-
th
,c,
atieseand
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:
[email protected] (H. Bao), qi
[email protected] (S.S. Liao), [email protected].(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
[email protected] (Q. Li),cn (S. Song), [email protected]
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
C Ut;i vN i
CivUt;v
!C
vjiN v f gCiv Ut;v
N i CvUt;
! 11
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