th

,c,

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Micro-bloggingUser interest predictionTemporal and social probabilistic matrixfactorization model

anal watio

sharing their daily activities, exchanging opinions and establishing friendships with others. By analyzing, one can explore users' potential interests, which helps micro-blogging provide

the Int

social media marketing and so on. Micro-blogging is becoming one important in their products, new market dynamics and so on. Micro-

Decision Support Systems 55 (2013) 698709

Contents lists available at SciVerse ScienceDirect

Decision Supp

j ourna l homepage: www.eof the most popular social media platforms where users can sharetheir daily activities, exchange opinions, publish posts on sometrending topics and follow others to get relevant information abouttheir interested topics. If A is following B, B is called A's friend, andA is called B's follower. Thus friendships can either be reciprocatedor one-way [10]. The convenience and high frequency of updates ofinformation in micro-blogging have attracted a large number ofusers to actively participate. For example, Sina-weibo, one of themost popular micro-blogging services in China, has had over 300 Munique visitors since December 31, 2011 and around 100 M tweets

blogging has become an important e-commerce marketing channel,and the promotion of merchandise is accessible to micro-bloggingusers around every corner of this platform. Users' interest plays avital role in the process of micro-blogging's development [7], whichinuences the effect of micro-blogging marketing soon afterwards.The research ndings in [5] point out that the accurate prediction ofusers' interest will improve their satisfaction and promote their buyingdecisions, which will increase the e-commerce business benets un-doubtedly. Decisionmakerswill also benet from the interest predictionwork; Chen and Cheng and Zhao and Lu [4,28] proposed that decisionper day.3 Nowadays, more and more corp

Corresponding author. Tel.: +86 10 8261 4835.E-mail addresses: hongyun.bao@ia.ac.cn (H. Bao), qi

issliao@cityu.edu.hk (S.S. Liao), shuangyong.song@ia.ac.(H. Gao).

1 Tel.: +86 10 62636334.2 Tel.: +852 34427552.3 http://news.xinhuanet.com/tech/2012-02/29/c_122

0167-9236/$ see front matter 2013 Elsevier B.V. Allhttp://dx.doi.org/10.1016/j.dss.2013.02.007ernet, social media hasveryday lives, providingprise inuence through

Corporations utilize micro-blogging not only to introduce theirproducts but also to formulate customer-driven marketing plans byobtaining rich information such as which features customers considerplayed an increasingly signicant role in our ereports on world events, improving enterInterest variation

1. Introduction

With the rapid development ofand changes in their interests over time. Based on these intuitions, in this paper we propose a temporal andsocial probabilistic matrix factorization model to predict users' potential interests in micro-blogging. Byexploiting the matrix factorization technique to learn latent features of users and topics, our model analyzesthe impacts of time information and users' activities, including posting of tweets and establishing friendshipswith others, on the latent feature space of users and topics of their interests. The proposed model provides aunied way to fuse the time information and the social network structure to predict users' future interestsaccurately. The experimental results on Sina-weibo, one of the most popular micro-blogging sites in China,demonstrate the efciency and effectiveness of our proposed model.

2013 Elsevier B.V. All rights reserved.

user accounts on Sina-weibo for marketing. For example, Nokia suc-cessfully held a product release conference for N8 on August 25, 2010.Keywords: users with better personalized information services. Users' behaviors are affected by opinions of their friendsAvailable online 24 February 2013the user-generated contentsA new temporal and social PMF-based mein micro-blogging

Hongyun Bao a,1, Qiudan Li a,, Stephen Shaoyi Liao b

a State Key Laboratory of Management and Control for Complex Systems, Institute of Automb Department of Information Systems and Advanced Transportation Information Systems Rc Department of Electronic Commerce and Information Management, School of Economics a

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

Article history:Received 15 May 2012Received in revised form 20 November 2012Accepted 4 February 2013

Micro-blogging is becominging information about the reThe fast diffusion of informorations are registering

udan.li@ia.ac.cn (Q. Li),cn (S. Song), heng.gao@ia.ac.cn

769084.htm.

rights reserved.od to predict users' interests

2, Shuangyong Song a,1, Heng Gao a,1

on, Chinese Academy of Sciences, Beijing 100190, Chinarch Center, City University of Hong Kong, Hong KongManagement, Southwest Jiaotong University, Chengdu 610031, China

increasingly popular social media platform where users can discover interest-orld and especially corporations are able to understand customers' demands.n and the convenience of micro-blogging have resulted in large audiences

ort Systems

l sev ie r .com/ locate /dssmakers need to grasp users' interest for raising up their satisfactionand providing reasonable results. Asur and Huberman [2] tell us thatthe box-ofce revenues of movies can be successfully forecasted inadvance of their release by analyzing users' interest in micro-blogging.If the forecasted box-ofce revenues are below expectations, decisionmakers can provide ways of lm promotion with some incentives intime, or some other methods for coming up to their expectations. Allin all, it's valuable and meaningful to predict users' interest in social

699H. Bao et al. / Decision Support Systems 55 (2013) 698709media, whether for e-commerce business or decision makers. On onehand, it can help micro-blogging systems provide users with betterpersonalized information and advertising services to motivate users tobe more active. On the other hand, corporations can easily captureusers' future interest and make marketing decisions.

In micro-blogging, trending topics are popular topics, whichmay berelated to emerging events and breaking news or topics under the dis-cussion by a large fraction of micro-blogging users [19]. In Sina-weibo,trending topics are edited and complemented, and users are availableto enter into the trending topics and take part in the discussion bypublishing posts on them. Trending topics often have a clear meaning[11], mainly relating to entertainment, sports, current events and soon. If the user is interested in a trending topic, he/she may publishposts on it. In other words, if a user has published posts on a trendingtopic, it shows that the user has interest in this topic. Posts publishedon some trending topics can well reect users' interests. Thus, in thispaper, we use trending topics to represent users' interests.

