A Robust Collaborative Filtering Recommendation Algorithm Based on Multidimensional Trust Model

JOURNAL OF SOFTWARE, VOL. 8, NO. 1, JANUARY 2013 11

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

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 . similarity and the user’s trustworthiness.

A. Reliability of Item Recommendation 1 Definition 1. The reliability of item recommendation is defined as the degree of a user to provide an accurate 0.9 prediction for every item. For user uU∈ and the item k 0.8 IiR=≠∈{|φ , iI } set rated by uk, kjkjj, , the user uk’s f(x) k=1 0.7 k=2 reliability of recommendation for item iIjk∈ is k=3 j 0.6 k=4 described as Rk . k=5 To measure the reliability of item recommendation, we 0.5 employ the item-level computational model of trust 0 5 10 15 20 25 30 x proposed by O’Donovan. Using the “leave-one-out” Figure 1. The curve of f(x) with k=1,2,…,5 approach, choosing ∀∈uUk as the only recommender user, every item iIj ∈ k as target item, and every user ua As shown in Figure 1, no matter what value the k is, in the user set UuRjaaja=≠∈≠{|, φ , uUuu , ak } as target user, the f(x) will be close to 1 infinitely when x is greater than a certain value x . We can also get Ssimuu≈ (,) using we can compute the predict rating for the target user on 0 ab, a b the target item using (3). (7). So we call x0 the threshold of the number of co-rated Based on the deviation between the predict rating and items between users. Table 1 gives the comparison of the actual rating, we can compute the user uk’s reliability value of x0 when k takes different values. of recommendation for item ij as: TABLE I. ||U j COMPARISON OF THE VALUE OF X WITH DIFFERENT K VALUE j 0 ∑ satak, R j = a=1 , (4) k 1 2 3 4 5 k ||U j x0 6 11 16 22 27 Table 1 shows that with k increasing gradually, the ⎧⎪1 PRaj,,− aj ≤ ε j value of x0 increases. Considering the sparity of user-item satak, = ⎨ , (5) ⎩⎪0 else rating matrix, we set x0 =16 and k =3 to compute the rating similarity between two users. where Pa,,j is the predict rating for the user ua on item ij, Ra,,j is the actual rating of user ua on item ij, ε is a C. User’s Trustworthiness threshold, we set ε=1.2 in this paper. Definition 3. Trustworthiness of a user is defined as the degree of his ratings that reflect the user’s actual B. Rating Similarity opinions. For user uU∈ and the item set rated by u , Definition 2. Rating similarity is defined as the b b IiRbjbjj= {|, ≠∈φ , iI } , we can compute ub’s similarity between two users. For user uUa ∈ and user trustworthiness Tb using the information of the similarity uUb ∈ , the rating similarity between the two users is of any two items in Ib and the ub’s ratings on the computed based on the item set corresponding items. IiRRab=≠≠∈{| k a,, kφ , b kφ , iI k }, and it is described as Sa,b. Based on the user-item rating matrix, the similarity The traditional similarity measures rely on the items between two items is computed by using Person co-rated between users. Due to the sparity of user-item correlation coefficient: rating matrix, the computation of similarity has greater ()()RRRR−− ∑uU∈ ki,, i k j j occasionality. To reduce its impact, we employ a sim(, i i )= kij, , (8) relevance weighting function f(x) and set a threshold for ij 22 ∑∑()RRki,,−− i ( R k j R j ) the number of co-rated items between two users by uUkij∈∈,, uU kij specifying the k value: where sim(ii,ij) is the similarity between item ii and item ij, 1 Ui,j is the set of users who have both rated the item ii and fx()= x . (6) − item ij, UuRRij,,,= {| k ki≠≠∈φ , kjφ , uU k }, Rk,i and Rk,j are 1+ e k the ratings of uk on item ii and item ij respectively, Ri The similarity S between user u and user u is a,b a b and R are the average rating of item i and i computed as: j i j respectively. 1 We can get a real value in the range [-1,+1] from (8), Ssimuuab, =×(,) a b ||I , (7) − ab which is mapped to the range [0,1] by using 1+ e k 1(,)+ sim iij i sim(, iij i )'= . where sim(ua, ub) is calculated according to (2), |Iab| is the 2 number of items co-rated by user ua and user ub, k is a Consequently, the user ub’s trustworthiness Tb is threshold, the method of setting its value is as follows. computed as: Let k=1, 2 , … ,5, the curve of f(x) is shown in Fig. 1.

