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.
@cite_28: 
@cite_41: Unlike in general recommendation scenarios where a user has only a single role, users in trust rating network, e.g. Epinions, are associated with two different roles simultaneously: as a truster and as a trustee. With different roles, users can show distinct preferences for rating items, which the previous approaches do not involve. Moreover, based on explicit single links between two users, existing methods can not capture the implicit correlation between two users who are similar but not socially connected. In this paper, we propose to learn dual role preferences (truster trustee-specific preferences) for trust-aware recommendation by modeling explicit interactions (e.g., rating and trust) and implicit interactions. In particular, local links structure of trust network are exploited as two regularization terms to capture the implicit user correlation, in terms of truster trustee-specific preferences. Using a real-world and open dataset, we conduct a comprehensive experimental study to investigate the performance of the proposed model, RoRec. The results show that RoRec outperforms other trust-aware recommendation approaches, in terms of prediction accuracy.
@cite_27: The most critical challenge for the recommendation system is to achieve the high prediction quality on the large scale sparse data contributed by the users. In this paper, we present a novel approach to the social recommendation problem, which takes the advantage of the graph Laplacian regularization to capture the underlying social relationship among the users. Differently from the previous approaches, that are based on the conventional gradient descent optimization, we formulate the presented graph Laplacian regularized social recommendation problem into a low-rank semidefinite program, which is able to be efficiently solved by the quasi-Newton algorithm. We have conducted the empirical evaluation on a large scale dataset of high sparsity, the promising experimental results show that our method is very effective and efficient for the social recommendation task.
@cite_45: 
@cite_31: Recommender systems are becoming tools of choice to select the online information relevant to a given user. Collaborative filtering is the most popular approach to building recommender systems and has been successfully employed in many applications. With the advent of online social networks, the social network based approach to recommendation has emerged. This approach assumes a social network among users and makes recommendations for a user based on the ratings of the users that have direct or indirect social relations with the given user. As one of their major benefits, social network based approaches have been shown to reduce the problems with cold start users. In this paper, we explore a model-based approach for recommendation in social networks, employing matrix factorization techniques. Advancing previous work, we incorporate the mechanism of trust propagation into the model. Trust propagation has been shown to be a crucial phenomenon in the social sciences, in social network analysis and in trust-based recommendation. We have conducted experiments on two real life data sets, the public domain Epinions.com dataset and a much larger dataset that we have recently crawled from Flixster.com. Our experiments demonstrate that modeling trust propagation leads to a substantial increase in recommendation accuracy, in particular for cold start users.
@cite_12: With the fast development of social media, the information overload problem becomes increasingly severe and recommender systems play an important role in helping online users find relevant information by suggesting information of potential interests. Social activities for online users produce abundant social relations. Social relations provide an independent source for recommendation, presenting both opportunities and challenges for traditional recommender systems. Users are likely to seek suggestions from both their local friends and users with high global reputations, motivating us to exploit social relations from local and global perspectives for online recommender systems in this paper. We develop approaches to capture local and global social relations, and propose a novel framework LOCABAL taking advantage of both local and global social context for recommendation. Empirical results on real-world datasets demonstrate the effectiveness of our proposed framework and further experiments are conducted to understand how local and global social context work for the proposed framework.
Jamali and Ester @cite_31 built a new model (SocialMF) on top of SoRec by reformulating the contributions of trusted users to the formation of the active user's user-specific vector rather than to the predictions of items. @cite_27 proposed a graph Laplacian regularizer to capture the potentially social relationships among users, and form the social recommendation problem as a low-rank semidefinite problem. proposed a social recommendation method in @cite_45 , which the authors utilize as trust network information in the experimental process. @cite_28 proposed a hybrid method (TrustMF) that combines both a truster model and a trustee model from the perspectives of trusters and trustees. @cite_12 considered both global and local trust as the contextual information in their model. @cite_41 took into consideration both the explicit and implicit interactions among trusters and trustees in a recommendation model.