Using Trust in Collaborative Filtering Recommendation

Transcription

1 Using Trust in Collaborative Filtering Recommendation Chein-Shung Hwang and Yu-Pin Chen Department of Information Management, Chinese Culture University, 55, Hwa-Kang Road, Yang-Ming-Shan, Taipei, Taiwan, R.O.C. Abstract. Collaborative filtering (CF) technique has been widely used in recommending items of interest to users based on social relationships. The notion of trust is emerging as an important facet of relationships in social networks. In this paper, we present an improved mechanism to the standard CF techniques by incorporating trust into CF recommendation process. We derive the trust score directly from the user rating data and exploit the trust propagation in the trust web. The overall performance of our trust-based recommender system is presented and favorably compared to other approaches. Keywords: Trust, Collaborative Filtering, Recommender System. 1 Introduction The ever-increasing popularity of the Internet has led to an explosive growth of the sheer volume of data. Recommender systems are emergent to solve the information overload problem by suggesting users items that they might like or find interested. Collaborative filtering (CF) [1][2][3] is one of the most successful and widely used recommender systems. The main idea behind CF model is to automate the process of word-of-mouth by which people recommend items to one another. For each user, CF model uses historical information to identify a neighborhood of people who have shown similar behavior in the past and then predicts the interest of new items by analyzing the neighborhood. The formation of neighborhood requires the computation and comparison between current user and every other user based on their ratings data. However, the number of ratings already collected is very small compared to the number of ratings needed to provide a prediction. As a result, CF model often has difficulty in finding a sufficient number of similar neighbors for a user and providing an effective recommendation. Recently, several researches have suggested that the incorporation of a notion of trust into the standard CF model can effectively solve the sparsity problem and thus provide better recommendations. A user can build his personalized web of trust by specifying those friends or users he trusts. The trust web can be constructed through the explicit trust ratings provided by users. For example, Massa et al. [4] build a trust model directly from users direct feedbacks. H.G. Okuno and M. Ali (Eds.): IEA/AIE 2007, LNAI 4570, pp , c Springer-Verlag Berlin Heidelberg 2007

2 Using Trust in Collaborative Filtering Recommendation 1053 This trust model is incorporated into the recommendation process for recommending various items (such as books, movie, music, software etc.) to on-line users. Users can express their personal web of trust by identifying those reviewers whose reviews and ratings are consistently found to be valuable. Massa et al. argue that it is possible to predict trust in unknown users by propagating trust even there were no direct connection between them. They also show, in their subsequent experiment [5], that the incorporation of trust metric and similarity metric can increase the coverage of recommender systems while maintaining the recommendation accuracy. Due to the limitation on trust value representation, in their experiments, the webs of trust are built on binary relationships among users and the propagating trusts are computed simply based on the distances between them. Avesain et al. [6] apply the trust model into the ski mountaineering domain. They present a community-based website in which users can share their opinions about the snow conditions of different ski routes and also express their trust on others opinions. The trust score of a user depends on the trust statements of other users on him/her and their trust scores. However, the trust model requires the direct feedback of users and the effectiveness of the trust model on the skiing community has not been validated. Golbeck et al. [7] describe an E mail filtering system based on trust ratings. The predicted trust of a user is given by a weighted average of her neighbors trust ratings. They have shown that the weighted average metric can provide better results than other metrics. However they still need the explicit trust ratings from users and do not use any mail ratings information. The explicit user participation for providing his trustworthiness to one another suffers from some limitations such as additional user effort and cold start that new users have to build up their trust webs before the filtering is effective. Alternatively, the trust web can be implicitly and directly derived from the item ratings data. Pitsilis et al. [8] view trust as a form of opinions which are always subjective and uncertain. Every opinion is expressed as a three-dimensional metric comprising belief, disbelief and uncertainty. The uncertainty is modeled from prediction error and the levels of belief and disbelief are derived based on correlation between every pair of users. The system presents a comparative performance to Beta distribution approach. However, no comparison to the traditional CF has been performed and reported. Donovan et al. [9] claim that the reliability of a user profile to deliver accurate recommendation in the past is an important factor for influencing recommendation and prediction. A user is viewed as more trustworthy if he has made more accurate predictions in the past than other users. The trust metrics are calculated at both the Item and Profile levels. Essentially these metrics summarize the relative number of correct recommendations that a given user has made, according to a predefined error bound. They have shown that the incorporation of trust metric into a standard CF has a positive impact on the prediction quality. However, this system only uses a global trust metric and provides neither any personalization nor trust propagation.