Despite the importance of user interest prediction in micro-blogging,existing works onmicro-blogging mainly focus onmining users' currentinterests; little work has been done on prediction of users' potentialinterests. Nori et al. [20] focused on computing the similarity betweena user and a set of resources to predict the user's interests. However,this method ignores the inuence of the user's friends on his/her inter-ests. Besides, it doesn't take the evolution of interests into account.

Some researchers have suggested that users are more affectedby opinions of their peers than inuentials [21,24,25]. By comparingquality of recommendations made by recommender systems to recom-mendations made by users' friends, Sinha et al. [23] showed that users'friends consistently provided better recommendations than recom-mender systems. In social recommendation, making use of the informa-tion in a social graph has recently been receiving increasing researchattention. The experimental results [6,9,1517] show that fusing thesocial network structure of users with the useritem rating matrix canhelp make more accurate and personalized recommendations in a so-cial rating network. From this viewpoint, a user's social network affectsusers' behaviors on the Web.

Additionally, interests of Web users change over time. For time-aware recommendation, it is important to capture users' temporalpreferences to make more accurate recommendations. Xiang et al.[12] stated that users' dynamic preferences are affected by boththeir long-term and short-term preferences. That means their interestsmay vary over time. In this case, to capture users' temporal preferences,it is necessary to follow the evolution of users' preferences. Generally,recent preferencesmay play amore important role in predicting currentpreferences while earlier preferences have relatively smaller contribu-tion to nal recommendation. Especially in micro-blogging, the richinformation and frequent updates make users' interests more extensiveand changeable over time. Therefore, to improve the accuracy of predic-tion of users' interests in micro-blogging, both the social networkstructure and time information should be taken into consideration.

SocialMF [9] is an effective method for detecting users' interestsby exploiting the matrix factorization techniques and analyzingthe inuence of users' friendships on their interests. Based on thismodel, we propose a temporal and social probabilistic matrix factor-ization model (TS-PMF) which fuses on social inuence and thetime information to predict users' interests in micro-blogging. Fol-lowing the evolution of users' interests, to import time informationin our model, we make the latent features of users and topics associ-ated with their previous latent features by adopting an exponentialtime decay function. Using this idea, our approach accuratelydescribes the change of the distribution of the latent feature spaceof users' interests. The proposed model can reect the impacts ofusers' interest evolution and users' friendships on their future inter-ests, thus realizing the prediction of users' interests. The experimentalresults on Sina-weibo demonstrate that our model can improve the

quality of prediction.The remainder of this paper is organized as follows. In Section 2,some related work is discussed. Section 3 introduces the proposedmodel. Results of the detailed experimental analysis are presentedin Section 4. Finally, we conclude the paper and present some direc-tions for future work in Section 5.

2. Related work

In this work we propose a novel model to predict users' interestsin micro-blogging. Our work is related to prediction of user interestin micro-blogging, trust-aware recommendation and time-awarerecommendation. In this section we review the related works.

2.1. User interest analysis and prediction

Banerjee et al. [3] gathered tweets data from Twitter across ten(worldwide) cities over a period of four weeks to generate an exhaus-tive list of keywords and then applied statistical and mining techniquesto discover the distribution of users' interest on categories such asmovie, food, game, dinner and so on. Xu et al. [30] proposed amodied author-topic model to discover users' topics of interest onTwitter by ltering out interest-unrelated tweets (noisy posts) fromthe aggregated user proles. These studies concentrated on the textlevel analysis of user interests. Yan et al. [27] established a humandynamic model co-driven by interest and social identity and showedthat users' interest in sending posts is positively correlated with thenumber of comments on their previous posts.

Existing works on micro-blogging mainly focus on mining users'current interests; little work has been done on prediction of users'potential interests. Nori et al. [20] proposed ActionGraph, a new graphicrepresentation for modeling users' multinomial, time-evolving actions,to compute the similarity between a user and a set of resources topredict the user's interest. ActionGraph is a bipartite graph whoseedge connects an action node at some point in time and the objectnodes representing users and resources. It preserves the time informa-tion for each user by representing the same action in different times asdifferent action nodes. However, it ignores the inuence of the user'sfriendships on his/her interest. Besides, it doesn't take the evolution ofinterest into account.

2.2. Trust-aware recommendation

In social networks, users can follow others whom they are inter-ested in, and then they may have social interactions or connectionsinstead of being independent and identically distributed. Many re-searchers have recently focused on trust-aware recommendersystems. Ziegler and Golbeck [29] established two frameworks for inves-tigating and analyzing the correlation between interpersonal trust andinterest similarity, and empirical results showed that themean similarityof trusting and trusted peers exceeded the arbitrary user similarity.Massa andAvesani [18] show that the idea of Trust-aware RecommenderSystem is not to search for similar users as CF (Collaborative Filtering)does but to search for trustable users by exploiting trust propagationover the trust network. The items appreciated by these users are thenrecommended to the active user. They present a complete evaluationof Trust-aware Recommender System, by comparing different algo-rithms, ranging from traditional CF ones to algorithms that utilize onlytrust information with different trust metrics and algorithms that com-bine both trust and similarity to baseline algorithms. Those methodsare all memory-based methods not scalable to very large datasets.