2 b TCF - User’s trustworthiness-based collaborative Ttbij= , , (9) ∑iI∈∈bb, jI filtering recommendation strategy. ||(||1)IIbb− With the number of neighbors increasing, we can get

||RRbi,,− b j the MAE values of each recommendation strategy tsimiib =−1[ ( )' + − 1]2 , (10) ij,, i j 5 respectively. Compared with the recommendation precision of CF, the percentage of improvement for each b where tij, is the trustworthiness of ub for item pair (ii,ij), recommendation strategy is calculated. Let prcf, pscf and p be the percentage of improvement for sim(, iij i )' is the similarity between item ii and item ij, tcf recommendation strategy of RCF, SCF and TCF R and R are the ratings of u on item i and item i bi, bj, b i j respectively, so we have: respectively. prcf D. Computation of Trust Degree α = , ppprcf++ scf tcf Based on the analysis above, we can compute the degree of trust of user u to user u as: p a b β = scf , j ppprcf++ scf tcf trustab,,=+α R bβγ S ab + T b, (11)

j ptcf where Rb is the reliability of item recommendation of γ = . ppprcf++ scf tcf user ub for item ij, Sa,b is the rating similarity between user ua and user ub, Tb is the trustworthiness of user ub, Obviously, the greater percentage of improvement the α , β , γ are the importance weights of each attribute recommendation strategy has, the larger the above, we can set their values according to the following corresponding importance weight is. Considering the method. values of α , β and γ are different using different Using the experimental dataset, we can simulate the dataset, so their values should be computed dynamically. performance of four recommendation strategies as Let’s take an example to illustrate the computational follows: process of the values of α , β and γ . Using the CF - Traditional user-based collaborative filtering MovieLens1 dataset, we randomly select 754 users’ recommendation strategy. profiles as the training set and the remaining as the test RCF - Reliability of item recommendation-based set to conduct the experiments and compare the collaborative filtering recommendation strategy. performances of the RCF, SCF and TCF with CF. Table 2 SCF - Rating similarity-based collaborative filtering shows the comparison of recommendation precision with recommendation strategy. different number of neighbors.

TABLE II. COMPARISON OF RECOMMENDATION PRECISION (MAE)

number of neighbors 10 20 30 40 50 60 70 80 90 100 CF 0.7254 0.7331 0.7287 0.7235 0.7091 0.7061 0.7096 0.7054 0.7045 0.7010 RCF 0.6309 0.6478 0.6506 0.6681 0.6676 0.6527 0.6600 0.6610 0.6648 0.6585 SCF 0.7276 0.7324 0.7275 0.7203 0.7055 0.7066 0.7071 0.7048 0.7034 0.6998 TCF 0.7008 0.6911 0.6964 0.6805 0.6860 0.6825 0.6841 0.6801 0.6892 0.6857

As shown in Table 2, the recommendation strategy of A. Description of Algorithm RCF, SCF and TCF all outperform the CF in terms of To improve the recommendation precision, a recommendation precision. Compared with the CF multidimensional trust model-based robust strategy, the average percentage of improvement for the recommendation algorithm (MTMRRA) is proposed. The RCF, SCF and TCF is 8.06%, 0.16% and 3.76% main steps of MTMRRA algorithm are described as respectively. So: follows: according to the rating information of users, 8.06% select the user set C(ua) who have rated the target item ij α ==0.6728 , 8.06%++ 0.16% 3.76% and use (11) to compute the degree of trust of target user ua to each user in C(ua). Based on that, select the top-k 0.16% users as the neighbors of target user u and compute the β ==0.0134 , a 8.06%++ 0.16% 3.76% predicted rating Pa,j for the target user ua on the target item ij as: 3.76% γ ==0.3139 . 8.06%++ 0.16% 3.76%

IV. MULTIDIMENSIONAL TRUST MODEL-BASED ROBUST 1 http://www.grouplens.org/node/73 RECOMMENDATION ALGORITHM

the target item. The second part, from line 2 to 23, is to ∑ T + ()RRSkj,,−⋅ k ak uUk ∈ compute the degree of trust of the target user to each user PRaj, =+ a , (12) T + Sak, in C(u ). The third part, from line 24 to 28, is to select the ∑uUk ∈ a neighbors for the target user and compute the predicted T + where U is the neighbor set of target user ua, rating Pa,j for target user ua on the target item ij.

