Knowledge-Based Systems 54 (2013) 310–317

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Knowledge-Based Systems

journal homepage: www.elsevier .com/locate /knosys

Collaborative filtering with social regularization for TV programrecommendation

0950-7051/$ - see front matter � 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.knosys.2013.09.018

⇑ Corresponding author. Tel.: +86 21 34204468; fax: +86 21 34204155.E-mail address: ya_zhang@sjtu.edu.cn (Y. Zhang).

1 http://www.twitter.com.2 http://weibo.com.

Ya Zhang ⇑, Weiyuan Chen, Zibin YinShanghai Key Lab. of Digital Media Processing & Transmissions, Shanghai Jiao Tong University, Shanghai 200240, China

a r t i c l e i n f o a b s t r a c t

Article history:Received 5 February 2013Received in revised form 23 September 2013Accepted 23 September 2013Available online 9 October 2013

Keywords:TV program recommendationMicroblogRecommender systemCollaborative filteringSocial regularizationItem similarity

In recent years, we have witnessed the explosive growth of microblogging services. As a popular platformfor users to communicate and share information with friends, microblog has opened up new opportunitiesfor recommendation. In this paper, we explore the possibility of recommending TV programs with microb-logs. In particular, we leverage the following two important features of microblogs: (1) the rich user gen-erated content reveals users’ preferences on TV programs as well as the properties of TV programs and (2)the social interactions of the users suggest the mutual influences among the users. Taking into consider-ation of the above two properties, we proposed a hybrid recommendation model based on probabilisticmatrix factorization, a popular collaborative filtering method. Two regularizers are added during matrixfactorization: the social regularizer and the item similarity regularizer. We validate the proposed algorithmwith Sina Weibo data set for TV program recommendation. The experimental results show that the pro-posed algorithm significantly outperforms the state-of-the-art collaborative filtering method, demonstrat-ing the importance of incorporating social trust and item similarity in recommendation. In addition, weshow that the proposed method is robust in recommending to new users, a typical cold-start scenario.

� 2013 Elsevier B.V. All rights reserved.

1. Introduction

In recent years, the dramatic increases in the number of TV pro-grams have made the accessibility to the TV programs a challengingissue. Recommendation plays an important role in enhancing users’ability to access relevant information. Over the last several years,many recommendation systems have been proposed for recom-mending TV programs according to users’ TV viewing behaviors[6,22,3]. The explosive growth of microblog services such as Twit-ter1 and Weibo2 has opened up new opportunities for improvingthe accuracy of TV program recommendation. As popular platformsfor users to communicate with friends and share information, microb-log services generates huge amount of content every day. The richcontent helps form a better understanding of the preferences of theusers as well as the characteristics of the items. Moreover, informa-tion about users’ social connections and their mutual interactionsare explicit with microblog services. All the above information maybe leveraged by recommender systems to improve the accuracy ofpredictions. In this paper, we explore the possibility of leveraging usersocial interactions as well as user generated content at microbloggingsites to improve the accuracy of TV programs recommendation.

Two widely used approaches in recommender systems are con-tent-based filtering [13] and collaborative filtering [23]. Content-based filtering methods are to recommend items similar to theones that a user liked in the past. Content-based filtering requiresknowledge of the characteristics of the items, which is not alwaysavailable. On the contrary, the collaborative filtering approaches donot rely on the characteristics of the items. User-based collabora-tive filtering methods assume that similar users tend to share sim-ilar preferences on items. By collecting and analyzing a largeamount of information on users’ behaviors, collaborative filteringmethods predict what users would like based on similarity amongthe users or items in terms of the observed behaviors. Collaborativefiltering approaches often suffer from three problems, cold start,data sparsity, and scalability. In fact, hybrid approaches combiningcollaborative filtering and content-based filtering have been dem-onstrated to be able to relief the above problems to some extend.See [1] for a complete review of recommender systems.

When leveraging the microblog services for recommendation, itis necessary to note that users’ social network and their respectivepreference form a dynamic equilibrium. People of similar interestsand preferences are more likely to be connected and interact witheach other. On the other hand, one tends to be influenced by his/her social connections in many aspects including interests andpreferences. For example, it is more likely for an individual towatch a new TV program if it has been watched by many of his/her friends. In fact, users’ interests and friendship networks are

Y. Zhang et al. / Knowledge-Based Systems 54 (2013) 310–317 311

revealed to be highly correlated [24]. Hence, a user’s social ties andinteractions embed important information about the user’s prefer-ences. Considering the following–follower relationship is verynoisy, we here measure the similarity in users’ interests using theirsocial interactions in terms of retweeting behaviors. Anotheradvantage of microblog platforms is the large volume of contentgenerated by users. For example, when individuals tweets abouta TV program, the names of its characters, the names of the actorsand actress, as well as the plot of the play are likely to be men-tioned recurrently. Such content makes it possible for us to learnabout the properties of TV programs, which is expected to contrib-ute positively to TV program recommendation.

