TrstSVD: Collaborative Filtering with Both the Explicit and Implicit Inflence of User Trst and of Item Ratings Gibing Go Jie Zhang Neil Yorke-Smith School of Compter Engineering Nanyang Technological University Singapore American University of Beirt Lebanon; and University of Cambridge UK {ggozhang}@nt.ed.sg nysmith@ab.ed.lb Abstract Collaborative filtering sffers from the problems of data sparsity and cold start which dramatically degrade recommendation performance. To help resolve these isses we propose TrstSVD a trst-based matrix factorization techniqe. By analyzing the social trst data from for real-world data sets we conclde that not only the explicit bt also the implicit inflence of both ratings and trst shold be taken into consideration in a recommendation model. Hence we bild on top of a state-of-the-art recommendation algorithm SVD++ which inherently involves the explicit and implicit inflence of rated items by frther incorporating both the explicit and implicit inflence of trsted sers on the prediction of items for an active ser. To or knowledge the work reported is the first to extend SVD++ with social trst information. Experimental reslts on the for data sets demonstrate that or approach TrstSVD achieves better accracy than other ten conterparts and can better handle the concerned isses. Introdction Incorporating trst into recommender systems has demonstrated potential to improve recommendation performance (Yang et al. 03; Fang Bao and Zhang 04 and to help mitigate some well-known isses sch as data sparsity and cold start (Go Zhang and Thalmann 0. Sch trstaware approaches are developed based on the phenomenon that friends often inflence each other by recommending items. However even the best performance reported by the latest work (Fang Bao and Zhang 04 can be inferior to that of other state-of-the-art models which are merely based on ser-item ratings. For instance a well-performing trstbased model (Yang et al. 03 obtains.0585 on data set Epinions.com in terms of Root Mean Sqare Error ( whereas the performance of a ser-item baseline (see Koren (008 Sect.. can achieve.047 in terms of. To investigate this phenomenon we condct an empirical trst analysis based on for real-word data sets (FilmTrst Epinions Flixster and Ciao throgh which two important observations are conclded. First trst information is Copyright c 05 Association for the Advancement of Artificial Intelligence (www.aaai.org. All rights reserved. Smaller vales indicate better predictive accracy. Reslt reported by the recommendation toolkit MyMediaLite (mymedialite.net/ examples/datasets.html. also very sparse yet complementary to rating information. Hence focsing too mch on either one kind of information may achieve only marginal gains in predictive accracy. Second sers are strongly correlated with their trst neighbors whereas they have a weakly positive correlation with their trst-alike neighbors (e.g. friends. Given that very few trst networks exist it is better to have a more general trst-based model that can well operate on both trst and trst-alike relationships. These observations motivate s to consider both explicit and implicit inflence of ratings and of trst in a trst-based model. The inflence can be explicit (real vales of ratings and trst or implicit (who rates what (for ratings and who trsts whom (for trst. The implicit inflence of ratings has been demonstrated sefl in providing accrate recommendations (Koren 008. We will later show that implicit trst can also provide added vale over explicit trst. Ths we propose a novel trst-based recommendation model TrstSVD. Or approach bilds on top of a state-ofthe-art model SVD++ (Koren 008 where both the explicit and implicit inflence of ser-item ratings are involved to generate predictions. To the athors knowledge or work is the first to extend SVD++ with social trst information. Specifically on one hand the implicit inflence of trst (who trsts whom can be natrally added to the SVD++ model by extending the ser modeling. On the other hand the explicit inflence of trst (trst vales is sed to constrain that serspecific vectors shold conform to their social trst