TT++ T UUU= I , UutrustTuU=≥∀∈{|kakk, , } , B. Complexity Analysis + UuS=>∀∈{|kak, 0, uU k }, T is the threshold of degree of In the process of computing the degree of trust of target user u to each user in C(u ), the computation of the trust between users, Sa,k is the similarity between target a a reliability of item recommendation, the rating similarity user ua and neighbor user uk, Rk,j is the rating of uk on the and the user’s trustworthiness is of complexity O(m), O(1) target item ij, R and R are the average ratings of the a k and O(l2) respectively, where m denotes the number of target user u and the neighbor u respectively. a k users in the recommender system, l denotes the number According to the steps of algorithm above, MTMRRA of ratings rated by one user. In the actual recommender algorithm is described as follows. system, the degree of trust between users is usually Algorithm : MTMRRA computed off-line, so its complexity is O(1). The Input: the user-item rating matrix R complexity of selecting neighbors and computing the Output: the predicted rating P for target user u on the a,j a predict ratings for the target user is O(m2) and O(k) target item i j respectively, where k denotes the number of neighbors. Begin 2 So the total complexity of computation online is O(m +k). 1: Cu()←≠∈ {| u Rφ , u U }; akkjk, Considering the fact that we often have k<

6: for each ut∈Uj do analysis. Theoretically, the correctness of MTMRRA depends on the correct computation of the degree of trust 7: Pedictuuitj, ← Pr ( t , k , j ) ; of target user to others. The computational approach of 8: satj ← Satisfactory(, u u ,) i ; tk, t k j trust proposed in this paper measures the credibility of j 9: sum__ satisfactory←+ sum satisfactory sattk, ; user’s ratings from three aspects, which not only 10: end for considers the potential relationship between user profiles, sum_ satisfactory but also evaluates the credibility of user profile itself 11: R j ← ; from both sides of horizontal and vertical. The algorithm k ||U j MTMRRA makes a multi-dimensional analysis for the 12: IiRRak←≠≠∈{| b a,, bφ , k bφ , iI b }; degree of trust between users, which is feasible and correct in theory. From the experiment point of view, the 13: sim(,) uka u← similarity (,) u ka u ; algorithm is correct in case that compared to other 14: SsimuufI←×(,) (||); ak, k a ak recommendation algorithms, it not only improves the 15: sum_ trustworthy ← 0 ; recommendation precision, but also has better robustness.

16: for ∀∈iibt,() I kb i ≠ i t do We can see that the MTMRRA is correct obviously through section Ⅵ. 17: sim(,) ibt i← similarity (,) i bt i ; 18: tk ← trustworthy(,,) u i i ; bt, k b t VI EXPERIMENTAL RESULTS AND ANALYSIS 19: sum__ trustworthy←+ sum trustworthy t k ; bt, A. Dataset 20: end for In our experiments we use the publicly available 2_× sum trustworthy 21: T ← ; dataset provided by MovieLens site k ||(||1)II− kk (http://movielens.umn.edu/), which contains 100,000 j 22: trustak,,←+α R kβγ S ak + T k ; ratings on 1682 movies by 943 users. All ratings are 23:end for integer values between 1 and 5, where 1 is the lowest 24: N()u←> {| u S 0, trust >∈ T , u C ()} u ; (disliked) and 5 is the highest (most liked). For the akakakka,, number of items which one user has rated in the dataset, 25:sort the degree of trust of the target user ua to every the minimum is 20, the maximum is 737 and the average user in the N(ua); number is 106. In the experiment, we divide the dataset T + 26:UuuNuik←∈{ii | ( a ), = 1,2,..., } ; into two groups, 80% are used as the training set and the

27: Paj, ← Pr edict _ MTRRA ( u a , i j ) ; remaining 20% are used as the test set.