Given the availability of user interaction data and user generatecontent on the microblog platforms, we attempt to leverage themto improve recommendation accuracy on top of Probabilistic Ma-trix Factorization (PMF), a model-based collaborative filteringmethod. The similarity of user interests is measured based on thesocial interactions among users on a microblogging platform. La-tent Dirichlet Allocation (LDA) algorithm is employed to derive to-pic models from the user generated content, based on which wemeasure the similarity of items. By incorporating the two typesof similarity in probabilistic matrix factorization through regulari-zation, we expect to partially relief the data sparsity problem andthe cold start problem. Specifically, two regularizers are added tothe objective function of probabilistic matrix factorization. The firstregularizer requires friends of similar interests as measured by so-cial interacts to have similar user profile. The second regularizer re-quires items associated with similar topic models to share similaritem profiles. It is worth noting that the regularization may also beapplicable to the objective function of other model-based collabo-rative filtering methods.

We validated the proposed algorithm with the task of recom-mending TV programs using data retrieved from Sina Weibo, thelargest microblog site in China. The experimental results indicatethat the proposed algorithm significantly outperforms the state-of-the-art-algorithms, demonstrating the effectiveness of the tworegularizers. We also test the proposed algorithm under data spar-sity and cold start scenarios and show that it is more robust thanprobabilistic matrix factorization in dealing with these problems.Finally, the methods are compared in terms of the coverage andpopularity of the recommended items. The proposed method isshown to keep a good balance of coverage and popularity by incor-porating the two regularizers.

The rest of the paper is organized as follows. In Section 2, wesummarize the related work and background of major approachesfor recommender systems. In Section 3, we introduce the definitionand notations of the problem. Section 4 briefly reviewed the prob-abilistic matrix factorization method. The proposed algorithm andthe learning method are shown in Section 5. Section 6 introducesthe data set we used to validate the proposed algorithm. Theexperimental results and discussion are presented in Section 7.Finally, we conclude in Section 8.

2. Related work

Recommender systems have been widely studied and imple-mented in recent years, both in academia and in industry. As oneof the most successful approaches to building recommender sys-tems, collaborative filtering uses the preferences of a group ofusers to make recommendations or predictions of users’ prefer-ences on unrated items.

There are three main categories of collaborative filtering tech-niques: memory-based, model-based, and hybrid collaborative fil-tering algorithms [23]. Memory-based collaborative filteringalgorithms are based on the entire collection of previously rated

items by the users. The prediction on the rating Rui of the user uto the item i is obtained by identifying the N most similar neigh-bors of a user or an item. Memory-based collaborative filteringalgorithms suffers significantly from the data sparsity problem.To overcome the drawback of memory-based collaborative filter-ing algorithms, model-based collaborative filtering algorithms de-velop a model of user ratings, thus enabling the system to learncomplex patterns based on training data. In general, classificationalgorithms are used when the user ratings are categorical andregression models or Singular Value Decomposition (SVD) basedmethods are used for numerical ratings.

There are many studies on model-based collaborative filteringalgorithms. Koren [7] merged the factor and neighborhood modelsand builded a more accurate combined model to exploit both ex-plicit and implicit feedback by the users. Paterek [15] tried severalmethods: addition of biases to the regularized SVD, postprocessingSVD with kernel ridge regression, using a separate linear model,and using methods similar to the regularized SVD. They proposea framework for combining them to obtain a good prediction. Guet al. [5] proposed a unified model for collaborative filtering basedon graph regularized weighted nonnegative matrix factorization.The proposed method not only inherits the advantages of model-based method, but also owns the merits of memory-based methodwhich considers the neighborhood information. It has the ability tomake use of content information and any additional informationregarding user–user such as social trust network. Zhen et al. [26]proposed a novel framework, called tag informed collaborativefiltering which seamlessly integrate tagging information into thecollaborative filtering procedure.

By modeling the actual choice process in recommender systems(i.e. users are presented with a few number of items for rating at atime), Yang et al. [25] proposed the collaborative competitive fil-tering framework for learning user preferences. Collaborative com-petitive filtering employs a multiplicative latent factor model tocharacterize the dyadic utility function. Unlike collaborative filter-ing, collaborative competitive filtering models the user behavior ofchoices by encoding a local competition effect.

Latent Dirichlet Allocation (LDA) is a three-level hierarchicalBayesian model which has be used in recommender systems[16,18]. Purushotham et al. [17] proposed a hierarchical Bayesianmodel to integrate social network structure (using matrix factor-ization) and item content-information (using LDA model) for itemrecommendation. Liu et al. [9] proposed an interest expansionstrategy via personalized ranking based on the topic model forbuilding an interest-oriented collaborative filtering framework.Agarwal et al. [2] proposed a novel matrix factorization methodto predict ratings in recommender system applications. To avoidoverfitting, user and item factors in this model are regularizedthrough Gaussian linear regression and LDA priors respectively.Krestel et al. [8] introduced an approach based on LDA for recom-mending tags of resources in order to improve search.