relationships. This ensres that ser-specific vectors can be learned from their trst information even if a few or no ratings are given. In this way the data sparsity and cold start isses can be better alleviated. Or novel model ths incorporates both explicit and implicit inflence of item ratings as well as ser trst. In addition a weighted-λ-reglarization techniqe is sed to frther avoid over-fitting for model learning. Experimental reslts on the for real-world data sets demonstrate that or approach achieves significantly better accracy than other trst-based conterparts as well as other ratings-only well-performing models (ten approaches in total and is more capable of coping with cold start sitations. Related Work Trst-aware recommender systems have been widely stdied given that social trst provides an alternative view of ser preferences other than item ratings (Go Zhang and
Yorke-Smith 04. Specifically Ma et al. (008 propose a social reglarization method ( by considering the constraint of social relationships. The idea is to share a common ser-featre matrix factorized by ratings and by trst. Ma King and Ly (009 then propose a social trst ensemble method ( to linearly combine a basic matrix factorization model and a trst-based neighborhood model together. Ma et al. (0 frther propose that the active ser s ser-specific vector shold be close to the average of her trsted neighbors and se it as a reglarization to form a new matrix factorization model (. Jamali and Ester (00 bild a new model ( on top of by reformlating the contribtions of trsted sers to the formation of the active ser s ser-specific vector rather than to the predictions of items. Yang et al. (03 propose a hybrid method (TrstMF that combines both a trster model and a trstee model from the perspectives of trsters and trstees that is both the sers who trst the active ser and those who are trsted by the ser will inflence the ser s ratings on nknown items. Tang et al. (03 consider both global and local trst as the contextal information in their model where the global trst is compted by a separate algorithm. Yao et al. (04 take into consideration both the explicit and implicit interactions among trsters and trstees in a recommendation model. Fang Bao and Zhang (04 stress the importance of mltiple aspects of social trst. They decompose trst into for general factors and then integrate them into a matrix factorization model. All these works have shown that a matrix factorization model reglarized by trst otperforms the one withot trst. That is trst is helpfl in improving predictive accracy. However it is also noted that even the latest work (Fang Bao and Zhang 04 can be inferior to other well-performing ratings-only models. To explain this phenomenon we next condct a trst analysis to investigate the vale of trst in recommender systems. Trst Analysis For data sets are sed in or analysis and also or later experiments: Epinions (trstlet.org/wiki/epinions datasets FilmTrst (www.librec.net/datasets.html Flixster (www.cs.sf.ca/ sa5/personal/datasets/ and Ciao (www.pblic.as.ed/ tang0/datasetcode/trststdy.htm. All the for data sets contain both item ratings and social relationships specified by active sers. The ratings in Epinions and Ciao are integers from to 5 while those in the other data sets are real vales i.e. [0.5 4.0] for FilmTrst [0.5 5.0] for Flixster both with step 0.5. Note that trst is asymmetric in Epinions FilmTrst and Ciao whereas it is symmetric in Flixster. A sbset of the Flixster data set is sed in this paper to avoid memory-consming isses. The data set statistics are illstrated in Table. Two important observations are conclded from these data sets. Observation Trst information is very sparse yet is complementary to rating information. On one hand as shown in Table the density of trst is mch smaller than that of ratings in Epinions FilmTrst and Flixster whereas trst is only denser than ratings in Ciao. Both ratings and trst are very sparse across all the data sets. ratio of sers 0.8 0.7 0.6 0.5 0.4 0.3 0. 0. 