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Matrix approximation (MA) methods are integral parts of today's recommender systems. In standard MA methods, only one feature vector is learned for each user/item, which may not be accurate enough to characterize the diverse interests of users/items. For instance, users could have different opinions on a given item, so that they may need different feature vectors for the item to represent their unique interests. To this end, this article proposes a mixture matrix approximation (MMA) method, in which we assume that the user-item ratings follow mixture distributions and the user/item feature vectors vary among different stars to better characterize the diverse interests of users/items. Furthermore, we show that the proposed method can tackle both rating prediction and the top-N recommendation problems. Empirical studies on MovieLens, Netflix and Amazon datasets demonstrate that the proposed method can outperform state-of-the-art MA-based collaborative filtering methods in both rating prediction and top-N recommendation tasks. [ABSTRACT FROM AUTHOR]

Matrix and tensor completion aim to recover a low-rank matrix / tensor from limited observations and have been commonly used in applications such as recommender systems and multi-relational data mining. A state-of-the-art matrix completion algorithm is Soft-Impute, which exploits the special "sparse plus low-rank" structure of the matrix iterates to allow efficient SVD in each iteration. Though Soft-Impute is a proximal algorithm, it is generally believed that acceleration destroys the special structure and is thus not useful. In this paper, we show that Soft-Impute can indeed be accelerated without comprising this structure. To further reduce the iteration time complexity, we propose an approximate singular value thresholding scheme based on the power method. Theoretical analysis shows that the proposed algorithm still enjoys the fast $O(1/T^2)$O(1/T2) convergence rate of accelerated proximal algorithms. We also extend the proposed algorithm to tensor completion with the scaled latent nuclear norm regularizer. We show that a similar "sparse plus low-rank" structure also exists, leading to low iteration complexity and fast $O(1/T^2)$O(1/T2) convergence rate. Besides, the proposed algorithm can be further extended to nonconvex low-rank regularizers, which have better empirical performance than the convex nuclear norm regularizer. Extensive experiments demonstrate that the proposed algorithm is much faster than Soft-Impute and other state-of-the-art matrix and tensor completion algorithms. [ABSTRACT FROM AUTHOR]

We propose TrustSVD, a trust-based matrix factorization technique for recommendations. TrustSVD integrates multiple information sources into the recommendation model in order to reduce the data sparsity and cold start problems and their degradation of recommendation performance. An analysis of social trust data from four real-world data sets suggests that not only the explicit but also the implicit influence of both ratings and trust should be taken into consideration in a recommendation model. TrustSVD therefore builds on top of a state-of-the-art recommendation algorithm, SVD++ (which uses the explicit and implicit influence of rated items), by further incorporating both the explicit and implicit influence of trusted and trusting users on the prediction of items for an active user. The proposed technique is the first to extend SVD++ with social trust information. Experimental results on the four data sets demonstrate that TrustSVD achieves better accuracy than other ten counterparts recommendation techniques. [ABSTRACT FROM PUBLISHER]

Due to its successful application in recommender systems, collaborative filtering (CF) has become a hot research topic in data mining and information retrieval. In traditional CF methods, only the feedback matrix, which contains either explicit feedback (also called ratings) or implicit feedback on the items given by users, is used for training and prediction. Typically, the feedback matrix is sparse, which means that most users interact with few items. Due to this sparsity problem, traditional CF with only feedback information will suffer from unsatisfactory performance. Recently, many researchers have proposed to utilize auxiliary information, such as item content (attributes), to alleviate the data sparsity problem in CF. Collaborative topic regression (CTR) is one of these methods which has achieved promising performance by successfully integrating both feedback information and item content information. In many real applications, besides the feedback and item content information, there may exist relations (also known as networks) among the items which can be helpful for recommendation. In this paper, we develop a novel hierarchical Bayesian model called Relational Collaborative Topic Regression (RCTR), which extends CTR by seamlessly integrating the user-item feedback information, item content information, and network structure among items into the same model. Experiments on real-world datasets show that our model can achieve better prediction accuracy than the state-of-the-art methods with lower empirical training time. Moreover, RCTR can learn good interpretable latent structures which are useful for recommendation. [ABSTRACT FROM AUTHOR]

In this paper, we describe the problem of recommending conference sessions to attendees and show how novel extensions to traditional model-based recommender systems, as suggested in Adomavicius and Tuzhilin [CHECK END OF SENTENCE], can address this problem. We introduce Recommendation Engine by CONjoint Decomposition of ITems and USers (RECONDITUS)—a technique that is an extension of preference-based recommender systems to recommend items from a new disjoint set to users from a new disjoint set. The assumption being that preferences exhibited by users with known usage behavior (e.g., past conference session attendance), which can be abstracted by projections of user and item matrices, will be similar to ones of new (different) users where the basic environment and item domain are the same (e.g., new conference). RECONDITUS requires no item ratings, but operates on observed user behavior such as past conference session attendance. The RECONDITUS paradigm consists of projections of both user and item data, and the learning of relationships in projected space. Once established, the relationships enable predicting new relationships and provide associated recommendations. The approach can encompass several traditional data mining problems where both clustering and prediction are necessary. RECONDITUS has been evaluated using data from the Oracle OpenWorld conference. [ABSTRACT FROM AUTHOR]