Furthermore, traditional recommender systems assume that allthe users are independent and identically distributed; this assump-tion ignores the connections among users, which is not consistentwith the real-world observations where we always turn to ourtrusted friends for recommendations. In recent years, several stud-ies attempted to exploit trust in making recommendations. A hy-brid trust-based multi-criteria recommendation approach wasproposed to handle business partner matching e-services, whichintegrates trust-based filtering with the multi-criteria collabora-tive filtering [19,20]. Within the framework of collaborativefiltering, Shambour and Lu [21] proposed a TrustSemantic Fusion(TSF)-based recommendation approach which leverages informa-tion from the users’ social trust network and the items’ semanticdomain knowledge to alleviate the problem of data sparsity andcold-start in recommendation. The approach was validated with

312 Y. Zhang et al. / Knowledge-Based Systems 54 (2013) 310–317

a business-to-business recommendation application. Nepal et al.[14] introduced the concept of engagement trust and popularitytrust, by combining which, the social trust of the community andindividuals are then derived. Different types of trust may be usedto recommend different things. Ma et al. [11,10,12] proposed a no-vel probabilistic factor analysis framework which naturally fusesthe preferences of the users and the preferences of their trustedfriends together.

Among the above studies, the ones that closely related to ourstudy is [12], where the user-specific vector of the user i is pro-posed to be a mixture of the user’s own vector and his/her friends’vector, formulated as follows:

ui aui þ ð1� aÞX

k2T ðiÞSikuk; ð1Þ

where the parameter a controls how much users trust themselvesor their trusted friends, T ðiÞ is the set of friends that the user i trustsand Sik which is normalized by jT ðiÞj denotes how much the user itrusts the user k. However, the global parameter a in their modeldoes not take into account the fact that different users have differ-ent willingness to trust their friends. And Sik is calculated by thesimilarity between two users based on their past ratings on items.The symmetric equation Sik = Ski in this model failed to explain thefact where the user i trusts the user k does not necessarily meanthe user k trusts the user i.

3. Problem description

For the rest of the paper, we use the application of TV programrecommendation through Sina Weibo as an example to derive ourrecommendation algorithms. We begin by providing a descriptionof the problem under study.

The user-item rating matrix of m users and n items is denoted asan m � n matrix R where Rij (i = 1, . . . ,m; j = 1, . . . ,n) represents therating of the user i for the item j. Typically, the values of Rij may beeither categorical or numerical. In our case, we consider the prob-lem whether a user likes an item or not. Thus the values of ratingsare binary (0 or 1).

With the Sina Weibo, we are provided with users’ following andfollower relationships, users’ tweeting and retweeting behaviors,as well as the content of the tweets. Given the above user-item rat-ing matrix, users’ social networks and their mutual interactions, aswell as the rich content information on Sina Weibo, we investigatethe problem of how to optimally integrate the above data to pre-dict the missing values from rating matrix.

4. Probabilistic matrix factorization

Before we introduce the proposed algorithm, we first give abrief review of probabilistic matrix factorization, based on whichwe derive the proposed algorithm with regularization. Probabilis-tic matrix factorization tries to characterize the users and itemson latent factor space, thus predicting users’ rating on items by cal-culating the similarity/correlation between the user vectors andthe target item vectors in the latent factor space. For most recom-mendation problems, the user-item rating matrix can be approxi-mate at low rank because only part of the factors contribute tousers’ preferences and items’ characteristics. The latent user anditem factors are denoted as U 2 Rl�m and V 2 Rl�n, respectively.Typically the dimension of the feature space l satisfies l�m, n.The column vectors ui and vj are the user-specific and item-specificfactor vectors that describe the preferences of the correspondingusers and the properties of the corresponding items, respectively.

The conditional distribution of the observed ratings can thus beformulated as:

pðRjU;V ; d2Þ ¼Ymi¼1

Yn

j¼1

N RijjgðuTi v jÞ; d2� �� �IR

ij ; ð2Þ

where Nðxjl; d2Þ represents the probability density function of aGaussian distribution with mean l and variance d2, g(x) is a logisticfunction g(x) = 1/(1 + exp(�x)), and IR

ij is the indicator functionwhich is equal to 1 if user i rated item j and 0 otherwise. The ratingsare binary in our case. We relax the predicted ratings bRij to [0,1] andemploy the logistic function g(x) to bound it in the range of [0,1].

bRij ¼ gðuTi v jÞ:

To estimate R̂ij, we place the zero-mean spherical Gaussianpriors on user and item vectors:

pðUjd2UÞ ¼

Ymi¼1

Nðuij0; d2UIÞ; ð3Þ

pðV jd2V Þ ¼

Yn

j¼1

Nðv jj0; d2V IÞ: ð4Þ

Through Bayesian inference, we maximize the posterior distri-bution by minimizing the regularized squared error given by

frsvd ¼12

Xm

i¼1

Xn

j¼1

IRij Rij � gðuT

i v jÞ� �2 þ kU

2

Xm

i¼1

uTi ui þ

kV

2

Xn

j¼1

vTj v j; ð5Þ

where kU ¼ d2=d2U and kV ¼ d2=d2

V . Here the regularization termscontrolled by kU and kI are used to prevent overfitting.

5. Regularized probabilistic matrix factorization

In this section we present the derivation of the proposed regu-larized probabilistic matrix factorization algorithm. Given theunderlying social network, messaging behaviors of the users, andthe content of the messages, two regularizers are introduced tothe objective function of probabilistic matrix factorization: oneregularizer requires one to share similar user profile to the friendsthat he/she frequently interacts with, and the other regularizer en-forces similar items as measured by topic similarity to share simi-lar item profiles.

5.1. The social regularizer

In real life, it is typical for individuals to seek recommendationsand opinions from their friends. As a result, individuals’ behaviorsare more or less influenced by their friends. On the microblog plat-form, if the user a follows the user b, the user a is likely to be influ-enced by the user b. However, users may follow hundreds ofpersons on microblog platform, the degree of trustiness measuredby the social network structure itself is error-prone. Instead, wedeem the social interactions among users such as retweetingbehaviors as signs of trustiness. Intuitively, the probability thatthe user i follows and retweets a message of the user j highly cor-relates with the degree of trustiness that the user i has on the userj. We thus empirically define the degree of trustiness Tik to be:

Tik ¼RTik

RTi; ð6Þ

where RTik is the number of retweets from the user i to the user kand RTi is the total number of retweets from the user i. One maywant to note two important properties of Tik:

Y. Zhang et al. / Knowledge-Based Systems 54 (2013) 310–317 313

� Tik is a measurement of a user’s relative trust to his/her friends.The sum of Tik over of the user i’s friends satisfies

Pk2T ðiÞ Tik ¼ 1.

� Trust relationship is unidirectional and unsymmetrical. In mostsituations, Tik – Tki. The user a retweets to the user b does notnecessarily mean the user b should retweet back to the user a.Even if the users a and b trust each other, it does not mean theytrust the other in the same degree.

To model the fact that different users may have different will-ingness to trust their friends, we introduce the parameter a to indi-cate a user’s originality as opposite to the tendency to trust others.Intuitively, the user i is more likely to be influenced by his friends ifretweeting constitutes a high proportion of his messaging behav-iors. Hence, we empirically set ai as the ratio of user i’s originaltweets to the total number of tweets/retweets from the user i.

We propose two forms of regularization terms to maximize thesimilarity of the user-specific factor vectors between the users andtheir trusted friends.

ru1 ¼ktrust

2

Xm

i¼1

ui � aiui þ ð1� aiÞX

k2T ðiÞTikuk

0@ 1A������������

2

¼ ktrust

2

Xm

i¼1

ð1� aiÞ2 ui �X

k2T ðiÞTikuk

������������

2

; ð7Þ

ru2 ¼ktrust

2

Xm

i¼1

ð1� aiÞ2X

k2T ðiÞTikkui � ukk2

; ð8Þ

where ktrust > 0 is the parameter to control the strength of the socialregularization. Eq. (7) can be seen as a user adaption of the average-based social regularization proposed in [12]. Eq. (8) is similar to theindividual-based regularization model [12], except that the valuesfor Tik and ai are computed for each individuals based on real inter-action data.

5.2. The item similarity regularizer

Previous studies have shown that item’s content informationcan provide helpful information for recommendation. For example,users tend to watch the TV programs that has same tags, of thesame genre or with the same actors/actresses as the ones theywatched before. Considering messages in microblog provide a richvolume of relevant information for items, we introduce a similaritymeasure to characterize item similarities based on the content. Weuse the LDA model proposed by Blei where documents are replacedby messages for the same items. We assume that each item is asso-ciated with a multinomial distribution over topics. Thus we can usethe item conditioned topic distributions to measure similarityamong items.

Assume there are k topics and t items. We treat messages thatmention the same item as one single document. Given the wordprobabilities b, the generative process for each item i can be shownas:

1. Draw topic proportions hi � Dirichlet(a).2. For each word wi,n:

(a) Choose a topic zi,n �Multinomial(hi).(b) Choose a word wi;n � Multinomialðbzi;n

Þ.