Ma et al. [6,15,16] studied the relationship between the trust net-work and the useritem matrix systematically and proposed themethods integrating social network structure and the useritem rat-ing matrix, which were based on probabilistic factor analysis. Jamaliand Ester [9] stated that the real world recommendation processes

are not reected in the model [6,15,16]. Due to social inuence,

ian1

wothi

the: th

Therefore,

700 H. Bao et al. / Decision Support Systems 55 (2013) 698709p UjC;2U ;2C

p U2U j

p 2C

m

i1N Uij0;2UI

m

i1N UiNj

vN i CivUv;

2CI

!i1 j1

where N(x|, 2) is the Gaussian distribution with mean and varand equal to 0 otherwise. The function g(x) is the logistic function g(x) =[0,1].

Social network researchers have pointed out that the social netSpecically, a user is more and more similar to his/her friends. Fromfactorization for recommendation in social network [9].

Because the behavior of a user ui is affected by his/her friends N(i),his/her friends uv N(i). For user latent features, there are two factorswhere each row of C is normalized, through Civ = 1/|N(i)| with v N(i).1

ce 2, and IijR is the indicator function that is equal to 1 if Rij = 1/ (1 + exp(x)), which makes it possible to bound xwithin the range

rk structure plays an important role in users' behavior [21,23,25].s perspective, SocialMF incorporates social inuence into the matrix

latent feature vector of ui is dependent on latent feature vectors of alle zero-mean Gaussian prior and the latent features of his/her friends.

2p R jU;V ;2R mn

N Rij g UTi V

;2R

iIRijrelated people in a social network inuence each other to become moresimilar. They proposed a SocialMFmodel by incorporating trust propaga-tion into a matrix factorization for recommendation in social network.Their experimental results demonstrate that SocialMF outperformsexisting methods for social network based recommendation.

In the advertising recommendation system of micro-blogging,some researchers are taking advantage of friendships of users [14].

2.3. Time-aware recommendation

Ding and Li [26] presented a new time weight collaborative lteringalgorithm using an exponential time decay function to compute timeweights for different items according to each user and each cluster ofitems. Xiang et al. [12] argued that user preferences often exhibitlong-term and short-term factors and proposed a STGmodel to captureusers' dynamic preferences by considering all items viewed by a user ashis long-term preferences and items viewed by him at a given time ashis short-term preferences. Xiong et al. [13] presented a Bayesian Prob-abilistic Tensor Factorization algorithm formodeling evolving relational

data by organizing the ratings into a three-dimensional tensor whosethree dimensions correspond to user, item and time slices, assumingeach time feature vector depends only on its immediate predecessor.Ahmed et al. [1] argued user proles were temporal and changed useractivity patterns, thus presenting a comprehensive statistical frame-work for user proling based on topic models. Their method modeledtopical interests of a user dynamically where both the user associationwith the topics and the topics themselves were allowed to vary overtime, ensuring that the proles remain current.

Thus, in extant literature, little work has been done on predictionof users' potential interests in micro-blogging; works on trust- andtime-aware recommendation show that both the social networkstructure and the time information are important for recommenda-tion in social network. In this paper, we propose a TS-PMF model topredict users' interests in micro-blogging, which provides a uniedway to integrate the social network structure and the time informa-tion. Specically, we express users' interests as a series of temporalmatrices and use the probabilistic matrix factorization technique tolearn the users' latent feature space and topics' latent feature spaceby employing users' social network and temporal matrices.

3. The proposed user interest prediction model

In this section, rst we introduce the theoretical background for our proposed model. Second, we illustrate how to fuse social network struc-ture and time information in our TS-PMF model to predict users' interests in micro-blogging.

3.1. Theoretical background

We introduce some notations rst. We have a set of users U = {u1,, um} and a set of topics Z = {z1,, zn} in a micro-blogging dataset. Weconstruct a usertopic matrix R Rm n to represent users' interests, where we set Rij = 1 if ui has published posts on zj. In micro-blogging,each user can follow others whom he is interested in. Then users' friendships can be described as a useruser matrix C Rm m, whereCij = 1 that denotes ui has followed uj. Furthermore, we record the set of ui's friends as N(i).

The task of predicting users' interests is to predict the relational scores for a given user ui on topics Z = {z1, , zn} in the futureusing R and C. Salakhutdinov and Mnih [22] have shown that it is very effective to employ matrix factorization techniques to learnthe latent characteristics of users and topics and predict the scores using these latent characteristics. Let U Rd m and V Rd nbe the latent user and topic feature matrices, with column vectors Ui and Vj representing d-dimensional user- and topic-latent featurevectors of ui and zj, respectively. The goal of matrix factorization is to model each score as the production of user- and topic-latentfeature vectors, i.e. Rij UiTVj, where UiT is the transpose of Ui. As is shown in the SocialMF model, the conditional probability of theknown scores is dened as:

jV iU

1vU

2vU1ivC2ivC

C

U CV701H. Bao et al. / Decision Support Systems 55 (2013) 698709Now, the posterior probability of latent variables U and V can be obtained through a Bayesian inference. Maximizing the log of the posteriordistribution is equivalent to minimizing the following sum-of-squared-errors objective function with quadratic regularization terms:

E R;C;U;V 12

Xmi1

Xnj1

IRij Rijg UTi Vj

2

U2

Xmi1

UTi Ui V2

Xnj1

VTj Vj

C2

Xmi1

Ui vN i

CivUi

!TUi

vN i CivUi

! !:

3

The above optimization can be done efciently using gradient descent. The graphical model for SocialMF is presented in Fig. 1.

3.2. Proposed user interest prediction model

R

ijRvlU

( )iNv mi ,...,1=nj ,...,1=

( )iNl =

.

.

