CONTINUOUS PLSI AND SMOOTHING TECHNIQUES FOR HYBRID MUSIC RECOMMENDATION

Transcription

1 10th International Society for Msic Information Retrieal Conference (ISMIR 2009) CONTINUOUS PLSI AND SMOOTHING TECHNIQUES FOR HYBRID MUSIC RECOMMENDATION Kayoshi Yoshii Masataka Goto National Institte of Adanced Indstrial Science and Technology (AIST) ABSTRACT This paper presents an extended probabilistic latent semantic indexing (plsi) for hybrid msic recommendation that deals with rating data proided by sers and with contentbased data extracted from adio signals. The original plsi can be applied to collaboratie filtering by treating sers and items as discrete random ariables that follow mltinomial distribtions. In hybrid recommendation, it is necessary to deal with msical contents that are sally represented as continos ectorial ales. To do this, we propose a continos plsi that incorporates Gassian mixtre models. This extension, howeer, cases a seere local optima problem becase it increases the nmber of parameters drastically. This is considered to be a major factor generating hbs, which are items that are inappropriately recommended to almost all sers. To sole this problem, we tested three smoothing techniqes: mltinomial smoothing, Gassian parameter tying, and artist-based item clstering. The experimental reslts reealed that althogh the first method improed nothing, the others significantly improed the recommendation accracy and redced the hbness. This indicates that it is important to appropriately limit the model complexity to se the plsi in practical. 1. INTRODUCTION The msical tastes of sers of online msic distribtion serices that proide millions of items are strongly inflenced by the characteristics of the msic atomatically recommended by those serices. Users often hae difficlty retrieing nknown items they might like. In sch case, sers consider recommendations and get aware of what kinds of items are their faorites. When only poplar items are always recommended, sers are not exposed to items they might enjoy more and get sed to enjoying only the safe recommendations. This in trn strengthens the tendency to recommend only poplar items. In other words, there is a seere limitation in serendipity of msic discoery. In fact, this negatie-feedback phenomenon has been obsered in many serices based on collaboratie filtering. We aim to enhance the serendipity by transforming the Permission to make digital or hard copies of all or part of this work for personal or classroom se is granted withot fee proided that copies are not made or distribted for profit or commercial adantage and that copies bear this notice and the fll citation on the first page. c 2009 International Society for Msic Information Retrieal. Rating data Content-based data 1 likes c a Featres 2 likes a b b Featres 3 likes b c Featres Example of recommendation 9 likes c Featres The objectie is to recommend Recommender Train continos-plsi model items to who likes c Topic 1 Topic 2 Topic 3 Topic 5 a b c Estimation of msical tastes is likely to select Topic 3 is recommended to Figre 1. Hybrid recommender based on continos plsi. passie experience in which sers only receie defalt recommendations into an interactie experience in which sers can freely cstomie (personalie) those recommendations. To achiee this, it is necessary to let sers clearly nderstand and express their own msical tastes that are estimated as bases of making defalt recommendations. The conentional reasoning like Yo like A, so yo wold like B becase other sers who like like A also like B is a relatie expression of msical tastes. We aim to obtain a direct expression of each ser s msical tastes that is easy to se as a basis for interactie recommendation. A promising way to do this is to se probabilistic latent semantic indexing (plsi) based on a mlti-topic model, which has been originally sed for docment modeling [1]. The model incldes latent ariables corresponding to the concepts of topics. How likely a docment and a word cooccr is predicted by stochastically associating each docment and word with a topic. Docments and words that are strongly associated with the same topic are likely to occr jointly. The model can be applied to collaboratie filtering based on rating histories by treating docments and words as sers and items [2]. Gien a ser, we