3 1054 C.-S. Hwang and Y.-P. Chen In general, while local trust metrics can be more precise and personalized than global trust metrics, they are also computationally more expensive. In this paper, we present an improved mechanism to the existing trust-based CF techniques. In particular, we will discuss how the local trust metrics can be incorporated into CF process and be efficiently propagated in the trust web. Formally, we aim to tackle the following problems: 1. How to directly derive trust ratings score from item ratings data? 2. How to define the global trust metric and the local trust metric? 3. How to propagate the trust score in the trust web? 2 System Architecture The main goal of our study is to design an effective recommender system by integrating trust metric into the traditional CF process. The proposed system consists of three modules: Trust Computation (TC) module, Similarity Computation (SC) module, and Rating Prediction (RP) module as shown in Fig. 1. Fig. 1. System Architecture The overall system can be viewed as a blackbox which takes as input the rating matrix and produces, as output, a prediction matrix. The ratings matrix R contains the rating scores r i,k standing for the rating of user u i for item i k,which can be either a numerical scale (representing his opinion) or (representing no rating). The TC module derives the trust score directly from rating data and computes the propagated trust. The SC module computes the correlation coefficient between each pair of users. The RP module integrates the trust matrix and the similarity matrix to produce predictions for unseen items. 2.1 Trust Computation Module The TC module involves a lot of works as shown in Fig. 2. Trust derivation module takes as input the rating matrix and computes the direct trust score of each pair of users. For every user, two trust metrics are computed. Global trust metric measures every user s global trust score reflecting the trustworthiness of all other users with the target user. The global trust score of a user is the same for every user. Local trust metric computes a user s trustworthiness with

4 Using Trust in Collaborative Filtering Recommendation 1055 respect to another user. Local trust metric takes as input the direct trust relationships resulting from the Trust derivation module and exploits the indirect trust relationships through trust propagation and path composition. Fig. 2. Trust Computation Module Trust Deviation. We believe that prediction accuracy of a user in the past is an important factor for measuring the trustworthiness of him. Therefore if a user delivers high accurate recommendations to another user in the past, then he is trustworthy and should obtain a high trust score from that user. Our system uses a simple version of Resnick s prediction formula [10] to compute the predicted rating. The predicted rating of item i for user u a by another user u b is given as follow: p b a,i = r a +(r b,i r b ), (1) where r a and r b refer to the mean ratings of u a and u b, respectively, and r b,i is the rating of item i given by u b. The trust score of u a with respect to u b is then derived by averaging the prediction error of co-rated items between them. t a b = 1 n(i a I b ) i (I a I b ) ( 1 pb a,i r ) a,i, (2) m where I a and I b refer to the set of rated items of u a and u b, respectively, and m is the size of the rating range. It should be noted that the computation of the trust score is performed based on the co-rated items. Global Trust Metric. A user s global trust with respective to another user combines the local trust with recommendations received from other users. We define the global trust score of a user u a as the average of the local trust scores given by neighbors who are directly connected to u a in the trust web. gt a = 1 n(nb(u a )) where NB(u a ) is the neighborhood of u a. j NB(u a) t j a, (3)

