Information Filtering via Implicit Trust-based Network

Information Filtering via Implicit Trust-based Network

Abstract

Based on the user-item bipartite network, collaborative filtering (CF) recommender systems predict users’ interests according to their history collections, which is a promising way to solve the information exploration problem. However, CF algorithm encounters cold start and sparsity problems. The trust-based CF algorithm is implemented by collecting the users’ trust statements, which is time-consuming and must use users’ private friendship information. In this paper, we present a novel measurement to calculate users’ implicit trust-based correlation by taking into account their average ratings, rating ranges, and the number of common rated items. By applying the similar idea to the items, a item-based CF algorithm is constructed. The simulation results on three benchmark data sets show that the performances of both user-based and item-based algorithms could be enhanced greatly. Finally, a hybrid algorithm is constructed by integrating the user-based and item-based algorithms, the simulation results indicate that hybrid algorithm outperforms the state-of-the-art methods. Specifically, it can not only provide more accurate recommendations, but also alleviate the cold start problem.

1Introduction

Information exploration is one of the results of internet and social network development. The swift and violent growth of information on the Internet makes it more and more difficult for users to find available and useful portions [1]. How to help the users find out the relevant information or products by using the user-item bipartite network is a promising way to solve the information overload problem [2]. Search engineering and recommender systems are two effective tools to help users filter out what pieces are relevant to their tastes. However, search engineering presents exactly same list to the same keywords regardless of users’ interests, habits and the history behavior information. Recommender systems filter out the irrelevant information and recommend the potentially interesting items to the target users by analyzing their interests and habits through their history behaviors, which have been successfully applied in a lot of e-commercial web sites [5].

Collaborative filtering (CF) algorithm is one of the most successful technologies for recommender systems, which firstly identifies the target user’s neighbors whose interests or habits are similar and then presents the recommendation list according to the neighbor users’ history selections [2]. Recently, the similar idea has been applied to the items. Generally speaking, CF algorithms can be systematically classified as user-based and item-based [1]. User-based methods, regarding each user’s ratings as a vector, measure the similarity between the target user and those like-minded people and predict the target user’s rating for the target item according to the history preferences. User-based CF algorithms have been investigated extensively [10]. For example, Herlocker et al. [2] proposed an algorithmic framework referring to user similarity. Luo et al. [12] introduced the local user similarity and global user similarity concepts based on surprisal-based vector similarity and the concept of maximum distance in graph theory. When the number of items is approximately constant, it is better to give the prediction according to items’ similarity network. Item-based methods, regarding each item’s ratings as a vector, measure the similarity between the target item and other items and predict the target rating relying on users’ preferences in history. Because of less updates for average items and comparatively static state, the item-based approaches are superior. Sarwar et al. [13] proposed item-based CF algorithm by comparing different items. Deshpande et al. [14] proposed item-based top- CF algorithm, in which items are ranked according to the frequency of appearing in the set of similar items and the top- ranked items are returned. Recently, Gao et al. [15] incorporated the user ranking information into the computation of item similarity to improve the performance of item-based CF algorithm.

In the previous work, a lot of rating information wasn’t taken into consideration to compute the user or item similarity, such as average ratings, rating ranges, the number of users’ common rated items and so on. We argue that, however, these information should be taken into account to measure users’ relationship.

When some new users enter into a recommender system, they only give ratings to a few items. Analogously, when some new items are added in the system, they only receive ratings from a few users, which is named cold start problem. It’s very hard to give high quality prediction based on less of history selection information. In order to solve the cold start problem, some researchers attempt to integrate user-based and item-based CF methods to avoid the limitation of one single algorithm. For instance, Kim et al. [16] built united collaborative error-reflected models that reflect the average pre-prediction errors of user neighbors and of item neighbors. Jeong et al. [17] proposed an iterative semi-explicit rating method that extrapolates unrated elements from similar users and items in a semi-supervised manner. Besides, Lee et al. [18] used ratings data horizontally and vertically to make two-way cooperative prediction for CF algorithm and thus categorized four possible cases of predictions, namely equivalent case, user-winning case, item-winning case and prediction-impossible case. Empirical experiments show integrating user-based and item-based methods could enhance the performance greatly.

