Enemy (0.23)Dr. Dre (0.28)Russell SimmonsRun-DMC (0.19) (0.25) chain length of the network. With sparse matrix represen-James Brownfive influential (1.0) andJames influenced Brown artists (1.0) of Jay-Z.James Finally, Brown we (1.0) 4 or further reducedother, for other weand can relations, song-to-genre compute the such relative influence. as artist-to-genre proportions of influence Rick Rubin (0.25)Marley MarlRick (0.29) Rubin (0.22)George ClintonKool & (0.25) the GangFab (0.19) 5 Freddy (0.23) between networks.Giventations, the thisAs linear amodification result, relationship we can can greatly analyze from reduced one how network computation, in- toDr. theDJ Dre Premier (0.34) (0.25)George ClintonFabDr. 5 (0.28) Freddy Dre (0.28) (0.22)Marley MarlMarley (0.25) MarlRun-DMC (0.18)George (0.25) Clinton (0.22) and song-to-genre influence. Material (0.24) PublicInfluential EnemyMaterial( (0.27) =0 (0.21).2) PublicInfluenced EnemyRick (0.23)Rubin( =0 (0.17).2)Russell Simmons (0.19)4 fluentialother, a givenincrease we song can the iscompute allowable to an overall the in-memory relative artist’s proportions network influence size, or of and influence addi-Marley Marl (0.29) George Clinton (0.25) Fab 5 Freddy (0.23) GeorgeFab 5 Clinton Freddy (0.24)Rick (0.28)The Rubin NotoriousRun-DMC (0.25)Marley B.I.G. (0.21) Marl (0.97)Rick (0.25) RubinGirlPublic Talk (0.22) (1.0) EnemyGeorge (0.17)Kool Clinton & the Gang (0.22) (0.19) Given the linear relationshiptionally from releases one any restriction network on to, allowing the the user to Hank ShockleeDJ (0.23) PremierDr. DreDJ (0.91) (0.25) Premier (0.21)Fab 5Lil Freddy WayneLarry (0.22) Smith(0.80) (0.16)Marley Marl (0.18) how influentialbetween an networks. artist is to As a genre a result, by taking we can ratios analyze be- howPublic in- Enemy (0.27) Public Enemy (0.23) Russell Simmons (0.19) other, we can computetween thefluential respective relativechoose a given any influence proportions suitable song graphs, weighting is to of an among influencefunction.overall other artist’s Application tasks. influence of this or MaterialPuff Daddy (0.24) (0.53) MaterialThe (0.21) Game (0.53) Rick Rubin (0.17) approach is found below in Section 4. Rick Rubin (0.25)FabNas 5 Freddy (0.5) Rick (0.24) RubinRun-DMC (0.22)DJ Premier (0.21) (0.40)KoolPublic & the Enemy Gang (0.17) (0.19) Secondly,how by solely influential computing an artist the is influence to a genre on the by acyclic, taking ratiosDJ be- Premier (0.25)HankJames Shocklee BrownFab (0.23) (0.42) 5 FreddyDJ Premier (0.22)Linkin (0.21) Park (0.39)MarleyLarry Marl Smith (0.18) (0.16) between networks. As a result, we can analyze how in- . ArtistArtist Sample-BasedJames Brown (1.0)Influence InfluenceJames Rank Brown for (1.0) =0 .0 James Brown (1.0) or further reduced for other relations, such as artist-to-genreTable 3 James Brown (1.0) James Brown (1.0) James Brown (1.0) unweightedtween song-level theor furtherrespective network, reduced influence we can for computeother graphs, relations,I amongS from such other a as tasks. artist-to-genreMaterial (0.24) Dr. DreMaterial (0.34) (0.21) Dr. Dre (0.28)Rick Rubin (0.17)Run-DMC (0.25) fluential a given song is to an overall artist’s influence or (left), =0.2 (middle),Dr. and Dre (0.34)=1.0 (right).Dr. Dre (0.28) Run-DMC (0.25)4 and song-to-genreJames influence. Brown4. APPLICATION (1.0) James Brown (1.0) JamesFab Brown 5 Freddy (1.0) (0.24) MarleyRun-DMC Marl (0.29) (0.21) George ClintonPublic (0.25) Enemy (0.17)Fab 5 Freddy (0.23) 4 or further reduced for other relations, such as artist-to-genreshort, finiteSecondly, linearand combination by song-to-genre solely computing of the influence. powers the influence of the adja- on the acyclic, Marley Marl (0.29) George Clinton (0.25) Fab 5 Freddy (0.23) Dr. Dre (0.34) Dr. Dre (0.28) Run-DMCHank (0.25) ShockleeTableTable (0.23) 4. Top 3George.Artist InfluentialDJ Clinton Premier Sample-Based and (0.28) (0.21) InfluencedMarley Influence Artists MarlLarry (0.25) of Smith Rank Jay-Z (0.16) . forGeorge =0 Clinton.0 (0.22) how influential ancency artist matrixunweighted isGiven to without a the genre song-level any linear iterative by relationship taking network, procedure ratios we from and can be- by compute one know- networkI from to a the 4 George Clinton (0.28) Marley Marl (0.25) George Clinton (0.22) and song-to-genre influence. Three levelsGivenMarley of influence the Marl linear (0.29) analysis relationshipGeorge and rank Clinton are from computed (0.25) oneS Fab network for 5 FreddyJames (0.23) to Brown the (1.0) James Brown (1.0) James Brown (1.0) or further reduced for other relations, such ask artist-to-genre (left), Public=0. Enemy2Public(middle), Enemy (0.27) (0.27) andPublic =1Public Enemy.0 Enemy(right). (0.23) (0.23) RussellRussell Simmons Simmons (0.19) (0.19) ing thatother, theshort, powers we finite can of thelinear computeGeorge adjacency combination Clinton the matrix (0.28) relative ofAMarley the, proportionsk =1 powers Marl, (0.25)2, 3... of of theGeorge influence adja- ClintonDr. Dre (0.22) (0.34) Dr. Dre (0.28) Run-DMC (0.25) Given the linear relationshiptween the from respective one network influence to thesong,other, graphs, artist, we and can amonggenre compute representations, other the relativetasks. providing proportions a small-to-ence of influence of an individualRick RubinartistRick (0.25) Rubin by looking (0.25) Rick at the RubinRick correspond- Rubin (0.22) (0.22) KoolKool & the & Gang the Gang (0.19) (0.19) Public Enemy (0.27) Public Enemy (0.23) Russell Simmonscan (0.19) also compute the relative proportion of influence cre-4 andwill song-to-genre gobetween tocency zero when matrix influence. networks.k withoutis greater As any than a iterative result, the maximum procedure we can sample analyze and by know- howing in- rowMarley or Marl column. 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• Top influential genres • Soul/funk/disco • Hip-hip/R&B • Rock/Pop • Jazz/Blues • Electronic/Dance • Top influenced genres • Hip-hop/R&B • Electronic/Dance • Rock/Pop • Reggae Acknowledgments & Thanks!

• Nadav Poraz & WhoSampled.com • National Science Foundation Creative IT grant No. IIS-0855758 • Reviewers! Musical Influence Network Analysis and Rank of Sample-Based Music

Nicholas J. Bryan and Ge Wang

Stanford University | CCRMA

ISMIR 2011