can predict how likely each item is prchased by estimating how likely the ser chooses each topic. The msical tastes of sers can be expressed as the strength of ser-topic associations. As shown in Figre 1, we propose continos plsi for hybrid recommendation that enhances serendipity by combining rating data with content-based data extracted from msical adio signals. Specifically, Gassian mixtre models (GMMs) are bilt into the collaboratie filtering model of plsi in order to address continos ectorial data. Unlike the major collaboratie methods relying on heristics [3,4], the plsi model can be extended in a consistent manner becase it is flexible and has a theoretical basis. 339

2 Oral Session 4: Msic Recommendation and Playlist Generation The continos plsi, howeer, sffers from a serios local optima problem becase a nmber of parameters linearly increases according to data sie. This cases the hb phenomenon [5], in which specific items are almost always recommended to sers regardless of their rating histories. Ths, the serendipity of recommendations is insfficient. Althogh a similar probabilistic model was proposed for genre classification [6], this problem was not addressed. To sole this problem, we propose three smoothing techniqes: mltinomial smoothing, Gassian parameter tying, and artist-based item clstering. The first techniqe is expected to aoid oerfitting and the other two redce the model complexity. We compared the effectieness of these techniqes experimentally. The rest of this paper is organied as follows. Section 2 introdces related work. Section 3 explains a model of the continos plsi. Section 4 describes the three smoothing techniqes. Section 5 reports or experiments. Section 6 smmaries the key findings of this paper. 2. RELATED WORK Msic recommendation is an important topic today in the field of msic information processing. Conentional stdies on recommendation hae been intended to deal with textal data (docments and words). In addition, many researchers hae proposed arios ideas to make the most of content-based data that is atomatically extracted from msical adio signals. For example, Logan [7] proposed a content-based recommender based on the cosine distance between a ser s faorite items and non-rated items. Magno and Sable [8] reported sbjectie experiments showing that a content-based recommender competes against Last.fm (a collaboratie recommender) and Pandora (a recommender based on manal annotations) in terms of ser satisfaction. These reports indicate the synergistic effect of integrating rating data with content-based data. Hybrid recommenders hae been actiely inestigated recently. Celma et al. [9] sed both content-based similarity and ser profiles gien in RSS feeds to choose sitable items. Tiemann et al. [10] integrated two weak learners (social and content-based recommenders) by sing an ensemble learning method. Another important isse is how to present recommendations to sers. Donaldson and Knopke [11] isalied the relationships of recommended items in a two dimensional space. Lamere and Maillet [12] proposed a transparent and steerable interface for a recommender based on crowds of social tags. A common concept of these stdies seems to be that sers had better actiely explore or control recommendations. This wold reslt in enhanced serendipity. The existence of hbs has recently been recognied as a serios problem. Interestingly, this problem was not reported in the field of text-based recommendation. In msic recommendation and retrieal, GMMs are generally sed to represent the distribtions of acostic featres. Acotrier et al. [5] pointed ot that this kind of modeling tends to create hbs that are wrongly ealated as similar to all other items. Berenweig [13] conclded that the hb phenomenon is related to the crse of dimensionality. Chordia et al. [14] discssed content-based recommendation based on the Earth-Moers distance between GMMs of indiidal items. They empirically fond that a homogeniation method can improe performance [15]. Hoffman et al. [16] tried to sole this problem by sing the hierarchical Dirichlet process (HDP) for modeling content-based data. Unlike the GMM, the HDP represents each item as a mixtre of an nfixed nmber of Gassians. The nmber is atomatically adjsted to match the data complexity. In addition, the same set of Gassians is sed to model all items, with only the mixtre weights arying from item to item. This is similar to Gassian parameter tying. 