Although recommendation systems based on the latent factor models provide an appealing solution to the collaborative filtering problem, some major issues such as data sparsity and cold-start problems, still remain open. In particular, for a large portion of items that there are not sufficient purchase records, their latent factors cannot be estimated accurately. In this paper, we aim to learn and exploit the preference of users in combination with the latent factor models to mitigate these issues and to improve recommendation accuracy. To this end, we propose a novel algorithm to accurately learn the preference of users from observed ratings and available taxonomy of items. We show that predictions made based on the extracted users' preferences enable to capture the taste of users and generates more effective recommendations than pure latent factor models. To the best of our knowledge, the proposed algorithm is the first to extract and exploit the implicit preference of users in the recommendation. We conduct thorough experiments on real datasets that demonstrate the proposed model improves significantly over state-of-the-art latent factor models.

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 thecold-startproblem, 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,decouplesthe 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.