28: return Pa,j; B. Evaluation Metrics End We use MAE and RMSE to evaluate the This algorithm consists of three parts. The first part, recommendation precision of algorithm, which are the first line, is to get the user set C(ua) who have rated

computed by measuring the deviation between the algorithm. The smaller the Prediction Shift is, the better prediction rating and the actual rating. Obviously, the robustness the algorithm has. It is computed as: [17] smaller MAE (or RMSE) is, the higher the 1 ' recommendation precision of algorithm is. MAE and PredShift ( u , i )=−∑ p ( ukj , i ) p ( u kj , i ) , (16) RMSE can be computed as: [16] n ' n where pu(,)kj i and pu(,)kj i are the predicted ratings pr− ∑ jj for user u on item i before and after the item i is MAE = j=1 , (14) k j j n attacked, n is the total number of prediction.

n C. Recommendation Precision Analysis 2 ∑()prjj− To evaluate the recommendation precision of RMSE = i=1 , (15) n algorithms, we have carried out the experiments with our multidimensional trust model-based robust where pj is the predicted rating given to the target user on recommendation algorithm (MTMRRA), the traditional target item ij, rj is the actual rating of the target user on collaborative filtering recommendation algorithm (CF) target item ij, n is the total number of prediction. and the recommendation algorithm proposed by Moreover, we use MAE, RMSE and Prediction Shift to O’Donovan. With the number of neighbors increasing evaluate the robustness of algorithm. The Prediction Shift gradually, Fig. 2 gives the comparisons of measures the deviation of prediction on the attacked item recommendation precision. (before and after attack) of the recommendation

0.74 0.98 CF CF 0.73 O’Donovan 0.96 O’Donovan 0.72 MTMRRA MTMRRA 0.94 0.71 0.92 0.7 0.9 0.69 MAE

RMSE 0.88 0.68 0.86 0.67 0.66 0.84

0.65 0.82

0.64 0.8 10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 the Number of Neighbours the Number of Neighbours (a) MAE (b) RMSE

Figure 2. Comparison of recommendation precision

As shown in Fig. 2, the MTMRRA algorithm D. Robustness Analysis outperforms the CF algorithm and the O’Donovan’s in term of recommendation precision. Compared with CF To evaluate the robustness of the algorithms, we inject algorithm, MTMRRA algorithm improves by some hybrid attack profiles (the same number of profiles 9.18%(MAE) and 8.95% (RMSE); compared with of random attack, average attack and bandwagon attack) O’Donovan’s algorithm, MTMRRA algorithm improves into the training set. Let the filler size be 1%, 3%, 5%, by 6.39% (MAE) and 6.01% (RMSE). That is to say that 10%, 25%, the attack size be 1%, 2%, 5%, 10%, and the it is helpful to improve the quality of chosen neighbors number of neighbors be 40, with the filler size and attack and the recommendation precision by measuring the size increasing gradually, the comparisons of credibility of users’ ratings from several aspects. recommendation precision of algorithm MTMRRA, CF Therefore, our MTMRRA algorithm has better and O’Donovan’s are shown in Table 3 and Table 4. recommendation precision.

TABLE III. COMPARISON OF MAE VALUES

attack size 1% 2% 5% 10% algorithm CF O’Donovan MTMRRA CF O’Donovan MTMRRA CF O’Donovan MTMRRA CF O’Donovan MTMRRA filler size=1% 0.7374 0.7028 0.6705 0.7359 0.7041 0.6770 0.7478 0.7057 0.6446 0.7642 0.7122 0.6783 filler size=3% 0.7337 0.6984 0.6755 0.7411 0.7046 0.6730 0.7441 0.7061 0.6717 0.7534 0.7104 0.6964 filler size=5% 0.7371 0.7015 0.6760 0.7409 0.7056 0.6707 0.7541 0.7303 0.6694 0.7651 0.7405 0.6918 filler size=10% 0.7340 0.7078 0.6596 0.7454 0.7143 0.6619 0.7550 0.7093 0.6780 0.7458 0.7092 0.6672 filler size=25% 0.7219 0.6963 0.6510 0.7488 0.7106 0.6563 0.7309 0.6976 0.6686 0.7381 0.7122 0.6869