Thus for given a item pair i and j, the similarity between them canbe simply defined as the cosine similarity of the topic proportions:

Sij ¼hT

i � hj

khik � khjk: ð9Þ

Similar to the regularization terms for user properties, we pro-pose two regularization terms using the content similarities. Theregularization is formulated with the following two functions:

ri1 ¼ksim

2

Xn

j¼1

v j �P

h2SðjÞ SjhvhPh2SðjÞ Sjh

����������

2

; ð10Þ

ri2 ¼ksim

2

Xn

j¼1

Xh2SðjÞ

Sjhkv j � vhk2; ð11Þ

where ksim > 0 is a parameter to control the strength of the itemsimilarity regularization and SðjÞ is the set of top N similar itemsof item j. Here, N is a parameter and a larger value for N may suggestthat users are more likely to be interested in items similar to theones they liked before. Eq. (10) can be seen as the average-baseditem similarity regularization and Eq. (11) is individual item-basedregularization.

5.3. The proposed hybrid model

By integrating the above social regularizer and item similarityregularizer into the probabilistic matrix factorization, we obtainthe new objective function as follows:

f ¼ frsvd þ ru� þ ri� ; ð12Þ

where � can be replaced by 1 or 2, representing different variationsof the regularization. Gradient descent in vectors ui and vj areapplied to optimize the functions f.

@f@ui¼ @frsvd

@uiþ @ru�

@ui; ð13Þ

@f@v j¼ @frsvd

@v jþ @ri�

@v j; ð14Þ

The gradient for each component of the function f may be derived asfollows. According to Eq. (5), the gradient for frsvd is:

@frsvd

@ui¼Xn

j¼1

IRij gðuT

i v jÞ � Rij� �

g0ðuTi v jÞv j þ kUui; ð15Þ

@frsvd

@v j¼Xm

i¼1

IRij gðuT

i v jÞ � Rij� �

g0ðuTi v jÞui þ kVv j; ð16Þ

where g(x) is a logistic function gðxÞ ¼ 1=ð1þ expð�xÞÞ, g0ðxÞ ¼expð�xÞ=ð1þ expð�xÞÞ2, IR

ij is the indicator function which is equalto 1 if user i rated item j and 0 otherwise, and Rij is the rating ofthe user i to the item j.

Based on Eqs. (7) and (8), we have the gradient of ru� as follows.

@ru1

@ui¼ ktrustð1� aiÞ2 ui �

Xk2T ðiÞ

Tikuk

0@ 1A� ktrust

Xg2T nðiÞ

Tgið1� agÞ2 ug �X

k2T ðgÞTgkuk

0@ 1A; ð17Þ

@ru2

@ui¼ ktrustð1� aiÞ2

Xk2T ðiÞ

Tikðui � ukÞ

þ ktrust

Xg2T nðiÞ

Tgið1� agÞ2ðui � ugÞ; ð18Þ

where T n ðiÞ is the set of users who interacts with the user i.Based on Eqs. (10) and (11), we have the gradient of ri� as

follows.

@ri1

@v j¼ ksim v j�

Xh2SðjÞ

S0jhvh

0@ 1A�ksim

Xg2SnðjÞ

S0gj vg�X

h2SðgÞS0ghvh

0@ 1A; ð19Þ

314 Y. Zhang et al. / Knowledge-Based Systems 54 (2013) 310–317

@ri2

@v j¼ ksim

Xh2SðjÞ

Sjhðv j � vhÞ þ ksim

Xg2SnðjÞ

Sgjðv j � vgÞ; ð20Þ

where S n ðjÞ is the set of items that has the item j in the top N sim-ilar items. To simplified the calculation, we normalize the values ofSjh in Eq. (20) to S0jh for each item j so that

Ph2SðjÞ S0jh ¼ 1.

6. Sina Weibo data set

We evaluate the proposed algorithms on a data set collectedfrom Sina Weibo, which provides twitter-like social network ser-vice in China. We leverage the interest group, a discussion groupfor people with shared interest, on Sina Weibo to collect the data.For the purpose of TV program recommendation, we select theinterest groups related to TV programs to begin with and use theusers in those groups as seeds. The users’ followers, their messag-ing behaviors, and the content of their messages are retrieved. Inaddition, we also retrieved the messages from their followers.The entire data set contains all tweets from 227,222 users. Forthe purpose of evaluation, we only keep the users who posted atleast ten tweets about TV programs and the TV programs thatare mentioned at least 100 times.

The distributions of the user activity and item popularity aredrawn in Fig. 1 (plot in log–log scale). The point (x, y) in Fig. 1ameans that there are y users that have at least x ratings. Similarly,the point (x, y) in Fig. 1b means that there are y items that havebeen rated by at least x users. The fact that the two lines are closeto linear on the log–log scale in Fig. 1 suggests that the user activityand item popularity both follow a power-law distribution.

