1344 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING,VOL.27,NO.5,MAY 2015 information into the model training and prediction proce- Experiments on real-world datasets show that RCTR dures.Some methods [45],[51]utilize the item content can achieve higher prediction accuracy than the (attributes)to facilitate the CF training.One representative state-of-the-art methods. of these methods is collaborative topic regression(CTR)[45] Note that CTR-SMF [31]tries to integrate the user relations which jointly models the user-item feedback matrix and the into the CTR model,which is different from the application item content information (texts of articles).CTR seamlessly scenarios of our RCTR model. incorporates topic modeling [9]with CF to improve the per- The rest of this paper is organized as follows.In Section 2, formance and interpretability.For new items,CTR is able to we briefly introduce the background of CF and CTR. perform out-of-matrix prediction (cold-start prediction) Section 3 presents the details of our proposed RCTR model. [381,[51]using only the content information.Some other Experimental results are described in Section 4 and finally methods [221,[291,[31]try to use social networks among Section 5 concludes the whole paper. users to improve the performance.Among these methods, CTR-SMF [31]extends CTR by integrating the social net- 2 BACKGROUND work among users into CTR with social matrix factorization (SMF)[29]techniques,which has achieved better perfor- In this section,we give a brief introduction about the back- mance than CTR. ground of RCTR,including CF based recommendation, In many real applications,besides the feedback and item matrix factorization (MF)(also called latent factor model) content information,there may exist relations(or networks) based CF methods [251,[351,[361,J491,[501,and CTR [45]. among the items [44],[46]which can also be helpful for rec- ommendation.For example,if we want to recommend 2.1 CF Based Recommendation papers(references)to users in CiteULike,the citation rela- The task of CF is to recommend items to users based on their tions between papers are informative for recommending past feedback of the users.For example,we can deploy a rec- papers with similar topics.Other examples of item net- ommender system to recommend papers (references)to works can be found in hyperlinks among webpages,movies researchers in CiteULike.Here users are researchers and directed by the same directors,and so on. items are papers.As in [451,we assume there are I users and In this paper,we develop a novel hierarchical Bayesian J items in this paper.The feedback on item j given by user i model,called Relational Collaborative Topic Regression is denoted by ri.Although our model is general enough to (RCTR),to incorporate item relations for recommendation. be used for other settings with explicit feedback such as the The main contributions of RCTR are outlined as follows: case with integer ratings ranging from 1 to 5,we assume ri e(0,1}in this paper which is the same setting as that in By extending CTR,RCTR seamlessly integrates CTR [45].Note that this is a setting with implicit feedback as the user-item feedback information,item content introduced in [21].This means that our model tries to predict information and relational (network)structure whether a user likes a item or not.In training data,rij=1 among items into a principled hierarchical Bayes- means that user i likes item j.rij =0 means that the element ian model. is unobserved (missing),i.e.,we do not know whether user i Even if a new item has been given feedback only by likes item j or not.As stated in Section 1,CF methods use one or two users,RCTR can make effective use of the only the feedback matrix frijli 1,2,...,I;j=1,2,...,J information from the item network to alleviate the for training and prediction data sparsity problem in CF,which will conse- There are two different cases of prediction [45]:in-matrix quently improve the recommendation accuracy. prediction and out-of-matrix prediction.For the item-ori- In cases where a new user has given feedback to only ented setting,in-matrix prediction tries to make recommen- one or two items,RCTR can also make effective use dation for items with at least one feedback from the users in of the information from the item network to improve the training data.On the contrary,out-of-matrix prediction the recommendation accuracy. tries to make recommendation for items without any In RCTR,a family of link(relation)probability func- feedback in the training data.The in-matrix prediction and tions is proposed to model the relations between out-of-matrix prediction for user-oriented settings are simi- items.This extension from discrete link probability lar except that we make recommendation for users rather functions like those in [14]to a family of link proba- than items.Out-of-matrix prediction is actually the so-called bility functions increases the modeling capacity of cold-start recommendation in some of the literature [38],[51]. RCTR with better performance. Compared with CTR,a smaller number of learning 2.2 Matrix Factorization for CF iterations are needed for RCTR to achieve satisfac- The existing CF methods can be divided into two main tory accuracy.As a consequence,the total empirical categories [24]:memory-based methods [18],[28],[37]and measured runtime of training RCTR is lower than model-based methods [19],[25],[35].Memory-based meth- that of training CTR even if the time complexity of ods adopt the(weighted)average of the feedback of similar each RCTR iteration is slightly higher than that of (neighborhood)users or items for prediction,while model- CTR. based methods try to learn a statistical model from the train- ● RCTR can learn good interpretable latent structures ing data.Many works have verified that model-based meth- which are useful for recommendation. ods can outperform memory-based methods in general. Hence,model-based methods have become more popular in 1.http://www.citeulike.org/ recent years.information into the model training and prediction proce￾dures. Some methods [45], [51] utilize the item content (attributes) to facilitate the CF training. One representative of these methods is collaborative topic regression (CTR) [45] which jointly models the user-item feedback matrix and the item content information (texts of articles). CTR seamlessly incorporates topic modeling [9] with CF to improve the per￾formance and interpretability. For new items, CTR is able to perform out-of-matrix prediction (cold-start prediction) [38], [51] using only the content information. Some other methods [22], [29], [31] try to use social networks among users to improve the performance. Among these methods, CTR-SMF [31] extends CTR by integrating the social net￾work among users into CTR with social matrix factorization (SMF) [29] techniques, which has achieved better perfor￾mance than CTR. In many real applications, besides the feedback and item content information, there may exist relations (or networks) among the items [44], [46] which can also be helpful for rec￾ommendation. For example, if we want to recommend papers (references) to users in CiteULike,1 the citation rela￾tions between papers are informative for recommending papers with similar topics. Other examples of item net￾works can be found in hyperlinks among webpages, movies directed by the same directors, and so on. In this paper, we develop a novel hierarchical Bayesian model, called Relational Collaborative Topic Regression (RCTR), to incorporate item relations for recommendation. The main contributions of RCTR are outlined as follows:
By extending CTR, RCTR seamlessly integrates the user-item feedback information, item content information and relational (network) structure among items into a principled hierarchical Bayes￾ian model.