0 Table : Statistics of the for data sets Featre Epinions FilmTrst Flixster Ciao sers 4063 508 533 7375 items 39738 07 897 99746 ratings 66484 35497 409803 8039 density 0.05%.4% 0.04% 0.03% trsters 33960 609 4709 679 trstees 4988 73 4709 797 trsts 48783 853 655054 78 density 0.09% 0.4% 0.03% 0.3% 0-5 6-0 # ratings per ser FilmTrst Flixster Epinions Ciao Average -0 >0 Percentage 0.5 0.45 0.4 0.35 0.3 0.5 0. 0.5 0. 0.05 0 0.4-0.5 0.3-0.4 0.-0. 0.0-0. <0 -.0 0.8-0.7-0.8 0.6-0.7 0.5-0.6 Correlation Ranges FilmTrst Flixster Epinions Ciao Average (a (b Figre : (a The distribtion of ratio of sers who have issed trst statements w.r.t. the nmber of ratings that they each have given. (b The correlations between a ser s ratings and those of her trsted neighbors in all the data sets. In this regard a trst-aware recommender system that focses too mch on trst (rather than rating tility is likely to achieve only marginal gains in recommendation performance. In fact the existing trst-based models consider only the explicit inflence of ratings. That is the tility of ratings is not well exploited. In addition the sparsity of explicit trst also implies the importance of involving implicit trst in collaborative filtering. On the other hand trst information is complementary to the rating information. Figre a shows that: ( A portion of sers have not rated any items bt are socially connected with other sers. ( For the cold-start sers who have rated few items (less than 5 in or case trst information can provide a complementary part of sorce of information with ratio greater than 0% on average. (3 The warm-start sers who have rated a lot of items (e.g. > 0 are not necessary to specify many other sers as trstworthy (% on the average. Althogh having differing distribtions across the data sets trst can be a complementary information sorce to item ratings for recommendations. This observation motivates s to consider both the explicit and implicit inflence of ratings and trst making better and more se of ratings and trst to resolve the concerned isses. Observation A ser s ratings have a weakly positive correlation with the average of her social neighbors nder the concept of trst-alike relationships and a strongly positive correlation nder the concept of trst relationships. Next we consider the inflence of trst in rating prediction i.e. the inflence of trsted neighbors on the active ser s rating for a specific item a.k.a. social inflence. Specifically we calclate the Pearson correlation coefficient (PCC between a ser s ratings and the average of her social neighbors. The reslts are presented in Figre b indicating that: ( A weakly positive correlation is observed be-
tween a ser s ratings and the average of the social neighbors in FilmTrst (mean 0.83 and Flixster (0.063. The distribtions of the two data sets are similar. Flixster adopts the symmetric friendship relationships whereas trst is directed. Althogh FilmTrst adopts the concept of trst (with vales from to 0 the pblicly available data set contains only binary vales (sch degrading may case mch noise. We regard these relationships as trst alike i.e. the social relationships that are similar with bt weaker (or more noisy than social trst. ( Under the concept of trst relationships on the contrary a ser s ratings are strongly and positively correlated with the average of trsted neighbors. Specifically a large portion (7.63% in Epinions 3.4% in Ciao of ser correlations are in the range of [.0] and (resp. 54.70% 39.4% of ser correlations are greater than 0.5. The average correlation is 0.446 in Epinions and 0.3 in Ciao. Since PCC vales are in the range of [ ] vales of 0.446 and 0.3 indicate decent correlations. In the social networks with relatively weak trst-alike relationships (e.g. friendship implicit inflence (i.e. binary relationships may be more indicative than explicit (bt noisy vales for recommendations. Hence a trst-based model that ignores the implicit inflence of ratings and trst may lead to deteriorated performance if being applied to sch cases. The second observation sggests that incorporating both the explicit and implicit inflence of ratings and trst may promote the generality of a trst-based model to both trst and trst-alike social relationships. Or approach presented next is