Recently, trust-based mechanism is introduced to alleviate the cold-start problem. Some of e-commerce web sites, such as Epinions, eBay and etc., try to apply trust mechanism to recommend products to consumers. In these web sites, the trust mechanism is implemented by collecting explicit or implicit trust statements. Explicit trust statements need users to indicate the trust values to their friends [19]. Massa et al. [20] suggested the explicit trust-aware CF recommender systems by searching trust neighbors in depth-first way according to trust propagation. Jamali et al. [19] built a model, named TrustWalker, by random walk in social trust network to find trust neighbors who have rated the target item or similar items. However, the above trust-based recommendation algorithms need explicit trust statements expressed by users, which are time-consuming and probably expose users’ privacy. Therefore, some implicit trust methodologies are proposed [21]. O’Donovan et al. [21] proposed computational models by implicit trust based on initial ratings, which only studied the effects of the errors between predicted ratings and actual ratings. Moreover, Kwon et al. [22] created a multidimensional credibility model for neighbor selection in CF algorithm by deriving source credibility attributes (i.e., expertise, trustworthiness, similarity and attraction) and extracting each consumer’s importance weight. Li et al. [23] applied fuzzy logic and inference to support peer recommendation service. Jeong et al. [24] developed user credit-based CF methods which incorporate the information of each user’s credit on rating items to compute the aggregation weight. What’s more, Lathia et al. [25] proposed the trusted -nearest recommenders algorithm which allows users to learn who and how much to trust others by evaluating the utility of the rating information they have received.

In previous work, the users’ rating habits wasn’t taken into account, such as average ratings, rating ranges, the number of common rated items and so on. We argue that these factors are very important and could be used to measure the implicit trust-based similarities between users or items. In this paper, by constructing the implicit trust-based network, we present three algorithms, say user-based, item-based and hybrid algorithms. The simulation results indicate that these factors are important and the hybrid algorithm outperforms the state-of-the-art methods and performs very well to the cold-start problem.

The following sections are organized as follows: Section 2, we describe the definition and measurement how to calculate the implicit trust-based user or item similarity, and the corresponding algorithms are also introduced. In Section 3, the simulation experiments on MovieLens, Netflix and Jester data sets are investigated and the results are analyzed in detail. Finally, the conclusions are presented and future work is discussed in Section 4.

2Collaborative filtering algorithms based on implicit trust-based network

2.1User-based Collaborative Filtering Algorithm

Definition of implicit trust-based user correlation network

The meaning of implicit trust-based users can be found in some previous work. For instance, O’Donovan et al. [21] supposed that the trustable partners have similar tastes and preferences to the target user and they should be trustworthy in the sense that they have a history of making reliable recommendations, whereas Kwon et al. [22] conceived that trustable neighbors have high expertise, trustworthiness, similarity, etc. In addition, Jeong et al. [24] set the trust-based user as the similarity of voting a rating score with others. Hereinafter, Trust in recommender system is defined in the following way. When a user agrees with another user about quality of certain products, she probably builds trust relationship with another, which further means that their similar opinions might be inferred in some ways.

In this paper, a trust-based user is defined as the user who has the implicit trust relationship with the target user. Since trust in e-commerce largely depends on similar views between users, implicit trust in this paper can be explained as the similarity of their opinions and interests on products, which are involved in average ratings, rating ranges and the number of common rated items.

Implicit Trust Measurement

In recommender systems, users express their opinions in the form of reviews, ratings, etc. Therefore, we could analyze their interests from different angles to build correspondingly implicit trust among them. In this paper, three factors are taken into consideration to learn about their interests: 1) users’ average ratings, 2) the ranges of their ratings, 3) their common experience. The details are discussed as follows:

1) Average ratings.