.

ivl

Fig. 1. Graphical model of the baseline SocialMF considering the social network in the matrix factorization.In the near future, micro-blogging users may focus on new topics, and they may also show different concerns to the topics which they havebeen interested in for a period of time. The above users' dynamic interests are mainly affected by their friends and their historical favorites.Based on these intuitions, the primary motivation of our model is to provide a unied way to fuse the social network structure and the evolutionof users' interests for predicting users' interests accurately. In this section, we extend SocialMF to predict users' future interests inmicro-blogging by taking time information into account.

3.2.1. Toy exampleWe use a simple toy example to demonstrate the proposed model for predicting users' interests in micro-blogging. There are 6 users

U = {u1,, u6} and 8 topics Z = {z1, , z8} in total. The relationships among users (nodes) are illustrated in Fig. 2(a), and the edge from uito uj denotes that ui has followed uj. We have segmented users' historical data into 3 time points (T1, T2, T3). As shown in Fig. 2(b, c, d), eachuser has published posts on some topics in Tt (t = 1, 2, 3) to express interest in those topics. Our main goal is to predict users' interests inthe future time T4. As elaborated in Section 1, a user's social friendships make his/her interest similar to his/her friends and the currentinterest is also affected by historical interest. Therefore, we minimize the sum-squared distance to the target matrix Rt by UtTVt to factorize

Fig. 2. Data of the toy example.

702 H. Bao et al. / Decision Support Systems 55 (2013) 698709the current usertopic matrix Rt fusing the social network structure and the evolution of users' interest, where Ut denotes the user latent

Z5

U1 U3

U2 U4

Social network

Temporal and social probabilistic matrix factorization

Z3 Z4 Z3 Z2 Z1Prediction results

Micro-blogging Data

Fig. 3. The framework of predicting users' interest.feature space and Vt represents the topic feature space in time t. If we use 5 dimensions to perform the matrix factorization, we obtain Utand Vt (t = 1, 2, 3) and then compute the mean matrices MU4 and MV4 of U4 and V4 for predicting the user-matrix R4 in T4:

MU4

0:3241 0:2288 0:8033 0:3353 0:4104 0:67430:8120 0:2772 1:1198 0:4928 0:8098 0:60440:8709 0:2190 0:0806 0:0979 0:4863 0:26430:3309 1:1181 0:8569 0:6012 0:1000 0:36770:5246 0:6829 0:3100 0:2823 0:9464 0:5734

266664

377775

MV4

0:5594 0:4758 0:5559 0:2031 0:2315 1:0572 0:2741 0:25900:6038 0:6740 0:6816 0:0477 0:3540 0:8846 0:8765 0:76270:0129 0:1069 0:0157 0:4844 1988 0:0478 0:5087 0:06910:7660 0:6818 0:8971 0:5544 0:6918 0:5148 0:1265 0:81640:2424 0:9689 0:3805 0:4788 0:0656 0:6503 0:0563 0:8368

266664

377775

where MU4 ;i and MV4 ;j are the column vectors and denote the latent feature vector of ui and topic zj, respectively, in T4. Then we use

R4MTU4Mv4 to predict all the values in R4, where we need to transfer the value of MTU4 ;i

Mv4 ;j using the function g(x) introduced inSection 3.1. And then according to the values in R4 as shown in Fig. 2(e), each user is provided a topic list he/she is likely to prefer in thefuture.

We take u4 as an example to explain the reasoning behind the prediction by our model. As shown in Fig. 2(a), u4 has followed u1 and u2. u4has focused on z8 in T2 and u2 has also focused on z8 in T2 and T3 as well as u1 does in T3. Considering the impacts of his/her friends and theevolution of interest, our model predicts u4 will be interested in z8 in T4 with the maximum probability of 0.67. Since u4 is interested in z6 inT3, and only u1 has paid attention to z6 in T1, our model provides z6 for u4 in the second place in the prediction list. While both u1 and u2 areinterested in z2 in T3, and u4 has never published posts on z2, our model places z2 in the third place.

3.2.2. The proposed modelIt's noticeable that users' interests are changing over time; users show their concerns to different topics at different times. For example, a user

was fond of some electronic products in early days, but lately, he took a great interest in the topic of new iPad for a few days. Two inuencingfactors may prompt him to perform like this; maybe he was informed of the message that the new iPad has been released, or he was likelyaffected by his friends who had focused on this topic for a while. The users' dynamically changing interests can be expressed as the collection

of users' sequential interest matrix at different times, each of which is constructed as a temporal usertopic matrix Rt Rm n, where t(t = 1, 2, , N) is the time label of the data section. In the usertopic matrix, the value of element Rt,ij equals 1 means that the user ui isinterested in the topic zj at time point t. Meanwhile, users' friendships can be expressed as a useruser matrix C. Our proposed model isdesigned to utilize users' sequential interest matrices {R1, , RN} at the existing time points (t = 1, 2, , N) and the users' friendshipsmatrix C, to predict users' interest in the near future.

The framework of our proposed model is shown in Fig. 3. At each time point, our model will nd the matrix Rt UtTVt (t = 1, , N) whichminimizes the sum-squared distance to the target matrix Rt under the constraints of the temporal and social impacts, where UtT and VtT representthe users' and topics' latent feature spaces in time t.

In time t, the conditional distribution probability of the observed items in Rt is similar to that in Eq. (1):

p Rt jUt ;Vt ;2Rt

m

i1n

j1N Rt;ij g U

Tt;iVt;j

;2Rt

iIRtij : 4

Ut,iT represents the latent feature vector of user ui in time t. The user's latent feature vector follows Gaussian distribution [6,9,15,16], which is

703H. Bao et al. / Decision Support Systems 55 (2013) 698709decided by the mean value of Gaussian distribution. Changes in mean values always reect changes in users' interests. Normally, users' currentinterests will be affected by his historical favorites; the inuence will be greater with the closer interest to the current time. Amazingly, theexponential decay function can describe the inuence process effectively [26], with the following mathematical expression:

f k exp tk

k 1;2;3;; t1f g > 0 : 5

In Eq. (5), the value of presents the kernel parameter, and the value of t k shows us the time interval between the k-th time point and thecurrent time t. The higher value t k presents the earlier time k from current time t, accompanied with the smaller inuencing value f(k). It'sevident that the exponential decay function can vividly illustrate the inuence that the historical favorites have on the current interests.