constrcted based on these two observations. TrstSVD: A Trst-based Model Problem Definition The recommendation problem in this paper is to predict the rating that a ser will give to an nknown item based on both a ser-item rating matrix and a ser-ser trst matrix. Sppose that a recommender system incldes m sers and n items. Let R = [r i ] m n denote the ser-item rating matrix where each entry r i represents the rating given by ser on item i. For clarity we preserve symbols v for sers and i for items. Let I denote the set of items rated by ser. Let p and q i be a d-dimensional latent featre vector of ser and item i respectively. The essence of matrix factorization is to find two low-rank matrices: ser-featre matrix P R d m and item-featre matrix Q R d n that can adeqately recover the rating matrix R i.e. R P Q where P is the transpose of matrix P. Hence the rating on item for ser can be predicted by the inner prodct of ser-specific vector p and item-specific vector q i.e. ˆr = q p. In this regard the main task of recommendations is to predict the rating ˆr as close as possible to the grond trth r. Formally we can learn the ser- and item-featre matrices by minimizing the following loss (obective fnction: L r = ( q + λ ( p r p F + q F I where F denotes the Frobenis norm and λ is a parameter to control model complexity and to avoid over-fitting. On the other hand sppose that a social network is represented by a graph G = (V E where V incldes a set of m nodes (sers and E represents the directed trst relationships among sers. We can se the adacency matrix T = [t v ] m m to describe the strctre of edges E where t v indicates the extent to which sers trsts v. We denote p and w v as the d-dimensional latent featre vector of trster and trstee v respectively. We limit the trsters in the trst matrix and the active sers in the rating matrix to share the same ser-featre space in order to bridge them together. Hence we have trster-featre matrix P d m and trstee-featre matrix W d m. By employing the low-rank matrix approximation we can recover the trst matrix by T P W. Ths a trst relationship can be predicted by the inner prodct of a trster-specific vector and a trsteespecific vector ˆt v = wv p. The matrices P and W can be learned by minimizing the following loss fnction: L t = ( w + λ ( v p t v p F + w v F v v T where T is the set of sers trsted by ser. The TrstSVD Model In line with the two observations of the previos section or TrstSVD model is bilt on top of a state-of-the-art model known as SVD++ proposed by Koren (008. The rationale behind SVD++ is to take into consideration ser/item biases and the inflence of rated items other than ser/item-specific vectors on rating prediction. Formally the rating for ser on item is predicted by: ˆr = b + b + µ + q ( p + I i I y i where b b represent the ser and item biases respectively; µ is the global average rating; and y i denotes the implicit inflence of items rated by ser in the past on the ratings of nknown items in the ftre. Ths ser s featre vector can be also represented by the set of items she rated and i I y i rather than sim- finally modeled as ( p + I ply as p. Koren (008 has shown that integrating implicit inflence of ratings can well improve predictive accracy. Previosly we have stressed the importance of trst inflence for better recommendations and its potential to be generalized to trst-alike relationships. Hence we can enhance the trst-naware SVD++ model by incorporating trst inflence. Specifically the implicit effect of trsted sers on item ratings can be considered in the same manner as rated items given by: ˆr = b + ( b + µ +q p + I y i + T i I v T w v where w v is the ser-specific latent featre vector of sers (trstees trsted by ser and ths q w v can be explained by the ratings predicted by the trsted sers i.e. the inflence of trstees on the rating prediction. In other words the inner prodct q w v indicates how trsted sers inflence