Every user has his/her independent rating schema, i.e. his/her average rating in a recommender system, as a result of his/her distinct personal characteristics. When users pay attention to their favorable items, they may express their opinions by variant ratings. In consequence, their independent rating schemas are generated, which reflect their own characteristics. In traditional CF recommendation algorithms, the rating schema is presented as the average rating of a user. For example, lots of measurements are proposed to define the similarities among users, such as Pearson correlation coefficient [2], adjusted cosine similarity [13], mass diffusion [7], heat conduction [3] and so on. Empirical studies show that these measurements with average rating get better results than those without average rating (e.g., cosine similarity) [26]. In mathematics and statistic domains, average rating reflects the general level and the central tendency. Accordingly, in recommender systems, those measurements are used to analyze how far users’ ratings are away from their average ratings and how their ratings evolve. In other words, whatever the ratings are, if only the differences and extents between users come close, the users are considered similar. In this article, average ratings are taken into account to measure the implicit trust values between users.

2) Rating ranges.

The range of ratings given by a user is probably different for another due to the diversity of users’ habits, mood and contexts. In the practical evaluation, some pessimistic users under bad mood and contexts fall into the habit of giving low ratings for all items. On the contrary, some positive users under good mood and contexts are accustomed to giving high ratings for all items. Since the users do not belong to the standard-rating sets, they should be treated specifically. Therefore, the range of ratings for every user should be taken into consideration when implicit trust weight is calculated.

3) Common rated items

We suppose the more information we receive from one person, the more we know about her. Analogously, in recommender systems, users’ experience is supposed to be stressed. In recommender systems, the common experience of users that they contribute to recommendation should be observed in order to improve the performance of recommender systems. For example, for the target user and two neighbors, say and , suppose the similarities between and , are equal, but user has more common rated items with than , therefore, it is reasonable to believe the similarity between and is stronger. In our algorithm, common experience between the target user and trustable neighbors is employed entirely.

The main principle of implicit trust-based user correlation related to the mentioned three factors is shown in Fig. ?. For user and , their implicit trust-based correlation is calculated based on their average ratings, say and , rating ranges, say and and the number of their common rated items .

[0.5](Color Online) Implicit trust-based user correlation. For user u and v, their common experience is co-rated item i and k. For item i (red rectangle), user u gives normalized distance from concrete rating value to average rating within his rating range, and so does user v. The definition could be used to measure the complement of absolute difference between the two users’ distances combining their common experience.

Considering the above three factors, we present the formulation to calculate implicit trust between user and :

where and is the number of common rated items for user and . The sigmoid function, , is used to rectify weight by the number of common rated items, , which has ever been distinctly used to adjust Pearson Correlation coefficient [19].

Prediction Based on Implicit Trust-based User Correlation Network

In this paper, -nearest neighbors of the target user are evaluated to investigate the effect of implicit trust-based correlation on cold start problem. Afterwards, the predicted rating, from user to the target item is given according to the following formulation.

where is a set of the nearest neighbors of user , and is the implicit trust-based correlation between user and obtained by Eq.(1).

2.2Item-based Collaborative Filtering Algorithm

Introducing a similar idea on the item correlation definition, the effect of the implicit trust-based correlation on item-based CF algorithm is investigated.

Definition of implicit trust-based items

When we are satisfied with products that we have purchased, we usually place them in trusted zone. Perhaps, in the future, we will buy them again. On the contrary, if we complain about some bad products, we place them in restricted zone and we may never buy them again.

In this paper, items based on implicit trusts are considered relying on proximity of items that a user has evaluated in her history. From this point of view, trusted items can be explained as the items that are close to those that one user trusts. In other words, while a user set a certain item in her trusted zone, the trust-based items, in terms of intrinsic attributes, accepted degrees, rating values and common popularity, are very similar to it. The process to search implicit trust-based items is to analyze all users’ opinions about these items.

Implicit trust measurement

In the paper, like implicit trust-based user correlation definition, three factors are referred to compute items’ implicit trust-based relationship, which can be described as: 1) the internal or intrinsic attributes of an item, 2) the accepted degree of an item, 3) the common rated times between any pairs of items. The detail is described as follows:

1) Intrinsic attributes of an item

The internal attributes of an item determine all users’ opinions about it. In other words, the average rating reflects intrinsic attributes of the item. If the quality of an item is good, users generally like it and give it high ratings, and vice versa. The more users have evaluated an item, the closer the average rating is to the internal characteristics of the item. The average rating implies all users’ opinions about the item.

