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Low rank matrix factorisation is often used in recommender systems as a way of extracting latent features. When dealing with large and sparse datasets, traditional recommendation algorithms face the problem of acquiring large, unrestrained, fluctuating values over predictions. Imposing bounding constraints has been proven an effective solution. However, existing bounding algorithms can only deal with one pair of fixed bounds, and are very time-consuming when applied on large-scale datasets. In this paper, we propose a novel algorithm named Magnitude Bounded Matrix Factorisation (MBMF), which allows different bounds for individual users/items and performs very quickly on large scale datasets. The key idea of our algorithm is to construct a model by constraining the magnitudes of each individual user/item feature vector. By converting coordinate system with radii set as the corresponding magnitudes, MBMF allows the above constrained optimisation problem to become an unconstrained one, which can be solved by unconstrained optimisation algorithms such as the stochastic gradient descent. We also explore an acceleration approach and the choice of magnitudes are given in detail as well. Experiments on synthetic and real datasets demonstrate that in most cases the proposed MBMF is superior over all existing algorithms in terms of accuracy and time complexity. [ABSTRACT FROM AUTHOR]

The low-rank matrix completion problem is fundamental in both machine learning and computer vision fields with many important applications, such as recommendation system, motion capture, face recognition, and image inpainting. In order to avoid solving the rank minimization problem which is NP-hard, several surrogate functions of the rank have been proposed in the literature. However, the matrix restored from the optimization problem based on the existing surrogate functions seriously deviates from the original one. In this paper, we first design a new non-convex Schatten capped $p$ p norm which generalizes several existing non-convex matrix norms and balances between the rank and the nuclear norm of the matrix. Then, a matrix completion method based on the Schatten capped $p$ p norm is proposed by exploiting the framework of the alternating direction method of multipliers. Meanwhile, the Schatten capped $p$ p norm regularized least squares subproblem is analyzed in detail and is solved explicitly. Finally, we evaluate the performance of the proposed matrix completion method based on extensive experiments in the field of image inpainting. All the experimental results demonstrate that the proposed method can indeed improve the accuracy of matrix completion compared with the existing methods. [ABSTRACT FROM AUTHOR]

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]

Although the matrix completion paradigm provides an appealing solution to the collaborative filtering problem in recommendation systems, some major issues, such as data sparsity and cold-start problems, still remain open. In particular, when the rating data for a subset of users or items is entirely missing, commonly known as the cold-start problem, the standard matrix completion methods are inapplicable due the non-uniform sampling of available ratings. In recent years, there has been considerable interest in dealing with cold-start users or items that are principally based on the idea of exploiting other sources of information to compensate for this lack of rating data. In this paper, we propose a novel and general algorithmic framework based on matrix completion that simultaneously exploits the similarity information among users and items to alleviate the cold-start problem. In contrast to existing methods, our proposed recommender algorithm, dubbed DecRec, decouples the following two aspects of the cold-start problem to effectively exploit the side information: (i) the completion of a rating sub-matrix, which is generated by excluding cold-start users/items from the original rating matrix; and (ii) the transduction of knowledge from existing ratings to cold-start items/users using side information. This crucial difference prevents the error propagation of completion and transduction, and also significantly boosts the performance when appropriate side information is incorporated. The recovery error of the proposed algorithm is analyzed theoretically and, to the best of our knowledge, this is the first algorithm that addresses the cold-start problem with provable guarantees on performance. Additionally, we also address the problem where both cold-start user and item challenges are present simultaneously. We conduct thorough experiments on real datasets that complement our theoretical results. These experiments demonstrate the effectiveness of the proposed algorithm in handling the cold-start users/items problem and mitigating data sparsity issue. [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]