ser s rating on item. Similar to ratings a ser s featre vector can be interpreted by the set of sers whom she trsts i.e. T v T w v. Therefore a ser is frther modeled by ( p + I i I y i + T v T w v in the social rating networks considering the inflence of both rated items and trsted sers. The obective fnction to minimize is then given as follows: L = ( + λ (ˆr r b + b I + p F + q F + y i F + w v F. i v To redce the model complexity we se the same reglarization parameter λ for all the variables. Finer control and tning can be achieved by assigning separate reglarization parameters to different variables bt it may reslt in great complexity when comparing with different models. In addition as explained earlier we constrain that the ser-specific vectors decomposed from the rating matrix and those decomposed from the trst matrix share the same featre space in order to bridge both matrices together. In this way these two types of information can be exploited in a nified recommendation model. Specifically we can reglarize the ser-specific vectors p by recovering the social relationships with other sers. The new obective fnction (withot the other reglarization terms is given by: L= + λ t (ˆr r (ˆt v t v I v T where ˆt v = wv p is the predicted trst between sers and v and λ t controls the degree of trst reglarization. Frther as sggested by Yang et al. (03 a techniqe called weighted-λ-reglarization can be sed to help avoid over-fitting when learning parameters. In particlar they consider more penalties for the sers who rated more items and for the items which received more ratings. However we arge that sch consideration may force the model to be more biased towards poplar sers and items. Instead in this paper we adopt a distinct strategy that the poplar sers and items shold be less penalized (de to smaller chance to be over-fitted and cold-start sers and niche items (those receiving few ratings shold be more reglarized (de to greater chance to be over-fitted. Therefore the new loss fnction to minimize is obtained as follows: L = + λ (ˆr r t (ˆt v t v I v T + λ I b + λ U b + ( λ I + λt T p ( F + λ U q F + λ U i y i F + λ T + v w v F where U U i are the set of sers who rate items and i respectively; and T v + is the set of sers who trst ser v. Since the active ser has rated a nmber of items and specified other sers as trstworthy the penalization on ser-specific vector p takes into accont both cases. i Model Learning To obtain a local minimization of the obective fnction given by Eqation we perform the following gradient descents on b b p q y i and w v for all the sers and items. b = e + λ I b I b p = e + λ U b U = e q + λ t e v w v I v T + ( λ I + λ t T ( p p + I q = e U + T v T w v + λ U q i I y i i I y i = e I q + λ U i y i I v T w v = I e T q +λ t e v p +λ T + v w v where e = ˆr r indicates the rating prediction error for ser on item and e v = ˆt v t v is the trst prediction error for ser towards ser v. In the cold-start sitations where sers may have only rated a few items the decomposition of trst matrix can help to learn more reliable ser-specific latent featre vectors than ratings-only matrix factorization. In the extreme case where there are no ratings at all for some sers Eqation ensres that the ser-specific vector can be trained and learned from the trst matrix. In this regard incorporating trst in a matrix factorization model can alleviate the cold start problem. By considering both explicit and implicit inflence of trst rather than either one alone or model can better tilize trst to frther mitigate the concerned isses. Complexity Analysis The comptational time of learning the TrstSVD model is mainly taken by evalating the obective fnction L and its gradients against featre vectors (variables. The time to compte the obective fnction L is O(d R + d T where d is the dimensionality of the featre space and R T refer to the nmber of observed entries. De to the sparsity of rating and trst matrices the vales will be mch smaller than the matrix cardinality. The comptational complexities for gradients b b p q w v y i in Eqation are O(d R O(d R O(d R + d T O(d R + d T O(d R k and O(d R p + d T p where k p are the average nmber of ratings and trst statements received by an item and a ser respectively. Hence the overall comptational complexity in one iteration is O(d R c+d T c where c = max(p k. De to c R or T the overall comptational time is linear with respect to the nmber of observations in the rating and trst matrices. To sm p or model has potential to scale p to large-scale data sets. Experiments and Reslts Data Sets. The for data sets presented in Table are sed. (