3. CONTINUOUS PLSI This section explains a continos plsi model and a training method sitable for efficient parallel processing. 3.1 Problem Statement We define seeral symbols from a probabilistic iewpoint. Let U = { 1, 2,, U } be the set of all sers, where U is the nmber of them, and let V = { 1, 2,, V } be the set of all items, where V is the nmber of them. Let and be discrete random ariables respectiely taking the ales of one member of U and one member of V.Let X = {x 1, x 2,, x V } denote content-based data that is a set of D-dimensional featre ectors extracted from indiidal items. Let x be a continos random ariable in the D-dimensional space. Probabilistic distribtions are represented as p(ariable) or p(ariable1 ariable2),e.g.,a discrete distribtion p() or a conditional continos distribtion p(x ). For example, probabilities or probability densities are gien by p( = i ) or p(x = x j = i ), which are simply described as p( i ) or p(x j i ). As to aailable rating data, we mainly assme implicit ratings sch as prchase histories or listening conts, which are recorded atomatically een when sers do not explicitly express their preferences for indiidal items. In general, the nmber of implicit ratings tends to be mch larger than that of explicit ratings. We ths think that the former are more sitable to probabilistic approaches becase for them the sparseness problem is less serios. The total aailable data (combinations of rating data and content-based data) is gien by O = {( (1), (1), x (1) ),, ( (N), (N), x (N) )}, where( (n), (n), x (n) )(1 n N) is a ser-item-featre co-occrrence that ser (n) has prchased (iewed or listened to) item (n) with featre x (n) and N is the nmber of co-occrrences. Let c(, ) be the nmber of times that co-occrrence (,, x) was obsered. Obiosly, N = c(, ). An easy way to tilie explicit ratings (e.g., nmerical rating scores sch as the nmbers of stars in an one-to-fie scale rating system adopted by Amaon.com) is to set the ale of c(, ) to one if a ser likes item, i.e., the rating score is greater than a netral score (three stars). Alternatiely, we cold se rating scores for weighting c(, ). The final objectie is to estimate the probabilistic distribtion p( ), which indicates how likely it is that ser likes item. Recommendations are then made by ranking items not rated by ser in a descending order of p( ). 340

3 10th International Society for Msic Information Retrieal Conference (ISMIR 2009) 3.2 Model Formlation The graphical representation of a continos plsi model is shown in Figre 2. This is an extended ersion of threeway aspect models [17, 18] in which all ariables are discrete. We assme that sers, items, and featres are conditionally independent throgh latent topics. In other words, once a latent topic is specified, there is no mtal information between three kinds of ariables. Althogh this seems a strong assmption, it is a reasonable way to aoid the local optima problem. Introdcing a dependency edge from items to featres in order to model the real world accrately wold increase the nmber of parameters drastically. The plsi model can explain the process generating cooccrrence ( (n), (n), x (n) ).LetZ = { 1,, Z } be asetoftopics,where Z is the nmber of them. Let be a latent ariable that takes the ale of one of Z. Each topic can be regarded as a soft clster that is simltaneosly associated with sers and items. That is, each ser and each item stochastically belong to one of the topics. The model ths treats triplet ( (n), (n), x (n) ) as incomplete data that is latently associated with (n) Z. The complete data is gien by qartet ( (n), (n), x (n), (n) ). An interpretation of the generatie process is that ser (n) stochastically selects topic (n) according to his or her taste p( (n) (n) ), and (n) stochastically generates item and its featres x in trn. For conenience, we let S be { (1),, (n) }. A niqe featre of the continos plsi is that p(x ) is modeled with a Gassian mixtre model (GMM) in order to deal with continos obseration x. LetM be the nmber of mixtres (Gassian components). Each topic k Z has a GMM defined by the mixing proportions of Gassians {w k,1,,w k,m } and their means and coariances {μ k,1,, μ k,m } and {Σ k,1,, Σ k,m }.As in the original plsi, p(), p( ),andp( ) are mltinomial distribtions. We practically se an eqialent definition of the model obtained by focsing on p(), p( ), and p( ). The parameters of these mltinomial distribtions are simply gien by (conditional) probability tables of target ariables. Let θ be the set of all parameters of Z GMMs and Z (1 + U + V ) mltinomial distribtions. 