Recommendation plays an increasingly important role in our daily lives. Recommender systems automatically suggest items to users that might be interesting for them. Recent studies illustrate that incorporating social trust in Matrix Factorization methods demonstrably improves accuracy of rating prediction. Such approaches mainly use the trust scores explicitly expressed by users. However, it is often challenging to have users provide explicit trust scores of each other. There exist quite a few works, which propose Trust Metrics to compute and predict trust scores between users based on their interactions. In this paper, first we present how social relation can be extracted from users' ratings to items by describing Hellinger distance between users in recommender systems. Then, we propose to incorporate the predicted trust scores into social matrix factorization models. By analyzing social relation extraction from three well-known real-world datasets, which both: trust and recommendation data available, we conclude that using the implicit social relation in social recommendation techniques has almost the same performance compared to the actual trust scores explicitly expressed by users. Hence, we build our method, called Hell-TrustSVD, on top of the state-of-the-art social recommendation technique to incorporate both the extracted implicit social relations and ratings given by users on the prediction of items for an active user. To the best of our knowledge, this is the first work to extend TrustSVD with extracted social trust information. The experimental results support the idea of employing implicit trust into matrix factorization whenever explicit trust is not available, can perform much better than the state-of-the-art approaches in user rating prediction.
Specifically, @cite_24 clustered users by multi-views of similarity and trust, in order to resolve the relative low accuracy. @cite_32 proposed a social regularization method (SoRec) by considering the constraint of social relationships. Ma, King, and Lyu @cite_3 proposed a social trust ensemble method (RSTE) to linearly combine a basic matrix factorization model and a trust-based neighborhood model together. They proposed SoReg method that the active user's user-specific vector should be close to the average of her trusted neighbors, and use it as a regularization to form a new matrix factorization model @cite_7 .
@cite_24 @cite_7 @cite_32 @cite_3
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Social recommender systems exploit users' social relationships to improve the recommendation accuracy. Intuitively, a user tends to trust different subsets of her social friends, regarding with different scenarios. Therefore, the main challenge of social recommendation is to exploit the optimal social dependency between users for a specific recommendation task. In this paper, we propose a novel recommendation method, named probabilistic relational matrix factorization (PRMF), which aims to learn the optimal social dependency between users to improve the recommendation accuracy, with or without users' social relationships. Specifically, in PRMF, the latent features of users are assumed to follow a matrix variate normal (MVN) distribution. The positive and negative dependency between users are modeled by the row precision matrix of the MVN distribution. Moreover, we have also proposed an efficient alternating algorithm to solve the optimization problem of PRMF. The experimental results on real datasets demonstrate that the proposed PRMF method outperforms state-of-the-art social recommendation approaches, in terms of root mean square error (RMSE) and mean absolute error (MAE). Although demonstrated to be efficient and scalable to large-scale data sets, clustering-based recommender systems suffer from relatively low accuracy and coverage. To address these issues, we develop a multiview clustering method through which users are iteratively clustered from the views of both rating patterns and social trust relationships. To accommodate users who appear in two different clusters simultaneously, we employ a support vector regression model to determine a prediction for a given item, based on user-, item- and prediction-related features. To accommodate (cold) users who cannot be clustered due to insufficient data, we propose a probabilistic method to derive a prediction from the views of both ratings and trust relationships. Experimental results on three real-world data sets demonstrate that our approach can effectively improve both the accuracy and coverage of recommendations as well as in the cold start situation, moving clustering-based recommender systems closer towards practical use. Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in statistics, machine learning, computer vision, as well as signal and image processing. In theory, this problem can be solved by the natural convex joint mixed relaxations (i.e., l 1 -norm and trace norm) under certain conditions. However, all current provable algorithms suffer from superlinear per-iteration cost, which severely limits their applicability to large-scale problems. In this paper, we propose a scalable, provable and structured robust bilinear factorization (RBF) method to recover low-rank and sparse matrices from missing and grossly corrupted data, i.e., robust matrix completion (RMC), or incomplete and grossly corrupted measurements, i.e., compressive principal component pursuit (CPCP). Specifically, we first present two small-scale matrix trace norm regularized bilinear factorization models for RMC and CPCP problems, in which repetitively calculating SVD of a large-scale matrix is replaced by updating two much smaller factor matrices. Then, we apply the alternating direction method of multipliers (ADMM) to efficiently solve the RMC problems. Finally, we provide the convergence analysis of our algorithm, and extend it to address general CPCP problems. Experimental results verified both the efficiency and effectiveness of our method compared with the state-of-the-art methods. We propose a regularization approach that incorporates social network information.Biclustering algorithm is used to calculate the number of realistic friends.The friendships are used to calculate the similarities between users.The correlation between user and item is taken into consideration.We examine the impacts of parameters to the experimental results. The traditional recommender systems, especially the collaborative filtering recommender systems, have been studied by many researchers in the past decade. However, they ignore the social relationships among users. In fact, these relationships can improve the accuracy of recommendation. In recent years, the study of social-based recommender systems has become an active research topic. In this paper, we propose a social regularization approach that incorporates social network information to benefit recommender systems. Both users' friendships and rating records (tags) are employed to predict the missing values (tags) in the user-item matrix. Especially, we use a biclustering algorithm to identify the most suitable group of friends for generating different final recommendations. Empirical analyses on real datasets show that the proposed approach achieves superior performance to existing approaches.