Table : Performance comparison in two testing views where * indicates the best performance among all the other methods and colmn Improve indicates the relative improvements that or approach TrstSVD achieves relative to the * reslts. All Metrics UserAvg ItemAvg PMF TrstMF SVD++ TrstSVD Improve FilmTrst MAE 0.636 0.75 0.74 0.68 0.68 0.674 0.638 0.63 0.63* 0.609 0.65% d = 5 0.83 7 49 0.80 0.80 0.878 0.837 0.80 0.804* 0.789.87% MAE 0.636 0.75 0.735 0.640 0.638 0.668 0.64 0.63 0.6* 0.607 0.65% d = 0 0.83 7 68 0.835 0.83 0.875 0.844 0.89 0.80* 0.787.87% Epinions MAE 30 8 79 50 0.88 94 0.85 0.88 0.88* 0.804.7% d = 5.03.094.90.96.4.35.070.069.057*.043.3% MAE 30 8 09 58 0.884 3 0.86 0.89 0.88* 0.805.59% d = 0.03.094.97.78.4.3.08.095.057*.044.3% Flixster MAE 0.79* 0.858 0.84 0.75 0.750 0.80 0.770 0.890 0.794 0.76 0.4% d = 5 79*.088.076 75 74.087 94.46.06 48 3.7% MAE 0.79* 0.858 0.769 0.784 0.785 0.785 0.784.6 0.8 0.77 0.7% d = 0 79*.088.009.05.08.034.009.44.09 50.97% Ciao MAE 0.78 0.760 0 0.767 0.765 0.899 0.749 0.74* 0.75 0.73.56% d = 5.03.06.06.00.03.83 8* 83.03 55.65% MAE 0.78 0.760 0.8 0.763 0.76 0.85 0.749* 0.753 0.748 0.73 3.47% d = 0.03.06.078.03.00.076 76*.04.00 56.05% Cold Start Metrics UserAvg ItemAvg PMF TrstMF SVD++ TrstSVD Improve FilmTrst MAE 0.709 0.7 0.84 0.680 0.670* 0.88 0.697 0.674 0.677 0.66.34% d = 5 79.079 0.884 0.857*.04 6 0.867 0.897 0.853 0.47% MAE 0.709 0.7 0.767 0.674 0.668* 0.77 0.680 0.687 0.680 0.663 0.75% d = 0 79.009 00 0.897*.034 07 00 05 0.853 4.9% Epinions MAE.047 0.85*.45.05 0.89.398 0.884 0.89 0.889 0.868 -.88% d = 5.430.7.770.66.38.735.33.5*.6.05.78% MAE.047 0.85.53 8 0.846*.39 0.857 0.853 0.89 0.868 -.60% d = 0.430.7*.43.33.80.437.5.76.66.08.69% Flixster MAE 0.869 06.097 0.87 0.87.058 0.88 0 0.868* 0.855.50% d = 5.55.4.390.097.096*.358.03.38..066.74% MAE 0.869* 06 49 0.889 0.89 5 0.884 76 0.869* 0.858.7% d = 0.55.4.06.37.44.8.*.38.*.070 3.78% Ciao MAE 0.89 0.735*.033 57 0.789.73 0.774 0.75 0.759 0.79 0.8% d = 5.38.005.334.3 98.430.00 54*.039 53 0.0% MAE 0.89 0.735 6 0.803 0.730* 49 0.74 0.770 0.749 0.7.3% d = 0.38.005.9.04.03.4 78*.096.00 6.64% Cross-validation. We se 5-fold cross-validation for learning and testing. Specifically we randomly split each data set into five folds and in each iteration for folds are sed as the training set and the remaining fold as the test set. Five iterations will be condcted to ensre that all folds are tested. The average test performance is given as the final reslt. Evalation Metrics. We adopt two well-known metrics to evalate predictive accracy namely mean absolte error (MAE and root mean sqare error ( defined by: MAE= ˆr r = (ˆr r N N where N is the nmber of test ratings. Smaller vales of MAE and indicate better predictive accracy. Testing Views. Two data set views are created for testing. First the All view indicates that all ratings are sed as the test set. Second the Cold Start view means that only the sers who rate less than five items will be involved in the test set. Similar testing views are also defined and sed in (Go Zhang and Thalmann 0; Yang et al. 03. Comparison Methods. Three kinds of approaches are compared with or method TrstSVD : ( Baselines: UserAvg and ItemAvg make predictions by the average of ratings that are given by the active ser and received by the target item respectively; ( Trst-based models: (Ma et al. 008 (Ma King and Ly 009 (Ma et al. 0 (Jamali and Ester 00 TrstMF (Yang et al. 03 and Fang s (Fang Bao and Zhang 04; (3 Ratings-only state-of-the-art models: PMF (Salakhtdinov and Mnih 008 and SVD++ (Koren 008. Parameter Settings. The optimal experimental settings for each method are determined either by or experiments or sggested by previos works. Specifically the common settings are λ = 0.00 and the nmber of latent featres d = 5/0 the same as all the previos trst-based models. The other settings are: ( : α = 0.4 for Epinions and.0 for the others; ( : λ c = 0..0 0.00 0.0 corresponding to FilmTrst Epinions Flixster and Ciao respectively; (3 : β =.0 for Flixster and 0. for the others; (4 TrstMF: λ t = ; (5 SVD++: λ = Sorce code is inclded in the LibRec library at www.librec.net.