3.3 Model Training The training method we explain here ses the Expectation- Maximiation (EM) algorithm [19] and is a natral extension of preios methods [17, 18] (c.f., discrete HMM.s. continos HMM). Instead of maximiing the incomplete log-likelihood, log p(o), the EM algorithm maximies the expected complete log-likelihood E S [log p(s, O)] iteratiely, where E [f()] means an expected ale of fnction f() with respect to p(); E [f()] = p()f(). The completelikelihood of (,, x,) is gien by p(,, x,)=p()p( )p( )p(x ). (1) This can be easily calclated for gien obserations when parameters θ are obtained. In the E-step we define a Q fnction as Q(θ θ crrent )=E S [log p(s, O)] (2) = c(, ) p(,, x)logp(,, x,), (3) User s taste User (discrete) p( ) Mltinomial p ( ) p( x ) Mltinomial Gassian mixtre model Item (discrete) Topic x Featre (continos) Figre 2. Graphical representation of continos plsi. where p(,, x) is a posterior distribtion of latent ariable and can be calclated by sing the crrent parameters θ crrent as follows: p(,, x,) p(,, x) = (4) p(,, x,). In the M-step we pdate the crrent parameters by maximiing Eqn. (3). Note that log p(,, x,) can be decomposed into log p()+logp( )+logp( )+logp(x ). This means that the parameters of each distribtion can be pdated independently. To pdate p(), for example, we only focs on a term related to p() as follows: Q p() = c(, ) p(,, x)logp(). (5) Using a Lagrange mltiplier λ for a constraint of probability standardiation, we define a new fnction F p() as ( F p() = Q p() + λ 1 ) p(). (6) We then calclate the differential of Eqn. (6) with respect to p() and set it to ero as follows: F p() p() = 1 λ 0. (7) p() The pdated distribtion p() can be obtained by p() = (8),. The other two mltinomial distribtions p( ) and p( ) can be similarly pdated as follows: p( ) =, (9) p( ) =. (10) To pdate continos distribtion p(x ), we focs on Q p(x ) = c(, ) p(,, x)logp(x ) (11) = K M c(, ) p( k )log p(y k,m )p(x k,y k,m ), (12) k=1 where to improe legibility we wrote p(,, x) as p( ). 341

4 Oral Session 4: Msic Recommendation and Playlist Generation y k {y k,1,,y k,m } is a latent ariable that indicates which Gassian in the GMM of topic k generates x. p(y k ) represents a probability distribtion oer M Gassians, i.e., p(y k,m )=w k,m,andp(x k,y k,m ) is the likelihood that featre x is generated from a Gassian indicated by y k,m. Becase the logarithmic operation for the smmation makes Eqn. (12) hard to maximie directly, we focs on the expected ale of Q p(x ) with respect to y k : E yk [Q p(x ) ]= K c(, ) p( k ) k=1 M ( ) p(y k,m x, k ) log w k,m +logn (x µ k,m, Σ k,m ), (13) where p(y k,m x, k ) is a posterior probability gien by p(y k,m x, k )= p(y k,m )p(x k,y k,m ) M p(y k,m)p(x k,y k,m ). (14) To obtain optimied w k,m, we define the following fnction by introdcing a Lagrange mltiplier β: ( ) M = E yk [Q p(x ) ]+β 1 w k,m. (15) F wk Calclating the partial partial differential of Eqn. (15) with respect to w k,m and setting it to ero, we obtain w k,m = c(, )p( k )p(y k,m x, k ) M c(, )p( k )p(y k,m x, k ). (16) Setting the partial differential of Eqn. (13) to ero, the mean and ariance μ k,m and Σ k,m are obtained by µ k,m = c(, )p( k )p(y k,m x, k )x c(, )p( k )p(y k,m x, k ), (17) Σ k,m = c(, )p( k )p(y k,m x, k )(x µ k,m ) 2 c(, )p(. (18) k )p(y k,m x, k ) Gien a ser i, recommendations are made by ealating p( i )= p( )p( i), wherep( i ) is proportional to p()p( i ) and indicates the msical tastes of ser : how likely it is ser i selects (likes) topic. 