When performing sentiment analysis with this data set, we findthat about 90% of the tweets mentioned the TV programs are posi-tive reviews because users usually will not comment a TV programif they dislike it. Hence, we generate the user-TV program ratingmatrix by assigning a value 1 to the corresponding entry if a usermentioned a TV program at least once. For the items/TV programsthat a user does not comment, we are not sure about the user’spreference as a user may not always comment even if he/she likesthe show. In general, we may assume that the more often a usercomment on TV programs, the more likely that he/she dislike theshows that he/she does not comment on. In order to add explicitnegative feedback to the data set, if a user rated N items, we thenrandomly choose N items not mentioned by the user and assigntheir rating as 0. In total we retrieve 1,253,149 ratings from40,581 users on 1920 TV programs. The density of the data is1.6%. There are 1,910,370 following–follower relationships among

100 101 102 103

101

102

103

104

Number of ratings

Num

ber o

f use

rs

(a) User Activity

Fig. 1. The statistics of the

these users. Among them there are 583,606 relationships with re-tweet behavior. On average, a user follows 47 users and retweetsmessage from 14 users.

7. Experiments

We experimented with 5 variations of the proposed algorithms.We compare our methods with probabilistic matrix factorization,and two state-of-the-art algorithms (SR1 and SR2 in [12]). SR1 usesthe average based social regularization and SR2 uses the individualbased social regularization. For SR1 and SR2, it has been shownthat the Pearson Correlation Coefficient (PCC) similarity basedmethods are more accurate than the Vector Space Similarity(VSS) similarity based method. Hence here we only evaluate thetwo methods with PCC similarity function. The settings and thecorresponding IDs of the algorithms are shown in Table 1.

We test the algorithms with the Sina Weibo data set and pres-ent the results in the rest of this section. For all methods, thedimensionality of the latent features are empirically set to be 10because similar results are obtained when varying its value. Wealways set kU and kV to be equal to each other. In gradient descend-ing, the step size for all methods is empirically set to 0.0005. As allof the methods are stable after 10,000 steps, we set the max stepfor each method to be 10,000.

7.1. Evaluation metric

We use Root Mean Square Error (RMSE) as the evaluation met-ric, defined as follows:

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPi;jðRij � bRijÞ

2

T

s; ð21Þ

where T denotes the total number of tested ratings and bRij denotesthe predict rating. A smaller RMSE value indicates a better recom-mendation accuracy.

7.2. Comparison of algorithms

We randomly select 30%, 50% and 80% of ratings for training,and use the rest for testing. The random selection was carriedout 5 times independently, and the average results are reportedin Table 2. To be fair, the parameters in each experiment are setas the best of what we found in parameter tuning, which are listedin Table 1. There are totally four hybrid versions of social

101 102 103 104 105

101

102

103

Number of ratings

Num

ber o

f ite

ms

(b) Item Popularity

Sina Weibo data set.

Table 1The settings of the algorithms under comparison.

Algorithm ID Objective function Optimal parameter setting

PMF frsvd (Eq. (5)) kU = kV = 1.2SR1 Eq. (8) in [12] kU = kV = 0.5, ktrust = 30SR2 Eq. (11) in [12] kU = kV = 0.5, ktrust = 1UR1 frsvd + ru1 (Eq. (7)) kU = kV = 0.5, ktrust = 30UR2 frsvd + ru2 (Eq. (8)) kU = kV = 0.5, ktrust = 30IR1 frsvd + ri1 (Eq. (10)) kU = kV = 1, ksim = 0.1, N = 5IR2 frsvd + ri2 (Eq. (11)) kU = kV = 1, ksim = 0.1, N = 5UR1 + IR2 frsvd + ru1 + ri2 kU = kV = 0.2, ktrust = 30, ksim = 0.1, N = 5

Y. Zhang et al. / Knowledge-Based Systems 54 (2013) 310–317 315

regularization and item similarity regularization. We here onlyreport the result of the best combination, UR1 + IR2. Table 2reports the RMSE for all methods. As can be seen from the experi-mental results, all of the proposed methods achieve a better perfor-mance than PMF, suggesting the effectiveness of the socialregularization and the item similarity regularization. When 80%of the data are used for training, the proposed hybrid model out-performs the PMF method by over 4% in terms of RMSE. And theimprovement is even larger when less data are used for training(6% improvement with 50% of data for training and 9% improve-ment with 30% of data for training), suggesting that the proposedhybrid model is robust in handling the data sparsity problem.The algorithms UR1 and UR2 consistently outperform thealgorithms SR1 and SR2 in all training setting, indicating that ourestimation of trustiness is more reasonable.