We primarily pay attention to the distance from concrete rating to average rating. That means, the nearer to average rating the concrete rating value is, the more trustworthy an item is. In a word, average rating plays a significant role to implement recommendation based on implicit trust-based items.

2) Accepted degree of an item

The accepted degree of an item can be observed from two perspectives, minimum rating and maximum rating, which can be inferred from the rated range of the item. To an item, the minimum rating shows how bad the item a user thinks and the maximum one shows how good the item she considers. In brief, the minimum and maximum ratings describe the accepted degree of an item derived from all users’ opinions. For instance, if a movie is rated with low ratings.

3) Common rated times between items

The number of users who have commonly rated the items could affect the trustworthy levels of the items.

The more users give high ratings to two items, the more correlated these items are. Generally, the number of common rated times between the target item and its implicit trust-based neighborhood items should be taken into account.

The core principle of implicit trust-based item correlation is depicted in Fig. ?. For item and , the intrinsic attributes are denoted as their average ratings and respectively. The differences between maximum and minimum ratings are denoted as and . The number of common rated times is set as .

[0.5](Color Online) Three factors affecting implicit trust weight of credible items. For item i and j, their common popularity is the aggregation of over v’s and w’s ratings. For user v (red rectangle), item j gets normalized distance from concrete rating value to average rating within its rating range, and so does item i. The goal is to aggregate the complement of absolute difference between the two items’ distances combining their common popularity.

Therefore, the following formulation could be given,

where and denotes the number of users who have rated both item and . The sigmoid function, , is used to rectify weight by common users.

Prediction Based on Implicit Trust-based Item Correlation Network

To investigate the effect of implicit trust-based item correlation network on users’ cold start problem, the -nearest neighbors are evaluated in this paper. The predicted rating from user to item is given according to the following item-based CF algorithm.

where is a set of the nearest neighbors of item , and denotes the implicit trust weight between item and by Eq.(3).

2.3Hybrid algorithm

Traditional CF algorithm encounters cold start problem because of data set sparsity, which can be further divided into cold start users and cold start items [16]. A cold start user indicates the new user who has participated in recommendation but has expressed few opinions. In this situation, it is often the case that there is no intersection at all between two users, and it is difficult to calculate the user similarity based on common rated items. Even when the computation of similarity is possible, it may not be very reliable because of the insufficient information available. A cold start item is caused by the new item. In the CF-based recommender systems, this item cannot be recommended due to insufficient user opinions. The simulation results indicate that the hybrid algorithm could not only greatly enhance the accuracy, but also effectively solve the cold start problem.

In this paper, to alleviate the cold start problem, we present a hybrid recommendation algorithm by integrating implicit trust user-based and item-based CF algorithms, where the predicted rating is given in the following way

where is the prediction rating based on user-based CF algorithm in Eq.(2), is the prediction rating based on item-based CF algorithm in Eq.(4), and is a tunable parameter whose range is [0,1]. When , the hybrid algorithm degenerates to the user-based algorithm, and it becomes the item-based CF algorithm when . We can adjust value to control the ratios from the above two algorithms and find the optimum solution.

3Simulation Results

3.1Data Description and Statistical Properties

In this paper, our simulation experimental data comes from MovieLens 1, Netflix2 and Jester. The Movielens data is collected by the GroupLens Research Project during the seven-month period from September 19th, 1997 through April 22nd, 1998. The dataset consists of 100,000 ratings from 943 users on 1,682 movies and rating scale is from 1 (awful) to 5 (must see), which has been cleaned up so that users who had less than 20 ratings or did not have complete demographic information were removed from this dataset. The Netflix and Jester data are random samples of the whole records of user activities in Netflix.com and Jester, in which the Netflix data consists of 10000 users, 6000 movies and 824802 links, and the Jester data has 2350 users, 100 jokes and 169,655 connections. Table gives the statistical properties of the test data sets.

Basic statistics of the test data sets.
Data Sets Users Objects Links Sparsity
MovieLens 6,040 3,592 750,000
Netflix 10,000 6,000 701,947
Jester 2,350 100 169,655 0.7219

3.2Evaluation metrics

In order to measure the performances of the present algorithms, the mean absolute error (MAE) [27], the root mean square error (RMSE) [19] and the hit rate (HR) are used.