3.4 MapRedcing EM Algorithm Comptational efficiency, a ery important isse in msic recommendation when the database and model become large, is especially critical when sed data cannot be loaded on the memory of a single machine. Elegant implementations, howeer, hae scarcely been addressed. A remarkable adantage of plsi-based recommenders is that we can easily implement them in parallel processing enironments that consist of mltiple machines sch as clsters. Google News, for example, ses a distribted comptation framework called MapRedce [20]. We can implement the continos plsi by sing MPI or Hadoop [21]. Sppose we hae G U G V machines (CPUs). Let {U 1,,U GU } and {V 1,,V GV } be exclsie sets of sers and items, where U 1 U GU = U and V 1 V GV = V. To pdate p(), for example, we calclate c (U i,v j )=. (19) U i, V j This can be separately calclated in each machine. To calclate p(,, x), we need only p(), p( ) ( U i ), p( )( V j ),andp(x ). The nmber of parameters of these distribtions is mch smaller than the total nmber of parameters. Finally, we can get an integrated reslt by p() c (U i,v j ). (20) 1 i G U,1 j G V 4. SMOOTHING TECHNIQUES To aoid oerfitting, one needs to se appropriate smoothing techniqes. In or stdy, we se three techniqes to improe accracy and redce hbness: mltinomial smoothing, Gassian parameter tying, and artist-based item clstering. The first relaxes the excessie inclination of mltinomial parameters, and the others limit model complexity. 4.1 Mltinomial Smoothing We add a conjgate prior called a Dirichlet distribtion to a Q fnction as a reglariation term. To estimate p(), for example, we consider the following fnction: Q p() = Q p() + Dir(α), (21) where α is a set of K parameters of a Dirichlet distribtion. This reslts in the additie smoothing method. We set all parameters to Maximiing Q p(),weget p() = +α 1 ( ). (22) +α 1 The pdating formlas of the other mltinomial distribtions are similarly gien by +α 1 p( ) =, (23) ( +α 1) +α 1 p( ) =. (24) ( +α 1) 4.2 Gassian Parameter Tying We force all GMMs to share the same set of Gassians and differ from each other in the mixing proportions of those Gassians. In the context of HMMs, this is called a tied mixtre model. The new pdating formlas are gien by,m µ k,m = c(, )p( k )p(y k,m x, k )x,m c(, )p( k )p(y k,m x, k ), (25),m Σ k,m = c(, )p( k )p(y k,m x, k )(x µ k,m ) 2,m c(, )p(. (26) k )p(y k,m x, k ) 4.3 Artist-based Item Clstering We replaceitem-based distribtion p( ) with artist-based distribtion p(a ), where ariable a represents one of the artists in the database. Let A be a set of items sng by artist a, That is, let all items be groped according to their artist names. We train an artist-based model for sers, artists, and featres by iteratiely pdating p(a ) as follows: A p(a ) =. (27) 342

5 10th International Society for Msic Information Retrieal Conference (ISMIR 2009) Score Conts Ratio 68.5% 18.7% 5.86% 2.71% 4.27% Table 1. Distribtion of rating scores. To recommend items rather than artists, we then constrct an item-based modelbyreplacingp(a ) with p( ). To do this, we se an incremental training method [18] that re-estimates a distribtion of nknown items p( ) withot affecting other trained distribtions p(), p( ),(x ): p( ) = c(, ) p()p( )p(x ) p()p( )p(x ) c(, ). (28) p()p( )p(x ) p()p( )p(x ) 5. EVALUATION We experimentally ealated the continos plsi in terms of accracy and hbness by sing arios combinations of the smoothing techniqes. 5.1 Data The msic items we sed were Japanese songs recorded in single CDs that were ranked in weekly top-20 sales rankings from Apr to Dec To se these items, we need real implicit ratings c(, ) sch as prchase histories and listening conts, bt most online serices do not release sch data to the pblic. We therefore instead collected explicit ratings (nmbers of stars ranging from one to fie) from Amaon.co.jp by sing official APIs [22] that let s download almost all the information aailable from Amaon.co.jp [22]. For reliable ealation, we exclded sers who had rated fewer than two items and exclded items that had been rated less than two times. As a reslt, U was 1872 and V was The nmber of artists was 471. If a rating score gien to item j by ser i was greater than three (the netral score), we set c( i, j ) to the score. Otherwise, we set c( i, j ) to ero. In other words, we considered only positie ratings. A similar approach has been sed preiosly [23]. Note that, as shown in Table 1, the distribtion of rating scores was strongly skewed. The density of 6794 positie ratings (scores 4 and 5) was 0.259% in the ser-item co-occrrence table. With regard to the content-based data, we focsed on ocal featres becase all the items inclded singing oices that strongly affected the msical tastes of sers. To extract these featres from polyphonic adio signals, we sed a method proposed by Fjihara et al. [24]. We calclated a 13-dimensional featre ector at each frame where singing oices were highly likely to be inclded, concatenated the mean and ariance of the featre ectors in each item into a 26-dimensional ector, and then sed principal component analysis to compress the dimensionality to 20 (D =20). 