Even if a new item has been given feedback only by one or two users, RCTR can make effective use of the information from the item network to alleviate the data sparsity problem in CF, which will conse￾quently improve the recommendation accuracy.
In cases where a new user has given feedback to only one or two items, RCTR can also make effective use of the information from the item network to improve the recommendation accuracy.
In RCTR, a family of link (relation) probability func￾tions is proposed to model the relations between items. This extension from discrete link probability functions like those in [14] to a family of link proba￾bility functions increases the modeling capacity of RCTR with better performance.
Compared with CTR, a smaller number of learning iterations are needed for RCTR to achieve satisfac￾tory accuracy. As a consequence, the total empirical measured runtime of training RCTR is lower than that of training CTR even if the time complexity of each RCTR iteration is slightly higher than that of CTR.
RCTR can learn good interpretable latent structures which are useful for recommendation.
Experiments on real-world datasets show that RCTR can achieve higher prediction accuracy than the state-of-the-art methods. Note that CTR-SMF [31] tries to integrate the user relations into the CTR model, which is different from the application scenarios of our RCTR model. The rest of this paper is organized as follows. In Section 2, we briefly introduce the background of CF and CTR. Section 3 presents the details of our proposed RCTR model. Experimental results are described in Section 4 and finally Section 5 concludes the whole paper. 2 BACKGROUND In this section, we give a brief introduction about the back￾ground of RCTR, including CF based recommendation, matrix factorization (MF) (also called latent factor model) based CF methods [25], [35], [36], [49], [50], and CTR [45]. 2.1 CF Based Recommendation The task of CF is to recommend items to users based on their past feedback of the users. For example, we can deploy a rec￾ommender system to recommend papers (references) to researchers in CiteULike. Here users are researchers and items are papers. As in [45], we assume there are I users and J items in this paper. The feedback on item j given by user i is denoted by rij. Although our model is general enough to be used for other settings with explicit feedback such as the case with integer ratings ranging from 1 to 5, we assume rij 2 f0; 1g in this paper which is the same setting as that in CTR [45]. Note that this is a setting with implicit feedback as introduced in [21]. This means that our model tries to predict whether a user likes a item or not. In training data, rij ¼ 1 means that user i likes item j. rij ¼ 0 means that the element is unobserved (missing), i.e., we do not know whether user i likes item j or not. As stated in Section 1, CF methods use only the feedback matrix frijji ¼ 1; 2; ... ; I; j ¼ 1; 2; ... ; Jg for training and prediction. There are two different cases of prediction [45]: in-matrix prediction and out-of-matrix prediction. For the item-ori￾ented setting, in-matrix prediction tries to make recommen￾dation for items with at least one feedback from the users in the training data. On the contrary, out-of-matrix prediction tries to make recommendation for items without any feedback in the training data. The in-matrix prediction and out-of-matrix prediction for user-oriented settings are simi￾lar except that we make recommendation for users rather than items. Out-of-matrix prediction is actually the so-called cold-start recommendation in some of the literature [38], [51]. 2.2 Matrix Factorization for CF The existing CF methods can be divided into two main categories [24]: memory-based methods [18], [28], [37] and model-based methods [19], [25], [35]. Memory-based meth￾ods adopt the (weighted) average of the feedback of similar (neighborhood) users or items for prediction, while model￾based methods try to learn a statistical model from the train￾ing data. Many works have verified that model-based meth￾ods can outperform memory-based methods in general. Hence, model-based methods have become more popular in 1. http://www.citeulike.org/ recent years. 1344 IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING, VOL. 27, NO. 5, MAY 2015