In regularization with SR� and UR� (� = 1,2), a user on average isconnected with 47 users and 14 users respectively as described inSection 6. In regularization with IR� (� = 1,2), an item is connectedto 5 items. In Ma’s experiments [12] with Douban and Epinions, auser trusts 10 users on average. In their experiments, SR2 performsslightly better than SR1. We may conclude that individual basedmethods perform better when the number of neighborhood is rel-atively small as we can see from IR1 and IR2. However, the averagebased methods are more stable when the number of neighborhoodis relatively large when comparing SR1 and SR2 using the SinaWeibo data set. Moreover, SR2 on 80% data performs even worsethan PMF. This suggests that when considering a large number ofneighborhood, we should carefully tune the parameter k that con-trols the contribution of regularization.

As can be seen from the results, the improvement of social reg-ularization is larger than that of the item similarity regularization.This is probably due to the fact that users tend to watch the pop-ular TV series. Items can spread further through friends’ recom-mendation even if users never watch similar types of TVprograms before. We test this hypothesis in Section 7.6. Moreover,among all the tested algorithms, the proposed hybrid model per-forms best, with smaller prediction error in terms of RMSE thanthe models with only social regularization or the ones with onlythe item regularization.

7.3. Impact of social regularizer

The parameter ktrust controls the contribution of socialregularization. In extreme cases, ktrust = 0 means there is no social

Table 2Comparison of the algorithms with Sina Weibo data in terms of RMSE.

Train(%)

PMF SR1 SR2 UR1 UR2 IR1 IR2 UR1 + IR2

30 0.412 0.397 0.393 0.383 0.386 0.409 0.407 0.37450 0.390 0.372 0.385 0.368 0.369 0.388 0.387 0.36480 0.376 0.361 0.379 0.360 0.361 0.374 0.373 0.357

regularization, and a very large value for ksim means that usersstrongly trust their friends for recommendations. The parameterktrust is tuned through grid search (ktrust = {1,5,10,20,30,50,100}).The impact of ktrust on the performance of UR1 is shown inFig. 2a. The impact of ktrust to UR2 shows a similar pattern.

The experimental results demonstrate that by leveraging theusers’ social interaction information for recommendation, onecan achieve lower prediction error in terms of RMSE. In addition,when tuning the parameters, we find that after integrating the so-cial regularization into the PMF model, the regularization parame-ters kU and kV in PMF assume smaller values without overfittingand in the meanwhile output more accurate recommendations.

7.4. Impact of item similarity regularizer

The parameter ksim controls the contribution of item’s contentregularization. ksim = 0 means that item similarity is not used forrecommendation, and a very large value for ksim means that userslike the items that share similar contents to the ones they haveliked before.

We tune the parameter ksim through grid search(ksim = {0.01,0.03,0.1,0.3,1}. The experimental result is show inFig. 2b. Based on the results, we can see that knowledge of similar-ity in item content does help improve the recommendation accu-racy based on the PMF model.

Another parameter in item similarity regularization is the num-ber of similar items N. A larger value for N can be interpreted asthat users like many similar items as the ones they liked before.Since the variation of N shares the same trends in IR1 and IR2,we only show the impact on IR2 with parameter settingskU = kV = 1, ksim = 0.1, l = 10. The parameter N is tuned by searchingthe grid {3,5,10,20}. Table 3 shows the change in RMSE whenvarying the value for the number of similar items N.

As we can see from Table 3, the best result is achieved whenN = 5. The item similarity regularization is in fact relatively sensi-tive to the number of similar items N. When N surpasses 10, we ob-serve the performance is even worse than PMF. One reason forsmall values for N can be that we have a relatively small set ofitems in our data set.

7.5. Cold start problem

In a recommender system, when a new user or a new itementers the system, due to the lack of information about the useror the item, recommendation becomes a difficult problem. To over-come this problem, some recommender systems provide a list ofitems for newly registered users to select. Users’ feedback to thesequestions may serve as a few ratings to describe the user [4]. Withmicroblog platform, even if a user seldom talks about TV programs,we may leverage his/her friends’ preference to help recommenda-tion. Using the information from social networks we expect toalleviate the cold start problem on new users.

As in our system, a user rated 30 items on average. To demon-strate how our algorithms performs on the cold start problem, werandom split the users into two teams: 80% for old users and 20%for new users. The ratings of old users are all kept in the trainingdata. For the new users, only n ratings are used for the trainingand the remaining ratings are used for testing. Because PMF cannotpredict the users without previous ratings, we set n = {3,5,10} forPMF and n = {0,1,3,5,10} for the proposed hybrid model. Theparameter settings for PMF and our hybrid model UR1 + IR2 arethe same as in subSection 7.2. Fig. 3 shows the comparison of thealgorithms in terms of RMSE with various values of ratings in train-ing. n = 0 is a strict cold-start setting.

As can be seen from the experimental results, the proposedhybrid method clearly outperforms PMF on the cold start problem

Fig. 2. The impact of regularization parameters for social regularizer and item similarity regularizer.