Based on the above analyses, we utilize exponential decay function with kernel parameter to compute the mean value matrix of user-latentfeature and the mean value matrix of topic-latent feature in time t. The computing formulation is listed below:

Ut Xt1k1

exp tk

Uk;Vt

Xt1k1

exp tk

Vk 6

where MUt, MVt are the mean matrices of Ut and Vt with spherical Gaussian priors, and is a weight parameter that indicates how important thewhole previous time points are to the current one.

In summary, the user's latent feature vector is affected by two factors, of which are the latent feature vectors of his historical interests and hisfriends' interests. Therefore, the conditional distribution probability of users' latent features can be expressed like this:

p Ut j R1;R2;;Rt1f g;C;2C ;2Ut

p Ut j R1;R2;;Rt1f g;2Ut

p Ut jC;2C

m

i1N Ut;ijUt;i ;

2UtI

m

i1N Ut;ij

vN i CivUt;v;

2C I

!:

7

The above normal distribution consists of two parts. The rst part, that is m

i1N Ut;i Ut;i ;

2Ut I

, informs us of the fact that the distributionvectors of users' latent feature space are close to their historical distribution vectors. The second part, which is

m

i1N Ut;i

vN i CivUt;v;2C I

! ,

tells us that the distribution vectors of users' latent feature space are also close to their friends' distribution vectors.

Table 1Summary of notations used in this paper.

Rt The usertopic matrix in time tC The useruser matrixUtT The users' latent feature space in time t

VtT The topics' latent feature space in time t

MUt The mean matrix of Ut with spherical Gaussian priors in time tMVt The mean matrix of Vt with spherical Gaussian priors in time t A weight that indicates how important the whole previous

time points are to the current one The kernel parameterd The dimension of latent feature spaceC The impact of the social network on users' interestU The impact of the users' latent feature vectors on users' interestV The impact of the topics' latent feature vectors on users' interestT The days for partitioning the data set

704 H. Bao et al. / Decision Support Systems 55 (2013) 698709After that, through a Bayesian inference, we have the following equation for the posterior probability over latent features of users and topics,

p Ut ;Vt j R1;R2;;Rt1;Rtf g;C;2C ;2Ut ;2Vt;2Rt

p Rt Ut ;Vt ;2Rt

p Ut C;2C p Ut R1;R2;;Rt1f g;2Ut p Vt R1;R2;;Rt1f g;2Vt

: 8

The log of the posterior distribution for our proposed model at time point t is given by

lnp Ut ;Vt j R1;R2;;Rtf g;C;2C ;2Ut ;2Vt;2Rt

122Rt

Xmi1

Xnj1

IRtij Rt;ijg UTt;iVt;j

212

Xmi1

Xnj

IRtij

0@

1A ln2Rt

122Ut

Xmi1

Ut;iUt;i T

Ut;iUt;i

122Vt

Xnj1

Vt;jVt;j T

Vt;jVt;j

122C

Xmi1

Ui vN i

CivUi

!TUi

vN i CivUi

! !

12

md ln 2Ut nd ln 2Vt

md ln2C

W:

9

Fig. 4. Accumulated error value of different dimensionality d with iterations.In this equation,W is a constant. Once the parametersRt , Ut , Vt , C are xed, maximizing the log of the posterior distribution with regardto Ut and Vt is equivalent to minimizing the following sum-of-squared-errors objective function:

E Ut ;Vt ; R1;R2;;Rtf g;C 12

Xmi1

Xnj1

IRtij Rt;ijg UTt;iVt;j

2 Ut2

UtUt 2

F

Vt2

VtVt 2

F C

2

Xmi1

Ut;i vN i

CivUt;v

!TUt;i

vN i CivUt;v

!:

10

In Eq. (10), C 2Rt=2C , Ut 2Rt=2Ut , Vt 2Rt=2Vt , and F2 are the Frobenius norm. The rst sum item in Eq. (10) represents thesum-squared error between Rt and UtTVt, while the second term and the third term denote the sum-squared distance from the users' and thetopics' latent feature space to the prior ones, we utilize the forth sum to represent the sum-squared deviation between the user's latent feature

Table 2Precison at top-N results of the ve models.

Dimensionality d = 10 Dimensionality d = 45 Dimensionality d = 50 MT1

PMF SocialMF T-PMF TS-PMF PMF SocialMF T-PMF TS-PMF PMF SocialMF T-PMF TS-PMF

Pr1 0.2612 0.2673 0.2816 0.3571 0.3388 0.3508 0.4878 0.4939 0.3408 0.3408 0.4510 0.4776 0.0571Pr3 0.2449 0.2524 0.2265 0.2782 0.2959 0.3041 0.3313 0.3531 0.3197 0.3224 0.3156 0.3463 0.0408Pr5 0.2241 0.2294 0.1955 0.2318 0.2637 0.2629 0.2661 0.2714 0.2722 0.2731 0.2600 0.2845 0.0322Pr10 0.1733 0.1749 0.1500 0.1645 0.1898 0.1916 0.1845 0.1859 0.1947 0.1973 0.1876 0.1865 0.0216

space and his friends' latent feature space. We can nd a local optimal value of the objective function in Eq. (10) by performing gradient descentin Ut,i and Vt,j, that is

EUt;i

Xnj1

IRtij g0UTt;iVt;j

g UTt;iVt;j

Rt;ij

Vt;j U Ut;iUt;i

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705H. Bao et al. / Decision Support Systems 55 (2013) 6987093.3. Complexity analysis

The main computation of learning parameters involves evaluating the object function E in Eq. (10) and its gradients against variables Ut andVt(t [1,N]) in Eqs. (11) and (12), including computing the mean matrices MUt and MVt in Eq. (6). In each time segment t, the complexity ofevaluation E is o Rt cd

, where Rt and c are the numbers of nonzero entries in matrices Rt and C, respectively. The cost of computing the

Table 3Performance on different users of our proposed model TS-PMF (d = 45).