TABLE IV. COMPARISON OF RMSE VALUES

attack size 1% 2% 5% 10% algorithm CF O’Donovan MTMRRA CF O’Donovan MTMRRA CF O’Donovan MTMRRA CF O’Donovan MTMRRA filler size=1% 0.9130 0.8823 0.8417 0.9143 0.8805 0.8494 0.9324 0.8814 0.8113 0.9621 0.8941 0.8422 filler size=3% 0.9135 0.8790 0.8480 0.9205 0.8806 0.8482 0.9248 0.8790 0.8400 0.9405 0.8816 0.8691 filler size=5% 0.9139 0.8821 0.8497 0.9137 0.8812 0.8494 0.9378 0.9053 0.8384 0.9460 0.9193 0.8723 filler size=10% 0.9070 0.8775 0.8224 0.9107 0.8802 0.8213 0.9157 0.8700 0.8475 0.9248 0.8682 0.8294 filler size=25% 0.8959 0.8685 0.8221 0.9183 0.8820 0.8261 0.8877 0.8595 0.8245 0.8942 0.8688 0.8560

As shown in Table 3 and Table 4, the MTMRRA 9.74%(MAE) and 8.56% (RMSE); compared with the algorithm outperforms the CF algorithm and the recommendation precision of O’Donovan’s, MTMRRA O’Donovan’s algorithm in term of recommendation algorithm improves by 5.32% (MAE) and 4.6% (RMSE). precision whatever the attack size is. Also, with the attack It can be proved that our MTMRRA algorithm has better size increasing gradually, the recommendation precision robustness. of three algorithms follows to descend. It is now clear Under the hybrid attack, let the filler size be 1%, 3%, that the more attack users in the system, the lower quality 5%, 10% and the attack size be 1%, 2%, 5%, 10%, with of recommendation. Compared with the recommendation the attack size increasing gradually, the comparisons of precision of CF, MTMRRA algorithm improves by prediction shift are shown in Figure 3.

1.4 2 CF CF 1.2 O'Donovan O'Donovan MTMRRA MTMRRA 1.5 1

0.8 1 0.6 prediction shift prediction shift prediction 0.4 0.5 0.2

0 0 1% 2% 5% 10% 1% 2% 5% 10% attack size attack size (a) Filler size=1% (b) Filler size=3%

2 2 CF CF O'Donovan O'Donovan MTMRRA MTMRRA 1.5 1.5

1 1 prediction shift prediction shift prediction 0.5 0.5

0 0 1% 2% 5% 10% 1% 2% 5% 10% attack size attack size (c) Filler size=5% (d) Filler size=10%

Figure 3. Comparison of prediction shift with different filler size

As shown in Fig. 3, under the same filler size, with the recommendation precision and the robustness becomes attack size increasing gradually, the prediction shift of all more and more important. We have made some beneficial algorithms increases. So the more attack users in the explorations in this area. In this paper we propose a system, the lower quality of recommendation. In addition, multidimensional trust model which measures the under the same attack size and filler size, the MTMRRA credibility of users’ ratings from three attributes. Based algorithm outperforms the CF and O’Donovan’s in terms on the model of trust, we present a robust collaborative of prediction shift. filtering recommendation algorithm. Compared with other algorithms, the proposed algorithm not only VII CONCLUSIONS improves the recommendation precision, but also has better robustness. The experiments conducted on With the wide application of the collaborative filtering MovieLens prove the effectiveness of the proposed algorithm in e-commerce, how to improve the

algorithm. With the new ratings adding into the system [13] H. Ma, T.C. Zhou, M.R. Lyu, I. King, “Improving gradually, how to design an incremental recommendation Recommender Systems by Incorporating Social Contextual algorithm and generate recommendation for the target Information”, ACM Transactions on Infromation Systems, user accurately will be our future work. 29(2), article 9, 2011. [14] H. Ma, I. King, M.R. Lyu, “Learning to Recommend with Explicit and Implicit Social Relations”, ACM Transactions ACKNOWLEDGMENT on Intelligent System and Technology, 2(3),article 29, The work described in this paper was supported by the 2011. [15] H.F. Sun, P. Yong, J.L. Chen, C.C. Liu, Y.Z. Sun, “A New Natural Science Foundation of Hebei Province, China Similarity Measure based on Adjusted Euclidean Distance (No. F2011203219). for Memory-based Collaborative Filtering”, Journal of software, 6(6), pp. 993-1000, 2011. REFERENCES [16] F. Cacheda, V. Carneiro, D. Fernandez, V. Formoso, “Comparison of Collaborative Filtering Algorithms: [1] H.L. Xu, X. Wu, X.D. Li, B.P. Yan, “Comparison Study of Limitations of Current Techniques and Proposals for Internet Recommendation System”, Journal of Software, Scalable, High-performance Recommender System”, ACM 20(2), pp. 350-362, 2009 (in Chinese). Transactions on the Web, 5(1),article 2, 2011. [2] Y. Koren, R. Bell, Recommender Systems Handbook, [17] B. Mehta, W. Nejdl, “Attack Resistant Collaborative Springer, 2011, pp. 145-186. Filtering”, In Proc. of the 31st annual Int’l ACM SIGIR [3] B. Mobasher, R. Burke, R.Bhaumik, C. Williams, “Toward Conf. on Research and Development in information Trustworthy Recommender Systems: an Analysis of retrieval. New York, NY, USA: ACM, 2008, pp. 75-82. Attack Models and Algorithm Robustness”, ACM