.5..5..05 5 0.85 0.8 TrstMF TrstSVD -5 6-0 -0-40 4-00 Trst Degrees.3.5..5..05 5 TrstMF TrstSVD -5 6-0 -0-40 4-000-500>500 Trst Degrees (a FilmTrst (b Epinions (c Flixster (d Ciao Figre : Performance comparison on sers with different trst degrees (d = 0 [best viewed in color]..5..05 5 0.85 TrstMF TrstSVD -5 6-0 -0-40 4-000-500 Trst Degrees.5..05 5 0.85 TrstMF TrstSVD -5 6-0 -0-40 4-000-500>500 Trst Degrees Table 3: Comparing with (Fang Bao and Zhang 04 Fang s vs. Epinions Ciao FilmTrst TrstSVD d = 5 d = 0 d = 5 d = 0 d = 5 d = 0 MAE 0.806 0.84 0.737 0.745 0.66 0.65 0.804 0.805 0.73 0.73 0.609 0.607.047.059 7 85 0.793 0.80.043.044 55 56 0.789 0.787 0. 0.35 0.03 0. (resp.; (6 TrstSVD: λ =. λ t = for FilmTrst λ = λ t = 0.5 for Epinions λ = 0.8 λ t = 0.5 for Flixster and λ = 0.5 λ t = for Ciao. Comparison with other models. The experimental reslts are presented in Table. For all the comparison methods in the testing view of All SVD++ otperforms the other comparison methods in FilmTrst and Epinions and UserAvg performs the best in Flixster. This implies that these trst-based approaches cannot always beat other wellperforming ratings-only approaches and even simple baselines in trst-alike networks (i.e. FilmTrst and Flixster. Only in Ciao trst-based approach ( gives the best performance. On the contrary or approach TrstSVD is consistently sperior to the best approach among the others across all the data sets. Althogh the percentage of relative improvements are small Koren (00 has pointed ot that even small improvements in MAE and may lead to significant differences of recommendations in practice. For all the comparison methods in the testing view of Cold Start and SVD++ perform respectively the best in FilmTrst and Flixster (trst-alike while no single approach works the best in Epinions and Ciao (trst. Generally or approach performs better than the others both in trst and trst-alike relationships. Althogh some exceptions are observed in Epinions in terms of MAE TrstSVD is more powerfl in terms of. Since all the trst-based models aim to optimize the sqare errors between predictions and real vales is more indicative than MAE and ths TrstSVD still has best performance overall. Besides the above-compared approaches some new trstbased models have been proposed recently. The most relevant model is presented in (Fang Bao and Zhang 04; for clarity we denote it by Fang s. It is reported to perform better than other trst-based models and than SVD++ (except in Ciao. Table 3 shows the comparison between Fang s and or approach TrstSVD. The reslts of Fang s approach are reported in (Fang Bao and Zhang 04 and directly re-sed in or paper. Note that we sampled more data for Flixster than Fang s and ths their experimental reslts are not comparable. Table 3 clearly shows that or approach performs better than Fang s in terms of both MAE and. One more observation from Tables and 3 is that the performance of TrstSVD when d = 5 is very close to that when d = 0 indicating the reliability of or approach with respect to the featre dimensionality. We ascribe this featre to the consideration of both the explicit and implicit inflence of ratings and trst in a nified recommendation model. In conclsion the experimental reslts indicate that or approach TrstSVD otperforms the other methods in predicting more accrate ratings and that its performance is reliable with different nmber of latent featres. Comparison in trst degrees. Another series of experiments are condcted to investigate the performance on sers with different trst degrees. The trst degrees refer to the nmber of trsted neighbors specified by a ser. We split the trst degrees into seven categories: -5 6-0 -0-40 4-00 0-500 >500. The reslts of trst-based models are illstrated in Figre where we only present the performance in when d = 0 de to space limitation; similar trends in other cases. In general or approach TrstSVD