5 1056 C.-S. Hwang and Y.-P. Chen Trust Propagation Metric. Due to the large number of items existing in a recommender system, the ratings matrix is very sparse. The sparsity of rating matrix often makes two users have no co-rated items, which results in no direct trust relationships between them. The problem can be handled by means of trust propagation to infer the indirect relationships. Trust propagation implies that, in the trust web, there exists a trust path between a source user u s and a target user u t. Suppose that there is an intermediate user u m in the trust path connected u s and u t. The inferred trust score of u t given by u s through u m is computed by the weighted average of the two direct relationships of u s u m and u m u t [11]. t s m t = t s m t m t = n(i s I m )t s m + n(i m I t )t m t, (4) n(i s I m )+n(i m I t ) The rational behind this computation is that if two users have more co-rated items then their direct relationship should be more reliable and desiring more weight. The propagation operator can be repetitively applied for computing the indirect trust relationship between any two users in the trust web. Path Composition. It is possible that there are multiple paths between two users in the trust web. Each path contributes its own inferred trust score. The inferred trust score in each path is independent of each other. We need to decide how to combine these trust scores to give a single composite measure. In our current study, we simply compute the average of all the inferred trust scores contributed by each of the alternative paths. 2.2 Similarity Computation Module The SC module is one of the standard steps in the standard CF algorithms. SC module computes the similarity between users. Recent studies [12][13] have shown a strong and significant correlation between trust and similarity. The more similar the two users are the higher trust they have. We take the ratings matrix as an input and produce a similarity matrix containing the similarity value of any user against every other user. We calculate the similarity as Pearson correlation coefficient [14]. i (I sim a,b = a I b ) (r a,i r a )(r b,i r b ) i (Ia Ib) (r a,i r a ) 2. (5) i (Ia Ib) (r b,i r b ) Rating Prediction Module The RP module is the final step in the standard CF algorithms. A common used algorithm is Resnick s standard prediction formula [10]. The predicted rating of item i for a user u a is the weighted sum of the ratings given by users in his neighborhood. k NB(u p a,i = r a + (r a) k,i r k ) w a,k k NB(u w, (6) a) a,k

6 Using Trust in Collaborative Filtering Recommendation 1057 where, w a,k represents the weight of user u a assigned to his neighbor u k. w a,k can be taken either from the similarity score sim a,k, the local trust score t a k or the global trust score gt k. 3 Experimental Evaluation 3.1 Data Sets We use the movielens dataset collected by the GroupLens Research at the University of Minnesota. It contains 100,000 ratings from 943 users for 1628 movies. Each user has rated at least 20 movies, and each movie has been rated at least once. The original data set was converted into a new user-movie matrix R that had 943 rows (i.e. 943 users) and 1682 columns (i.e movies). We employ the 5-fold cross-validation approach. First, we randomly divide the dataset into five groups. Then we run five rounds of tests, each time choosing one group of data as test data and the other four groups as training data. The training set is used to generate the recommendation model. For each user in the test data, we employ the AllButOne protocol in which one item is selected at a time as the predicated item; all other ratings are used as input to the system. Our recommender system is then evaluated by comparing the predicted ratings with the actual ratings of the selected items. 3.2 Evaluation Metrics To measure the accuracy of the recommendations we computed the standard Mean Absolute Error (MAE) between ratings and predictions in the test data. MAE is a measure of the deviation of recommendations from their actual ratings. Specifically, given the set of actual/predicted pairs (r a,i,p a,i ) for all the movies rated by user u a, the MAE for user u a is computed as: i R(u MAE a = r a) a,i p a,i, (7) n(r(u a )) where R(u a ) represents the set of items that are rated by u a.theoverallmae is computed by averaging these individual MAEs over all users in the test data. Another important measure for discriminating between different recommendation approaches is coverage. Coverage is a measure of percentage that a recommender system can provide predictions. A prediction is impossible to be computed only when very people rated the movie or the active user has no correlation with other users. So a movie is predictable even only two users have rated it. Our pilot study reveals a near perfect coverage (around 99% in all experiments). To make a reasonable comparison,we examine the change of coverage with respect to different sparsity of user rating data.

