JOURNAL OF SOFTWARE, VOL. 8, NO. 1, JANUARY 2013 11 A Robust Collaborative Filtering Recommendation Algorithm Based on Multidimensional Trust Model Dongyan Jia, Fuzhi Zhang, Sai Liu School of Information Science and Engineering, Yanshan University, Qinhuangdao, China Email: [email protected], [email protected], [email protected] Abstract—Collaborative filtering is one of the widely used In order to measure the credibility of users’ ratings and technologies in the e-commerce recommender systems. It the degree of trust between users, many computational can predict the interests of a user based on the rating models of trust have been proposed. O’Donovan et al. [5] information of many other users. But the traditional proposed the profile-level and item-level computational collaborative filtering recommendation algorithm has the model of trust and drew a conclusion that the latter problems such as lower recommendation precision and performs better than the former by conducting weaker robustness. To solve these problems, in this paper we present a robust collaborative filtering recommendation experiments. Similarly, Lathia et al. [6] proposed an algorithm based on multidimensional trust model. Firstly, improved computational model of trust, which computed according to the rating information of users, a the degree of trust of target user to the recommender user multidimensional trust model is proposed. It measures the based on the error of predict rating. However, both of the credibility of user’s ratings from the following three aspects: models generate recommendation relying on the the reliability of item recommendation, the rating similarity similarity between two users. Due to the extreme sparsity and the user’s trustworthiness. Secondly, the computational of ratings, it is very difficult to compute the similarity model of trust and the traditional collaborative filtering between two users accurately, which leads to the approach are combined to select the reliable neighbor set inaccurate computation of degree of trust, poor scalability and generate recommendation for the target user. Finally, the performances of the novel algorithm with others are and inapplicable in large-scale dataset. Pitsilis et al. [7,8] compared from both sides of recommendation precision and analyzed the trust relationship between users from the robustness using MovieLens dataset. Compared with the point of view of subjective logic and proposed a existing algorithms, the proposed algorithm not only computational model of trust based on the theory of improves the quality of neighbor selection and the uncertain probabilities. But the computation of recommendation precision, but also has better robustness. uncertainty is based on the co-rated items between users. Consequently, it can’t compute the degree of trust Index Terms—multidimensional trust model, robustness, between users accurately in the case of the extreme collaborative filtering, recommender system sparsity of ratings. Aims at the limitations of traditional collaborative filtering recommendation algorithm when selecting neighbors, Kwon et al. [9] proposed a I. INTRODUCTION multidimensional credibility model based on the source Recommender systems, as a kind of information credibility theory [10]. They analyzed and measured the filtering technology, have provided an effective way to degree of trust from three aspects such as the expertise, solve the information overload problem [1]. Specially, the the trustworthiness and the similarity. However, it only collaborative filtering [2] is one of the most successful takes into account the heterogeneous of ratings of users recommendation technologies. It generates and still has the vulnerability when there are attack recommendation for the target user by collecting the profiles in the system. preference information of similar users. However, due to Recently, the model-based recommendation algorithms the sparsity of ratings, the quality of neighbor selection have attracted significant attention. These algorithms use for target user is poor based on the similarity between statistical methods or techniques of machine learning to users. In addition, with the emergence of shilling attacks construct a recommendation model of which the [3,4] and the lack of credibility evaluation mechanism of parameters are estimated from the rating data of users. ratings, how to improve the recommendation precision The recommendation is generated for the target user and robustness has become the key issue to be solved. based on the model. Jamali et al. [11] proposed a random walk model named TrustWalker, in which the predict rating for the target user on the target item would be the Manuscript received January 21, 2012; revised June 1, 2012; expected value of ratings returned by performing many accepted June 27, 2012. random walks. But this model is greatly affected by the Corresponding author: Fuzhi Zhang. sparsity of ratings. Ma et al. [12] proposed a © 