110 1120 >20

PMF SocialMF T-PMF TS-PMF PMF SocialMF T-PMF TS-PMF PMF SocialMF T-PMF TS-PMF

Pr1 0.2684 0.2711 0.3919 0.3730 0.4878 0.4878 0.7439 0.8415 0.6316 0.6316 0.8684 0.9211Pr3 0.2026 0.2079 0.2261 0.2207 0.5000 0.5163 0.5813 0.6870 0.7105 0.7281 0.8158 0.8947Pr5 0.1642 0.1621 0.1627 0.1681 0.4854 0.4927 0.4780 0.5220 0.7105 0.7053 0.7632 0.7895Pr10 0.1039 0.1068 0.1027 0.1051 0.3659 0.3683 0.3439 0.3598 0.6184 0.6079 0.6132 0.6211Our proposed model provides an effective method to predict users' interests by integrating users' friendships and users' historical interests. Ourmodel can effectively take various factors that will have inuence on users' interests change into account, thus achieving accurate forecasts of users'future interests. The process of predicting users' interests with our model is described in Algorithm 1. And the notations used throughout the paperare summarized in Table 1.

convergence parameter: ;

Step 4: compute E1 in Eq. (10) If | E0- E1|

cd

and the usertopic matrix are very sparse. take the social network structure and the evolution of users' interestinto account for proving the effectiveness of these factors in shaping

rfor

706 H. Bao et al. / Decision Support Systems 55 (2013) 698709In this paper, the rst 15 days' data is used for training and the lastday's data for testing. Because the average time of duration of eachtopic is 2.72 days in our data set, we set T = 3 days, and accordingly

future interest of users in micro-blogging. For the second question,we illustrate the impacts of parameters with different values. Forand 2.04 following links.We can observe that both the userusermatrix For the rst question, we conduct a set of experiments to separatelygradients is o Rt d 2c d=m

. Then all cost in one iteration is o Rt d

datasets when Rt and C are sparse.

4. Experimental analysis

In this section, comprehensive and systematic analyses areconducted to evaluate the proposed user interest prediction model.The process of collection of the dataset used in the empirical workand the evaluation metrics are presented rst. Next, we explain thepurpose of our experiments in detail. Finally, the performance ofour model is compared with results of the other four models; resultsof the comparison verify the efcacy of the proposed model.

4.1. Description of the Sina-weibo dataset

In this paper, we use Sina-weibo API to gather users' following linksand data of topics of their interest fromOct 29, 2011 to Nov 13, 2011. Inthis data set, a timestamp is available for each user. After removingusers with less than 16 posts, we had 1170 users and 2788 topics. Inthis dataset, each user has on average 1.57 expressed topics per day

Fig. 5. Impact of different values of c on the peget N = 5.

4.2. Evaluation metric

Prediction results are evaluated by ranking the topics for all usersaccording to the scores in RN + 1. Since users are concerned about thetop ranking topics, the metrics of precision in top-n [8] is, therefore,adopted to measure the prediction quality of our proposed approachin comparison with other methods, dened as:

Prn Ncorr n Nu n

14

where Pr n is the precision in top-n, and Nu is the number of users in thetesting data set. We consider the correct topics of a user as those whichappear in users' future posts in the testing data set. Ncorr(n) is thenumber of correct topics in top-n prediction list for users who are inthe testing data set. 2c d=m N1 =2

. Thus, our model is effective for handling large

4.3. Purpose of our experiments

Our model is based on the intuition that both the social networkstructure and the evolution of users' interest affect users' future inter-est. Our experiments are intended to address the following questions:

1 Do the social network structure and the evolution of users' interesthave impact on users' interest in micro-blogging in the future?

2 How do model parameters C and affect the accuracy ofprediction?

3 How does our model select an appropriate dimension of latentfeature space d?

4 Does the division of temporal sections T affect the resultingperformance?

5 Is our model effective for active users, who help improve the socialinuence of micro-blogging?

To answer these questions, we proceed in the following fashion.

mance of user interest prediction with d = 45.the third question, we will perform some further experiments toselect the appropriate dimensionality of our proposed model byminimizing the accumulated error. For the fourth question, we willtake further experiments to analyze the impact of division of temporalsections on the resulting performance.

The social inuence of micro-blogging is dependent upon fastfusion of information and the rich user-generated content. Therefore,active users who are keen on publishing posts on trending topics areimportant for micro-blogging. For the fth question, it intuitivelyshows that the performance of active users plays an important rolein prediction.

4.4. Experimental results

In this sub-section, to demonstrate the usefulness and effectivenessof our proposed model TS-PMF, we compare it with four other models:

1 Probabilistic matrix factorization (PMF): This is the baseline matrixfactorization approach proposed in [22], which only uses the usertopic matrix without temporal information.

different values of c for users publishing posts at least on one topicon the 16th day when d = 45. As shown in Fig. 5, TS-PMF obtains

Fig. 6. Impact of different values of on the performance of user interest predictionwith d = 45.