7 1058 C.-S. Hwang and Y.-P. Chen 3.3 Performance Results Table 1 shows the prediction accuracy of different trust settings in our recommender system in contrast to those produced by standard CF technique. In all experiments, we compare the recommendation quality of different trust settings in our recommender system with those produced by standard CF technique. We compare the global trust model to local trust model with different maximum propagation distance, precisely, 1, 2, 3, and 4. We define as global-cf the method that employs the global trust metric in the CF process. Local-CF-n represents the method in which the local trust metric with maximum propagation distance n is used. The MAE is expressed with respect to different neighborhood sizes. Table 1. MAE of trust-based CFs vs.standard CF recommendation Size of NB Standard CF Global-CF Local-CF-1 Local-CF-2 Local-CF-3 Local-CF In all approaches, the prediction accuracy improves as the number of neighbors increases but they reach the maximum performance at around 70 neighbors and any further increment makes no better or even worse results. However, the trust enhanced approaches result in an overall improvement in accuracy. Specifically, the local trust CFs perform the best under all cases and the global trust CF is slight better than the standard CF in a small neighborhood, but performs worse with increasing number of neighbors. The performance of the local trust CF varies with the propagation distances and reaches the best when the distance is 3. As discussed earlier, sparsity of ratings is one of the common problems that collaborative recommender system may encounter. The sparsity problem is one major reason causing poor prediction quality. In this experiment, we examine the effectiveness of trust in solving the sparsity problem. To evaluate the coverage of different approaches, we relax the size of neighborhood to all users, and perform an experiment with different sparsity levels. Table 2 shows the result of coverage for different CF approaches. As expected, when the sparsity level increases, the coverage drops gradually. The global-cf has the highest coverage as all users are involved for recommendations. Local-CF-1 gains a slight improvement in coverage compared with the standard CF. The coverage increases when the maximum propagation distance increases. Local-CF-2 provides a large improvement over Local-CF-1, but the improvement starts to converge to 0 with increasing propagation distance.

8 Using Trust in Collaborative Filtering Recommendation 1059 Table 2. Coverage of different CF approaches Sparsity (%) Standard CF Global-CF Local-CF-1 Local-CF-2 Local-CF-3 Local-CF Discussion and Future Work In this paper we have presented a trust-based CF recommender system which incorporates the trust notion into the standard CF process. We derive the trust score directly from the ratings data based on users prediction accuracy in the past. We investigate the effects of both the local trust metric and the global trust metric in the standard CF recommendation. The global metric has shown to have an advantage over other approaches in prediction coverage. The local metrics provide more accurate recommendations than those provided by standard CF technique. Experimental results verify that the incorporation of trust into CF process can indeed improve the prediction accuracy while maintain satisfactory prediction coverage. We have described the proposed trust-based CF approach in the context of the movie domain. A further application to a range of other domains would be investigated. In fact, we would suggest that any social community network could benefit from the web of trust, assuming that the ratings data are available. References 1. Shardanand, U., Maes, P.: Social Information Filtering: Algorithms for Automating Word of Mouth. In: Proceedings of Human Factors in Computing Systems, pp (1995) 2. Breese, J.S., Heckerman, D., Kadie, C.: Empirical Analysis of Predictive Algorithms For Collaborative Filtering. In: Proceedings of the 14th Conference on Uncertainty in Artificial Intelligence, pp (1998) 3. Herlocker, J., Konstan, J.A., Terveen, L., Riedl, J.: Evaluating Collaborative Filtering Recommender Systems. ACM Transactions on Information Systems 22, 5 53 (2004) 4. Massa, P., Bhattacharjee, B.: Using Trust in Recommender Systems: An Experimental Analysis. In: Proceedings of the 2nd International Conference on Trust Management, Oxford, England, pp (2004) 5. Massa, P., Avesani, P.: Trust-Aware Collaborative Filtering for Recommender Systems. In: Proceedings of the International Conference on Cooperative Information Systems (CoopIS), Agia Napa, Cyprus, pp (2004)

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