Transactions on Internet Technology, 7(4), pp. 1-38, 2007.

[4] B. Mobasher, R. Burke, R. Bhaumik, and J.J. Sandvig,

“Attacks and Remedies in Collaborative Dongyan Jia was born in Hebei Province, Recommendation”, IEEE Intelligent Systems, 22(3), pp. China in 1983. She received her M.S. in 56-63, 2007. Computer Application Technology from [5] J. O’Donovan, B. Smyth, “Trust in Recommender Yanshan University, China, in 2009. Systems”, In: Proc. of the 10th Int’l Conf. on Intelligent She is currently a Ph.D. Candidate in the User Interfaces. San Diego, California, USA: ACM Press, School of Information Science and 2005, pp. 167-174. Engineering, Yanshan University, [6] N. Lathia, S. Hailes, L. Capra, “Trust-based Collaborative Qinhuangdao, China. Her research Filtering”, In Joint iTrust and PST Conferences on Privacy, interests include collaborative filtering, Trust Management and Security (IFIPTM). Trondheim, trusted computing and information security. Norway: Springer, 2008, pp. 119-134.

[7] G. Pitsilis. L.F. Marshall, “A Model of Trust Derivation

from Evidence for Use in Recommendation Systems”,

Technical Report Series, CS-TR-874 [R], Newcastle Upon Fuzhi Zhang was born in Henan Province, Tyne, NEI 7RU, UK: University of Newcastle Upon Tyne, China in 1964. He received his Ph.D. in 2004. Computer Application Technology from [8] G. Pitsilis, L.F. Marshall, “Modeling Trust for Beijing Institute of Technology, China, in Recommender Systems using Similarity Metrics”, IFIP 2003 International Federation for Information Processing, Trust He is currently a professor in the School of Management II, 2008, volume 263, pp.103-118. Information Science and Engineering, [9] K. Kwon, J. Cho, Y. Park, “Multidimensional Credibility Yanshan University, Qinhuangdao, China. Model for Neighbor Selection in Collaborative His research domains cover intelligent Recommendation”, Expert Systems with Applications, network information processing, network 36(3), pp. 7114-7122, 2009. and information security, service-oriented computing. [10] M. Eisend, “Source Credibility Dimensions in Marketing

Communication-a Generalized Solution”, Journal of

Empirical Generalizations in Marketing, volume 10, pp.

1-33, 2006. Sai Liu was born in Henan Province, [11] M. Jamali, M. Ester, “TrustWalker: a Random Walk Model China in 1987. He received his B.S. in for Combining Trust-based and Item-based Computer Application Technology from Recommendation”, In: Proc. of the 15th ACM SIGKDD Zhengzhou University, China, in 2010. Int’l Conf. on Knowledge discovery and data mining. New He is currently a M.S. Candidate in the York, NY, USA: ACM Press, 2009, pp. 397-406. School of Information Science and [12] H. Ma, I. King, R.L. Michael, “Learning to Recommend Engineering, Yanshan University, with Social Trust Ensemble”, In: Proc. of the 32nd Annual Qinhuangdao, China. His research ACM SIGIR Conf. on Research and Development in interests include collaborative filtering Information Retrieval. New York, NY, USA: ACM Press, and contextual recommendation. 2009, pp. 203-210.