Fig. 7. Impact different values of T on the performance of user interest prediction with

707H. Bao et al. / Decision Support Systems 55 (2013) 6987092 SocialMF: This is the model proposed in [9], which takes the socialnetwork into account and uses the useruser matrix and usertopicmatrix without temporal information. We set C = 0.001 forSocialMF in our experiments, which is the optimum value accordingto the best performance on our data.

3 Temporal probabilistic matrix factorization (T-PMF): This is themodel using a series of temporal matrices, in which we just importtemporal impact on users' interest into the PMF model.

4 MT1: This is the model presented in [18], using only the usersexplicitly followed by the target user.

In all the experiments, some parameters setting of our approachare = 3, U = V = 0.0001. And we take the users who havepublished posts at least on one topic on the 16th day for testing.Other parameters are set as c = 0.001 and = 0.2, which areexplained in Sections 4.6 and 4.7.

We perform some further experiments to select the appropriatedimensionality of our proposed model by minimizing the accumulatederror value, as shown in Fig. 4. In those experiments, we range thedimension of latent feature space d from 5 to 100 by an interval of 5,and nd the best performance at d = 45, eventually. And we showthe experimental results with the dimensionality d = 10, d = 45 andd = 50 in Table 2, where we indicate the best performance of thosemodels in bold type, with the same dimensionality d. From Table 2,we can observe that with different dimensionalities, both SocialMFand T-PMF improve the accuracy of prediction in comparison withPMF. That is, friendships and temporal factor are both useful for user in-terest prediction in micro-blogging. And T-PMF can also improve theprecision in comparison with SocialMF, i.e. it is necessary to take theevolution of users' interest into consideration to predict users' interest.More signicantly, our proposed model TS-PMF outperforms the othermethods except for the precision in top-10 (Pr10). With the dimension-ality d = 45, our model outperforms them in terms of accuracy by15.51%, 15.31%, 0.61% and 43.68% relative to PMF, SocialMF, T-PMFandMT1 at top-1, respectively.

Intuitively, increasing d should add more exibility to the modelsand improve the results. However, comparing results in Table 2, withthe dimensionality increasing more than 45, neither T-PMF norTS-PMF makes the accuracy increase in comparison with the resultsof d = 45, although they still outperform PMF and SocialMF. Thatmeans only increasing d in a certain range can improve the accuracyof prediction results by our proposed model.

4.5. Performance on different users

Users are grouped into 3 classes: 110, 1120 and >20,denoting on how many topics they have published posts on the16th day. The experimental results for different users with dimen-sionality d = 45 are shown in Table 3, where we indicate the highestaccuracy of thosemodels in bold type, with the same user class; T-PMFoutperforms other models on users with the label 110, and TS-PMFhas better performance than PMF and SocialMF. TS-PMF greatly im-proves the accuracy of users with labels 1120 and >20 relativeto other models, especially improving the precision in top-1 morethan 25% in comparison with SocialMF and PMF. Although the perfor-mance of TS-PMF for users with different labels is not always the bestamong all algorithms, our model still generates better predictionsthan PMF and SocialMF. Furthermore, our model is more effective forpredicting interest of active users with a large number of tweets.

4.6. Impact of c on the results

Parameter c controls the impact of the social network on users'interest. Larger values of c in Eq. (10) show relatively more inuenceof the social network structure on users' interest in comparison with

the usertopic matrix. Fig. 5 compares the precision of our model forthe best performance for c = 0.001.

4.7. Impact of on the results

Parameter in Eq. (6) is a weight that indicates how important theprevious time points are to the current one, for user-latent featurematrix and topic-latent feature matrix. If = 0, our model is thesame as T-PMF, which takes only time information into account,and if = 1, we consider that the evolution of users' interest playsa decisive role in the current users' latent feature space and topicslatent feature space. Fig. 6 shows the inuence of for users publishingposts at least on one topic on the 16th day when d = 45. We observethat values of affect the accuracy of predicting users' interests. FromFig. 6, we can see TS-PMF has its best result for = 0.2.

4.8. Impact of T on the results

Parameter T denotes the days for partitioning the data set. In thispaper, we set T = 3 because of the average time of duration of eachtopic in our dataset. In addition, we take further experiments toanalyze the impact of T on the resulting performance. As is shownd = 45.

in Fig. 7, the X-axis represents the days for partitioning our data set,including 2, 3, 4 and 5 days respectively, and the Y-axis representsthe precision of predicting users' interest in the test data. And wecan observe that when we set T = 3 days for partitioning data sets,our proposed model achieve the best performance when d = 45.

4.9. Prototype system

Fig. 8 shows our prototype system interfaces, which allow users tosee not only a list of topics onwhich a given user has published posts inthe past and the ones he will prefer in the future, but also the relatedposts on the given topic, which appears in the user's topic list.

The upper graph of Fig. 8 gives an example of searching a given userThe vagrant 1885838067. His interests include costumedrama, comic,movie, daily life, Korean current star and so on. Since he focused on cos-tume drama Introduction of the Princess and Each step Escape for a

708 H. Bao et al. / Decision Support Systems 55 (2013) 698709Fig. 8. Search results of our prototype system.long time, ourmodel predicts hemay continue to prefer them aswell asothermodels.Meanwhile, some of his interests have changed over time.For example, he only paid attention to Korean Current star such asGirls' Generation and U-know at rst, and then he showed his inter-ests in TV series of stars such as Poseidon. Therefore, our model pro-vides him a TV series Skip beat of Korean Current star. Furthermore,he has published posts on Nokia N9, BYD G3, Gas station, Airquality, Highway, a sightseeing spot named Zhang jiajie andGood trip. This shows he is interested in some topics about travellingby car. Additionally, some of his friends have been paying attention to atopic named Posting tweets with mobile on trips. Our model offersPosting tweets with mobile on trips to him. From the above example,we can see that our proposed method can effectively detect users' fu-ture interests by considering the social network structure and the evo-lution of users' interest.