Mean Absolute Error

MAE is the mean absolute difference between an actual and a predicted rating value, which is generally used for the statistical accuracy measurements in various algorithms. The smaller MAE an algorithm achieves, the better the experimental result is. The metric MAE is defined as:

where and represent the predicted and actual rating respectively, and denotes the number of tested ratings.

Root Mean Square Error

RMSE has been typically used to measure the large errors in extreme cases. Analogously, the smaller the value of RMSE an algorithm obtains, the more precise the recommendation is. The metric RMSE is usually defined as follows

Hit Rate

The hit rate (HR) is also introduced to measure the accuracy of the recommendation. Here, HR is defined as the ratio of the number of hits (i.e., the fraction of the number of recommended items and actually chosen items) to the size of the recommendation list. In the information retrieval literature, it is usually equivalent to the metrics Precision and Recall. The bigger the value of HR is, the better an algorithm. Formally, HR is defined as

where is the length of recommendation list and is the percentage of items in the test set existing in the top- positions of recommendation list.

3.3Experiment results analysis

The implicit trust-based effects are implemented on user-based, item-based and hybrid algorithms separately. Since the prediction performance is influenced by the size of the nearest neighbors, it is essential to determine a proper size of the nearest neighbors Top , where is set as 3, 5, 10, 15 and 20 respectively. Since the typical length for recommendation list is ten items, our experiments set =10. The parameter is adjusted in the interval [0, 1] and the increment is 0.1.

Performance of Implicit Trust-based Effect on User-based Algorithm

In this section, we investigate the performance of the user-based CF algorithm (denoted as IU-CF) and compare it against the performances of classic user-based CF using well-known Pearson Correlation coefficient (denoted as PCF) and adjusted cosine-based CF algorithm [13] (denoted as AC-CF).

[0.6](Color Online) Comparison of results achieved by Pearson-based (PCF), adjusted cosine-based (AC-CF), implicit trust-based (IU-CF) and item-based CF (II-CF) algorithms. Note that both IU- and II-CF have the smallest MAE, RMSE and highest HR for Movielens, Netflix and Jester data sets.

Figure ? illustrates the results of MAE, RMSE and HR for PCF, AC-CF, IU-CF and II-CF algorithms respectively. The results demonstrate that IU-CF and II-CF algorithms enhance the performance of the initial two approaches, PCF and AC-CF. From Fig. ?, one can see that MAE of IU-CF algorithm has the lowest level in the three algorithms. As the number of the nearest neighbors increases, the MAE curves of all four algorithms tend to decrease, which implies that more neighbors can make better prediction although computation and time complexity is high. The RMSE results in Fig. ? show that IU- and II-CF algorithms have the smallest errors in the three algorithms while PCF algorithm gets results with the largest errors. In other words, our approach can predict more accurately than PCF and AC-CF algorithms. In addition, the similar RMSE downtrend for all algorithms appears in Fig. ? as the growth of the sizes of user neighborhood. Fig. ? illustrates the results of HR of three algorithms. As shown in Fig. ?, at most neighborhood sizes, HR of IU- and II-CF algorithms are remarkably better than the results of PCF and AC-CF algorithms. Even though only a minority of neighbors participate in prediction, the present IU- and II-CF algorithms outperform the other two methods. And, when the number of nearest neighbors increases, the curves of the three methods gradually change upward and finally tend to become flat. From the results of Fig. ?, it can be concluded that the present user-based and item-based approaches can provide better recommendations.

[1.2](Color Online) Comparison of setting different \alpha values for HCF. Note that MAE and RMSE first fall down before \alpha =0.5 and then climb up after that for Movielens and Netflix data sets. HR obeys reverse distribution with the boundary \alpha=0.5. The conclusion is that the optimal \alpha is 0.5 for HCF.