consistently achieves the best performance in the cases of different trst degrees. Paired t-tests (confidence 5 shows that sch improvements are statistically significant (p<0 5 in three data sets bt not in FilmTrst (details are omitted to save space. Two possible explanations can be made: ( FilmTrst has a smaller data size than the others; ( de to the noise arising from converting real-valed trst to binary trst the trst may be less sefl in FilmTrst than in the others as indicated in (Fang Bao and Zhang 04. Conclsion and Ftre Work This paper proposed a novel trst-based matrix factorization model which incorporated both rating and trst information. Or analysis of trst in for real-world data sets indicated that trst and ratings are complementary to each other and both pivotal for more accrate recommendations. Or novel approach TrstSVD takes into accont both the explicit and implicit inflence of ratings and trst information when predicting ratings of nknown items. A weightedλ-reglarization techniqe was adapted and sed to frther reglarize the ser- and item-specific latent featre vectors. Comprehensive experimental reslts showed that or approach TrstSVD otperformed both trst- and ratingsbased methods in predictive accracy across different testing views and across sers with different trst degrees. For ftre work we intend to frther improve the proposed model by considering both the inflence of trsters and trstees.
Acknowledgements Gibing Go thanks the Institte for Media Innovation for a PhD grant at Nanyang Technological University Singapore. The work is also partially spported by the MoE AcRF Tier Grant M4000.00. Yao W.; He J.; Hang G.; and Zhang Y. 04. Modeling dal role preferences for trst-aware recommendation. In Proceedings of the 37th International ACM SIGIR Conference on Research & Development in Information Retrieval (SIGIR 975 978. References Fang H.; Bao Y.; and Zhang J. 04. Leveraging decomposed trst in probabilistic matrix factorization for effective recommendation. In Proceedings of the 8th AAAI Conference on Artificial Intelligence (AAAI 30 36. Go G.; Zhang J.; and Thalmann D. 0. A simple bt effective method to incorporate trsted neighbors in recommender systems. In Proceedings of the 0th International Conference on User Modeling Adaptation and Personalization (UMAP 4 5. Go G.; Zhang J.; and Yorke-Smith N. 04. Leveraging mltiviews of trst and similarity to enhance clsteringbased recommender systems. Knowledge-Based Systems (KBS in press. Jamali M. and Ester M. 00. A matrix factorization techniqe with trst propagation for recommendation in social networks. In Proceedings of the 4th ACM Conference on Recommender Systems (RecSys 35 4. Koren Y. 008. Factorization meets the neighborhood: a mltifaceted collaborative filtering model. In Proceedings of the 4th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD 46 434. Koren Y. 00. Factor in the neighbors: Scalable and accrate collaborative filtering. ACM Transactions on Knowledge Discovery from Data (TKDD 4(:: :4. Ma H.; Yang H.; Ly M.; and King I. 008. : social recommendation sing probabilistic matrix factorization. In Proceedings of the 3st International ACM SIGIR Conference on Research and Development in Information Retrieval (SIGIR 93 940. Ma H.; Zho D.; Li C.; Ly M. R.; and King I. 0. Recommender systems with social reglarization. In Proceedings of the 4th ACM International Conference on Web Search and Data Mining (WSDM 87 96. Ma H.; King I.; and Ly M. 009. Learning to recommend with social trst ensemble. In Proceedings of the 3nd International ACM SIGIR Conference on Research and Development in Information Retrieval (SIGIR 03 0. Salakhtdinov R. and Mnih A. 008. Probabilistic matrix factorization. In Advances in Neral Information Processing Systems (NIPS volme 0 57 64. Tang J.; H X.; Gao H.; and Li H. 03. Exploiting local and global social context for recommendation. In Proceedings of the 3rd International Joint Conference on Artificial Intelligence (IJCAI 7 78. Yang B.; Lei Y.; Li D.; and Li J. 03. Social collaborative filtering by trst. In Proceedings of the 3rd International Joint Conference on Artificial Intelligence (IJCAI 747 753.