Table 3RMSE comparison on number of similar items.

Training (%) N = 3 N = 5 N = 10 N = 20

50 0.3871 0.3869 0.3886 0.392180 0.3728 0.3726 0.3732 0.3747

316 Y. Zhang et al. / Knowledge-Based Systems 54 (2013) 310–317

for new users. Moreover, it is less affected by the numbers of pre-vious ratings. The prediction made by the proposed hybrid modelfor users with no previous ratings is actually even more accuratethan that of PMF for users with 10 previous ratings. However, be-cause item similarity regularization in our models needs the itemsbeing mentioned by the tweets before, our model is not designedto solve the cold start problem for new items.

7.6. The novelty and coverage

We also compare the following four models on 50% trainingdata in terms of novelty and coverage of the recommendation:PMF model, UR1, IR2 and the hybrid model UR1 + IR2. The systemrecommends a item j to the user i if the predicted rating score Rij

surpasses a given threshold value. We first plot the ROC (ReceiverOperating Characteristic) curves which are created by plotting the

0 2000 4000 6000 8000 100000.36

0.38

0.4

0.42

0.44

0.46

0.48

0.5

Iteration

RM

SE

PMF, n=3PMF, n=5PMF, n=10hybrid model, n=0hybrid model, n=1hybrid model, n=3hybrid model, n=5hybrid model, n=10

Fig. 3. RMSE on cold start problem.

true positive rate vs the false positive rate at various threshold.Here ratings with value 1 are positive and the ones with 0 are neg-ative. The ROC curves are shown in Fig. 4. The hybrid model isslightly better than UR1 and significantly outperforms IR2 andPMF model.

As can be seen from Section 6, there are a lot of long-tail itemsin the data set. Here we use coverage and novelty metrics to mea-sure the ability of the recommendation system to present long tailitems to users. Coverage is defined as the percentage of items inthe prediction over all the candidate items for system to recom-mend. Here we use I to denote the whole item set, and define Ri

as the item set that is recommended to the user i. Coverage is de-fined as:

Coverage ¼Sm

i¼1 Ri

�� ��jIj : ð22Þ

A high coverage can help users to explore the space of interest-ing items. Moreover, we use the average popularity in recommen-dation list to measure the novelty of recommendation system.Here we defined p(j) as the popularity of the item j (the rating

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

False Positive Rate

True

Pos

itive

Rat

e

hybrid modelUR1IR2PMF

Fig. 4. ROC curves.

Table 4Coverage and novelty comparison.

Algorithm Coverage (%) Popularity

PMF 49.4 7.851UR1 30.1 8.012IR2 48.4 7.802UR1 + IR2 31.1 7.852

Y. Zhang et al. / Knowledge-Based Systems 54 (2013) 310–317 317

count of the item j in training data), and NR as the total number ofrecommendationed items. The popularity based item novelty inrecommendation list is defined as:

Popularity ¼Pm

i¼1

Pj2Ri

logð1þ pðjÞÞNR

: ð23Þ

A lower popularity value means higher novelty, suggesting thatthe recommendated items may probably surprise the users.

We then compare these four models in top 10 recommendateditems with 50% training data. The results are shown in Table 4. Thelowest popularity with IR2 shows that recommendation throughsimilar items tends to present less popular items to users. Thehighest popularity and lowest coverage with UR1 shows that rec-ommendation through friends may enhance the influence of thepopular items, which confirms our hypothesis in Section 7.2.Although UR1 and the hybrid model almost share the same trendsin ROC curve in Fig. 4, hybrid model perform better than UR1 byhaving a higher coverage and higher novelty.

8. Conclusion

Recommender systems have played an important role in onlineinformation systems. In this paper, we propose a method that inte-grate the social network and microblog content information forcollaborative filtering. The above information is used as regulariza-tion terms on top of probabilistic matrix factorization. Experimentson Sina Weibo data set for TV program recommendation haveshowed that the proposed method outperforms the state-of-the-arts methods, demonstrating the effectiveness of the proposedhybrid framework. In addition, we show that the proposed methodis robust in the scenario of making recommendation for new users.Compared to other collaborative methods, the proposed method isless susceptible to the number of existing ratings for users. Wealso measure the proposed model with regarding to novelty andcoverage of the recommendations.

As the item’s content information is relatively stable, recomput-ing LDA is not needed when varying different social regularizationparameter or adding novel users. Hence, compared to other LDA-based matrix factorization model, our algorithm is more efficientin terms of computational cost.

Acknowledgments

This research was supported by the High Technology Researchand Development Program of China (Nos. 2011AA01A107,2012AA011702), Shanghai Science and Technology Rising StarProgram (No. 11QA1403500), Shanghai Talent Development Fund(No. 2010002), and National Basic Research Program of China(No. 2010CB731406).

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