The performance of hybrid recommendation

In this section, the effects of the implicit trust-based correlations on hybrid recommendation (HCF) are investigated by integrating the user-based and item-based CF algorithm. In the experiment, we compare hybrid recommendation against the above two pure algorithms with different values. Figure ? summarizes the experiment results of MAE, RMSE and HR for HCF algorithm according to the value variation. We examine the HCF results of the three metrics in order to choose optimal parameter . In the experiment, the value is continuously changed in the interval [0, 1] with the increment 0.1. From Fig. ?, MAE and RMSE apparently decrease as the value of increases from 0 to 0.5; after this point 0.5, the upward MAE and RMSE gradually appear for Movielens and Netflix data sets. On the contrary, the metric HR considerably ascends before the value 0.5 and after that it begins to descend steadily. The optimal parameter for Jester data set is not exactly 0.5, but also close to this value. The results indicate that the optimal value is 0.5 no matter which metric is evaluated for HCF.

Figure ? illustrates the comparison of IU-CF, II-CF and HCF in the metrics MAE, RMSE, and HR respectively at the increasing sizes of the neighborhood from 3 to 20 when the optimal parameter is 0.5. As shown in the Fig. ?, for Movielens, Netflix and Jester data sets, HCF obtains the remarkably lowest levels of MAE and RMSE in the three methods when is quite small, as well as highest HR values. Summing up the above three metric results, the conclusion can reasonably be drawn that HCF which integrates recommendations by implicit trust-based user and item similarity network can further improve the performance of recommendation in some degree than pure IU-F and II-CF. More importantly, HCF could efficiently solve cold start problem.

[0.6](Color Online) Comparison of results achieved by IU-CF, II-CF and hybrid CF (IU+II CF) algorithms algorithms. Note that hybrid CF algorithm has the smallest errors and highest hits.

4Conclusion and discussions

Information is explored dramatically in the social network era. According to the structural properties of web connections, search engineering could help us to dig out the most relevant web page according to the keywords. However, search engineering couldn’t help users find the fresh information or products related to their interests and habits, and couldn’t analyze their personation, either. Based on the user-item bipartite network, recommender system is a promising tool to dig out the valuable information for the users. However, the existing user or item correlation definition didn’t take into account the users’ rating habits and statistical properties in detail. Traditional CF algorithm suffers the cold-start problem, and explicit trust-based recommender systems require users to express explicit trust statements, which may be time-consuming and expose privacy of users. Besides, the existing implicit trust-based algorithms take few factors into consideration to calculate the trust weight. Therefore, their recommendation results are not sufficiently accurate. This work addresses these problems by introducing implicit trust-based correlation network. When computing implicit trust weight, we fully consider implicit trust-based factors about users (e.g. average ratings, rating ranges, and common experience) and items (e.g. internal attributes, accept degrees and common popularity). The simulation results show that the proposed implicit user-based, item-based and hybrid algorithms solve cold start problem and provide accurate recommendations.

Although our approaches presented in this article have shown encouraging results, we also have several interesting tasks for future work. First, we are going to focus on doing research on transitive trust. In this paper, we have just paid attention to computing the implicit trust weight, but have not studied trust propagation. In real social network, trust can propagate from one person to another. Due to trust propagation, perfect neighbors are easy to be accessed and the cold start problem could also be overcome in some degree. In the future, we are going to take transitive trust into consideration in order to improve the performance of implicit trust-based recommender system. Second, we attempt to append robust mechanisms against the attacks by malicious users to improve our proposed approaches. The reason is that some e-commerce online recommender systems at present are often attacked by negative canvassers. Therefore, it is worthwhile to emphasize the robustness of an algorithm as an important aspect of practical recommender systems. Finally, we plan to develop new evaluation metrics to assess the performance of trust-based algorithms because the current metrics seldom examine the robustness of recommender systems.

Acknowledgments

We acknowledge the GroupLens Research Group for MovieLens data. This work has been partly supported by the Natural Science Foundation of China (Grant Nos. 10905052, 71171136, 71031002), the Fundamental Research Funds for the Central Universities of China under Grant No. DUT11RW422, and the Innovation Program of Shanghai Municipal Education Commission (11ZZ135, 11YZ110). JGL is supported by the Shanghai Leading Discipline Project (S30501), Shanghai Rising-Star Program (11QA1404500) and Key Project of Chinese Ministry of Education (211057).

