Mathematical methods of tensor factorization applied to recommender systems

Abstract

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 their interest. Recommender Systems (RS) [14] are techniques for information filtering which 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. Recommendation algorithms need to be continuously updated because of a constant increase in both the quantity of information and ways 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 Contest, the open competition for the best algorithm to predict user ratings for films, based on previous ratings. The contest showed the superiority of mathematical methods that discover latent factors which drives user-item similarity, with respect to classical collaborative filtering algorithms. With the ever-increasing information available in digital archives and textual databases, the challenge of implementing personalized filters has become the challenge of designing algorithms able to manage huge amounts of data for the elicitation of user needs and preferences. In recent years, matrix factorization techniques have proved to be a quite promising solution to the problem of designing efficient filtering algorithms in the Big Data Era. The main contribution of this paper is an analysis of these methods, which focuses on tensor factorization techniques, as well as the definition of a method for tensor factorization suitable for recommender systems.