Matrix and Tensor Factorization Techniques applied to Recommender Systems: a Survey

On internet today, an overabundance of information can be accessed, making it difficult for users to process and evaluate options and make appropriate choices. This phenomenon is known as Information Overload. Over time, various methods of information filtering have been introduced in order to assist users in choosing what may be of interest to them. Recommender Systems (RS) are a technique for filtering information and play an important role in e-commerce, advertising, e-mail filtering etc. Therefore, RS are an answer, though partial, to the problem of Information Overload. Algorithms behind the recommendation techniques need to be continuously updated because of a constant increase in both the quantity of information and the availability of modes of access to that information, which define the different contexts of information use. The research of more effective and more efficient methods than those currently known in literature is also stimulated by the interests of industrial research in this field, as demonstrated by the Netflix Prize Competition. The Company, which gives its name to the award, has invested one million dollars in acknowledgement of the best collaborative filtering algorithm that improves the accuracy of its own adopted RS, evidently in the belief that the RS can provide a competitive advantage. The mathematical techniques discussed in this article seem to be, at present, the most feasible way to calculate more efficient and accurate recommendations. The main contribution of this paper is a survey about matrix and tensor factorization techniques adopted in the literature of RS. In particular, the discussion focuses on recent applications of High Order Singular Value Decomposition (HOSVD) in the area of information filtering and retrieval (Section IV). Finally, we suggest the application of PARAFAC (PARAllel FACtor) to multidimensional data for the computation of context-aware recommendations