5.2 Protocols To test all combinations of the three smoothing techniqes, we prepared eight models of the continos plsi. For conenience, throghot Section 5, the mltinomial smooth- Disabled SM1 SM2 SM1&2 Disabled SM Table 2. Expected tility of recommendations: Higher scores indicate better performance. Disabled SM1 SM2 SM1&2 Disabled SM Table 3. Entropy of recommendations: Higher scores indicate better performance (fewer hbs). ing, Gassian parameter tying, and item clstering are respectiely called SM1, SM2, and SM3. The nmber of latent ariables was 256 ( Z = 256). Althogh the nmber of mixtres was 32, when SM1 was disabled it was set to 1 in order to aoid oerfitting. We condcted 10-fold cross alidation by splitting the positie explicit ratings into ten grops. Nine grops were sed for making recommendations with the eight models. The other grop was considered to be not obsered and was sed for ealating the recommendations. 5.3 Measres Recommendation reslts gien as ranked lists of items were ealated in terms of accracy and hbness. To calclate accracy, we sed the expected tility of a ranked list [25], which for each ser is defined as R = V #(rated items) r=1 max(score,r 3, 0) 2 (r 1)/(γ 1), (29) where score,r is the rating score that ser actally gae the r-th ranked item althogh the item was considered a non-rated item (the score was hidden) in model training. When score,r was not aailable, its ale was set to 3. γ is a iewing half-life based on the assmption that the probability that a ser iews an r-th ranked item is twice the probability that the ser iews an (r + γ)-th ranked item. We set γ to 5 as in the literatre [25]. R was not sensitie to the ale of γ. The total score is gien by R = 100 R (0 R 100), (30) Rmax where R max is the maximm achieable tility if all items with aailable scores gien by ser had been at the top of the ranked list in order of those scores. Basically, higher ales indicate better performance, bt note that the probability of recommending known items is high. We propose the following hbness measre based the entropy of recommendations: V H = ( ) t(j), (31) U t(j) U log j=1 where t(j) is the nmber of times that item j was recommended with the highest (top 1) ranking. A larger H (higher entropy) indicates a smaller bias in how many times each item is recommended. 343

6 Oral Session 4: Msic Recommendation and Playlist Generation 5.4 Reslts As shown in Table 2, the accracies of recommendations were greatly improed by sing SM3. This can be explained from two aspects: the relationship between items and featres and that between items and sers. First, the items of each artist tend to be similar to each other in their msical featres. Second, most sers of Amaon.co.jp tend to like any of the items of the few artists they like. This wold be a common tendency of the sers of many online msic distribtion serices. Therefore, SM3 redced the complexity of the model while presering almost all the information of the rating data. SM2 improed the accracy of recommendations made regardless of the combinations in which it was sed. Interestingly, recommendations obtained by jointly sing SM2 and SM3 were mch more accrate than those made when these techniqes were sed independently. SM1, on the other hand, slightly redced the accracy becase it is based on additie smoothing. It is known that its approximation errors are larger than those of the other smoothing methods sch as the Good-tring method. Table 3 shows hbness of recommendations. SM2 significantly redced the hbness while the SM1 and SM3 had no gains. This is consistent with the reslts reported by Hoffman et al. [16], who fond that HDP and ector qantiation (VQ) did not prodce many hbs. VQ can be considered as a hard clstering ersion of the tied GMM, which is a soft clstering model. We conclde that combining SM2 and SM3 is the best approach to improing performance. In or experiments, it yielded accracy comparable with that of conentional methods of collaboratie filtering. 