Footnotes

  1. http://www.Movielens.com
  2. http://www.netflix.com

References

  1. G. Adomavicius, A. Tuzhilin. IEEE Tran. on Know. & Data Eng. 17 (2005) 734.
  2. J.L. Herlocker, J.A. Konstan, A. Borchers, J. Riedl. In Proc. of SIGIR ’99, 1999, pp. 230.
  3. T. Zhou, Z. Kuscsik, J.-G. Liu, M. Medo, J.R. Wakeling, Y.C. Zhang. Proc. Natl. Acad. Sci. U.S.A. 107 (2010) 4511.
  4. T. Zhou, R.-Q. Su, R.-R. Liu, L.-L. Jiang, B.-H. Wang, Y.-C. Zhang. New J. Phys. 11 (2009) 123008.
  5. G. Linden, B. Smith, J. York. IEEE Internet Computing 7 (2003) 76.
  6. L. Lu, Y.-C. Zhang, C.-H. Yeung, T. Zhou. PLoS One 6 (2011) e21202.
  7. T. Zhou, J. Ren, M. Medo, Y.-C. Zhang, Phys. Rev. E 76 (2007) 046115.
  8. J.-G. Liu, B.-H. Wang, Q. Guo. Int. J. Mod. Phys. C 20 (2009) 285.
  9. J.-G. Liu, T. Zhou, H.-A. Che, B.-H. Wang, Y.-C. Zhang. Physica A 389 (2010) 881.
  10. D. Sun, T. Zhou, J.-G. Liu, R.-R. Liu, C.-X. Jia, B.-H. Wang. Phys. Rev. E 80 (2009) 017101.
  11. J.-G. Liu, T. Zhou, Q. Guo. Phys. Rev. E 87 (2011) 037101.
  12. H. Luo, C. Niu, R. Shen, C. Ullrich. Machine Learning 72 (2008) 231.
  13. B. Sarwar, G. Karypis, J. Konstan, J. Riedl. In Proc. of ACM on WWW conference 2001, pp. 285.
  14. M. Deshpande, G. Karypis. ACM Tran. Info. Sys. 22 (2004) 143.
  15. M. Gao, Z.-F. Wu, F. Jiang. Info. Proc. Lett. 111 (2011) 440.
  16. H.N. Kim, A. El-Saddik, G.S Jo. Decision Support Systems 51 (2011) 519.
  17. B. Jeong, J. Lee, H. Cho. Expert Systems with Applicatios 36 (2009) 6181.
  18. J.S Lee, S. Olafsson. Expert Systems with Applicatios 36 (2009) 5353.
  19. M. Jamali, M. Ester. In Proc. of the 15th ACM SIGKDD, 2009, pp. 397.
  20. P. Massa, P. Avesani. In Proc. of Federated International Conference on the Move to Meaningful Internet, 2004, pp. 492.
  21. J. O’Donovan, B. Smyth. In Proc. of the 10th International Conference on Intelligent User Interfaces, 2005, pp. 167.
  22. K. Kwon, J. Cho, Y. Park. Expert Systems with Applicatios 36 (2009) 7114.
  23. Y.M. Li, C.P. Kao. Expert Systems with Applicatios 36 (2009) 3263.
  24. B. Jeong, J. Lee, H. Cho. Expert Systems with Applicatios 36 (2009) 7309.
  25. N. Lathia, S. Hailes, L. Capra. In Proc. of IFIPTM 2008:Joint iTrust and PST conferences on Privacy, Trust management and Security, 2008, pp.119.
  26. J.S. Breese, D. Heckerman, C. Kadie. In Proc. Of the 14th Conference on Uncertainty in Artificial Intelligence, 1998, pp.43.
  27. J.L. Herlocker, J.A. Konstan, L.G. Terveen, J. Riedl. ACM Transactions on Information Systems 22 (2004) 5.
10329
This is a comment super asjknd jkasnjk adsnkj
Upvote
Downvote
Edit
-  
Unpublish
""
The feedback cannot be empty
Submit
Cancel
Comments 0
""
The feedback cannot be empty
   
Add comment
Cancel

You’re adding your first comment!
How to quickly get a good reply:
  • Offer a constructive comment on the author work.
  • Add helpful links to code implementation or project page.