2013 ACADEMY PUBLISHER doi:10.4304/jsw.8.1.11-18 12 JOURNAL OF SOFTWARE, VOL. 8, NO. 1, JANUARY 2013 recommendation approach based on matrix factorization B. Similarity Measures named RSTE. The target user gets the recommendation The most popular approaches of computing user by learning the latent user and item features. Moreover, similarity are cosine-based similarity and the Person they proposed the recommendation approach by correlation coefficient [15]. incorporating social contextual information [13], and In cosine-based similarity approach, the ratings of each applied RSTE to the recommendation based on the user are treated as one vector in n-dimensional space. Let implicit social relations [14]. However, this the vector Ui and Uj denote the ratings of user ui and uj recommendation approach based on matrix factorization respectively, so the similarity between user ui and uj can is greatly affected by the sparsity of direct trust be measured as: information. Aim at the problems mentioned above, on the basis of UUij⋅ sim(, uij u )== cos(,UU i j ) . (1) the previous work, we propose a multidimensional trust UUij model-based robust recommendation algorithm (MTMRRA). It measures the credibility of ratings of Using Person correlation coefficient, the similarity users from different aspects. As a result, the best between user ui and uj can be measured as: neighbors are selected to generate recommendation for ()()RRRR−− ∑iI∈ ik,, i jk j the target user according to the computational model of sim(, u u )= kij , (2) trust. Our contributions are as follows. ij 22 ∑∑()RRik,,−− i ( R jk R j ) Firstly, a multidimensional trust model is proposed, iIkij∈∈ iI kij which measures the credibility of users’ ratings from the where Iij is the item set co-rated by user ui and uj, R reliability of item recommendation, the rating similarity ik, and R are the ratings of user u and u on item i and the user’s trustworthiness based on the user-item jk, i j k rating matrix. So the degree of trust between users is respectively, Ri and R j are the average ratings of user regarded as the sum of product of each attribute and its ui and uj respectively. importance weight. Secondly, a robust collaborative filtering C. Prediction recommendation algorithm is presented. Based on the Assume the target user is ua, the target item is ij, so the proposed model of trust, we can choose the best main idea of traditional user-based collaborative filtering neighbors for the target user, and then get the recommendation algorithm is as follow: based on the recommendation by combining the traditional user-item rating matrix, the users who have rated the item collaborative filtering recommendation approach. ij are selected, and the rating similarity between the target Thirdly, we conduct the experiments on the MovieLens user and each of these users is computed by using the dataset and compare the proposed algorithm with others similarity measures. Then the top-k users who have larger in terms of the MAE, RMSE and Prediction Shift metrics. user similarity are chosen as the neighbors of target user Experimental results indicate that our algorithm not only ua. As a result, according to the rating information of improves the recommendation precision, but also has neighbors, the predict rating Pa,j for user ua on item ij is better robustness. computed as: ()(,)Rkj, −⋅Rsimuu k a k II. BACKGROUND ∑uNuka∈ () PRaj, =+ a , (3) sim(,) uak u A. Description of User Rating Information ∑uNuka∈ () In collaborative filtering recommender systems, the where N(u ) is the neighbor set of target user u , R and rating database includes a set of m users, a a a Rk are the average ratings of target user ua and the Uuuu= {,12 ,K ,m }, and a set of n items, Iiii= {,12 ,K ,n }. Users rate some items they know with a discrete range of neighbor uk respectively, Rk,j is the rating of uk on item ij, sim(,) u u is the similarity between the target user u possible values {,,}minK max , for example, {1,K , 5} or ak a and the neighbor u . {1,K ,1 0} . Usually, the items with higher values are the k user’s favorite ones. So the user-item rating matrix can be described as: III. MULTIDIMENSIONAL TRUST MODEL Due to the sparsity of user-item rating matrix and the ⎡⎤RR1,1 1,2K R 1,n ⎢⎥ shilling attacks in collaborative filtering recommender RR2,1 2,2K R 2,n R = ⎢⎥, systems, it is unreliable to select neighbors for the target ⎢⎥KKKK user according to the similarity between users. As a result, ⎢⎥ ⎣⎦⎢⎥RRmm,1 ,2K R mn , the user’s satisfaction for the recommendation results declines. To improve the quality of selected neighbors, where, Ri,j(1≤i≤m,1≤j≤n) is the rating of user ui on item ij. we propose a multidimensional trust model which Due to the large number of items, each user often only analyses and measures the credibility of users’ ratings rated a certain number of items. If user ui hasn’t rated the using the reliability of item recommendation, the rating item ij, we represent that as Rij, = φ .