The bottom graph in Fig. 8 gives an example of querying the topicEpson, wherewe can observe some information on the topic, includingposters, release time and post content.

As we have mentioned in the paper body, our model accuratelyforecasts users' liking score for certain programs. With this valuableinformation, we can recommend these movies to the people whoseliking score exceeds a certain threshold, which will increase theprograms' viewership and help businesses make better screeningpolicies. For example, based on the users' interest predicted by ourmodel stated above, we can provide a TV series Skip beat to sometarget users, such as The vagrant 1885838067. The accurate recom-mendation not only improves users' satisfaction, but also increasesthe viewership of Skip beat, meanwhile, it helps merchants getmore benets. Besides, it is useful for corporations to make effectivemarketing decisions, for example, proper advertisements may beshown to a given user and businesses can enhance their services tosatisfy customers.

5. Conclusions and future work

Micro-blogging is one of the most popular social media platformswhere the convenience, high update frequency and rich informationhave attracted millions of active users to join in. Users can publishposts on their daily lives and some trending topics. Trending topicsare featured prominently to provide users with an up-to-date glimpseof what is happening in the real world and clearly reect users' inter-ests. Users enthusiastically follow other users they are interested in toget relevant information of their interest.

In this paper, we propose a novel model to predict users' inter-ests in micro-blogging to help micro-blogging systems provideusers better personalized information and advertising services. Ourmodel is a probabilistic matrix factorization based approach. Wepresent a user interest prediction framework fusing the social net-work structure and the evolution of users' interest. In micro-blogging, the rich information and frequent updates make users' in-terests more extensive and changeable over time, and then makeusers' latent feature space and topics' latent feature space changeover time. Therefore, our model uses exponential decay function toobtain the mean matrix of user-latent feature matrix and the meanmatrix of topic-latent feature matrix. The experimental results onSina-weibo, one of the most popular micro-blogging sites in China,demonstrate that our model can improve the accuracy of predic-tions of users' interest.

There are several directions future research can take. Firstly, thereare some parameters in our proposed model, and different values ofthose parameters should affect the performance. Therefore, we wouldlike to provide an efcient procedure for tuning the parameters auto-matically, such as Markov Chain Monte Carlo (MCMC) algorithm [13].Secondly, wemay unearth other effective factors to enhance the perfor-mance of the proposed model; for example, the retweeting relation-

ships and discussions among users.

Acknowledgments

This research is supported by the NNSFC grants (no. 61172106,no. 71090402, no. 71002064) and the BJNSF grant (no. 4112062).

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Hongyun Bao is a Ph.D. candidate in the State Key Laboratory of Management andControl for Complex Systems, Institute of Automation, Chinese Academy of Sciences.She received her B.S. degree in School of Mathematical Sciences from Capital NormalUniversity, China, in 2008. Her research interests include information retrieval andweb/text mining.

Qiudan Li (corresponding author) is an Associate Professor in the State Key Laboratoryof Management and Control for Complex Systems, Institute of Automation, ChineseAcademy of Sciences. She received a Ph.D. in Computer Science from Da Lian Universityof Technology, China, in 2004. Her research interests include web mining and mobilecommerce applications. Her articles are published in Communications of the AIS,Decision Support Systems, Journal of the American Society for Information Scienceand Technology, IEEE Transactions on SMC, and Expert Systems with Applications.

Stephen Shaoyi Liao is a Professor at the Department of Information Systems anddirector of Advanced Transportation Information Systems Research Center, CityUniversity of Hong Kong. He is also a Visiting Professor and a Ph.D. Supervisor in USTCand Southwest Jiaotong University. He received a bachelor's degree from BeijingUniversity and a Ph.D. from the University of Aix-Marseille III and Institute of FranceTelecom. His research focuses on use of IT in e-business systems and transportationsystems. His articles have been published in MISQ, Decision Support Systems, IEEETransactions, Communications of the ACM, Information Science, Computer Softwareand other SCI journals.

Shuangyong Song is a Ph.D. candidate in the State Key Laboratory of Management andControl for Complex Systems, Institute of Automation, Chinese Academy of Sciences.He received his B.S. degree in Biomedical Engineering from Beijing Jiaotong University,China, in 2007. His research interests include information retrieval and web/textmining.

Heng Gao is a Master Candidate in the State Key Laboratory of Management and Controlfor Complex Systems, Institute of Automation, Chinese Academy of Sciences. He receivedhis B.E. degree in Computer Science from China University of Mining and Technology,China, in 2010. His research interests include information retrieval, web/text miningand community question answering.[3] N. Banerjee, D. Chakraborty, K. Dasgupta, A. Joshi, S. Mittal, S. Nagar, A. Rai, S.

A new temporal and social PMF-based method to predict users' interests in micro-blogging1. Introduction2. Related work2.1. User interest analysis and prediction2.2. Trust-aware recommendation2.3. Time-aware recommendation

3. The proposed user interest prediction model3.1. Theoretical background3.2. Proposed user interest prediction model3.2.1. Toy example3.2.2. The proposed model

3.3. Complexity analysis

4. Experimental analysis4.1. Description of the Sina-weibo dataset4.2. Evaluation metric4.3. Purpose of our experiments4.4. Experimental results4.5. Performance on different users4.6. Impact of c on the results4.7. Impact of on the results4.8. Impact of T on the results4.9. Prototype system

5. Conclusions and future workAcknowledgmentsReferences