6. CONCLUSION This paper has presented a continos-plsi-based model for hybrid msic recommendation. The model ses GMMs to represent distribtions of acostic featres extracted from msical adio signals. As in the original plsi, sers and items are assmed to follow mltinomial distribtions. We deeloped an algorithm for parameter estimation and implemented it in a parallel processing enironment. Experimentally testing the abilities of three smoothing techniqes mltinomial smoothing, Gassian parameter tying, and artist-based item clstering, we fond that sing the second and third techniqes to adjst model complexity significantly improed the accracy of recommendations and that the second techniqe cold also redce hbness. In the ftre, we plan to introdce conjgate priors of all distribtions (GMMs and mltinomial distribtions) into the continos plsi to enable fll Bayesian estimation. Extending latent Dirichlet allocation (LDA) [23] and HDP- LDA [26] are worth considering. Acknowledgement: This stdy was partially spported by Grant-in-Aid for Yong Scientists (Start-p) REFERENCES [1] T. Hofmann and J. Picha. Probabilistic latent semantic indexing. In SIGIR, pages 50 57, [2] T. Hofmann and J. Picha. Latent class models for collaboratie filtering. In IJCAI, pages , [3] P. Resnick, N. Iacoo, M. Sshak, and P. Bergstrom. GropLens: An open architectre for collaboratie filtering of netnews. In CSCW, pages , [4] D. Lemire and A. Maclachlan. Slope one predictors for online rating-based collaboratie filtering. In SDM, pages 21 23, [5] J.-J. Acotrier, F. Pache, and M. Sandler. The way it sonds: Timbre models for analysis and retrieal of polyphonic msic signals. IEEE Transactions of Mltimedia, 7(6): , [6] P. Ahrendt, J. Larsen, and C. Gotte, Co-occrrence models in msic genre classification. In MLSP, pages , [7] B. Logan. Msic recommendation from song sets. In ISMIR, pages , [8] T. Magno and C. Sable. A comparison of signal-based msic recommendation to genre labels, collaboratie filtering, msicological analysis, hman recommendation, and random baseline. In ISMIR, pages , [9] O.Celma,M.Ramíre, and P. Herrera. Foafing the msic: A msic recommendation system based on RSS feeds and ser preferences. In ISMIR, pages , [10] M. Tiemann, S. Paws, and F. Vignoli. Ensemble learning for hybrid msic recommendation. In ISMIR, pages , [11] J. Donaldson and I. Knopke. Msic recommendation mapping and interface based on strctral network entropy. In ISMIR, pages , [12] P. Lamere and F. Maillet. Creating transparent, steerable recommendations. Late breaking in ISMIR, [13] A. Berenweig. Anchors and Hbs in Adio-based Msic Similarity. PhD thesis, Colmbia Uniersity, [14] P. Chordia, M. Godfrey, and A. Rae. Extending content-based msic recommendation: The case of Indian classical msic. In ISMIR, pages , [15] M. Godfrey and P. Chordia. Hbs and homogeneity: improing content-based msic modeling. In ISMIR, pages , [16] M. Hoffman, D. Blei, and P. Cook. Content-based msical similarity comptation sing the hierarchical Dirichlet process. In ISMIR, pages , [17] A. Popescl, L. Ungar, D. Pennock, and S. Lawrence. Probabilistic models for nified collaboratie and content-based recommendation in sparse-data enironments. In UAI, pages , [18] K. Yoshii, M. Goto, K. Komatani, T. Ogata, and H.G. Okno. An efficient hybrid msic recommender system sing an incrementally-trainable probabilistic generatie model. IEEE Transactions on ASLP, 16(2): , [19] A. Dempster, N. Laird, and D. Rbin. Maximm likelihood from incomplete data ia the EM algorithm. Royal Statistical Society, B-39(1):1 38, [20] A. Das, M. Datar, and A. Garg. Google news personaliation: Scalable online collaboratie filtering. In WWW, pages , [21] Hadoop. [22] Amaon web serices. [23] D. Blei, A. Ng, and M. Jordan. Latent Dirichlet allocation. Machine Learning Research, 3: , [24] H. Fjihara, T. Kitahara, M. Goto, K. Komatani, T. Ogata, and H.G. Okno. Singer identification based on accompaniment sond redction and reliable frame selection. In ISMIR, pages , [25] J. Breese, D. Heckerman, and C. Kadie. Empirical analysis of predictie algorithms for collaboratie filtering. In UAI, pages 43 52, [26] Y. Teh, M. Jordan, M. Beal, and D. Blei. Hierarchical Dirichlet processes. JASA, 101(476): ,