ABSTRACT
Representing data in lower dimensional spaces has been extensively used in many disciplines, such as natural language and image processing, data mining and information retrieval [DDF+90]. Recommender systems deal with challenging issues such as scalability, noise, and sparsity, and thus, matrix and tensor factorization techniques appear as an interesting tool to be exploited. Symeonidis et al. [SNPM06, Sym07], for example, used SVD for the prediction of items/ratings in recommender systems. They assumed that there is only a small number of factors influencing the users’ preferences, and that a user’s preference for an item is determined by how each factor applies to the user and the item. More
recently, due to the Netflix challenge, research on matrix factorization methods, a class of latent factor models, gained renewed momentum in the recommender systems literature, given that many of the best performing methods used on the challenge were based on matrix factorization techniques [Kor08, SM08, Kor09]. Please note that the Netflix challenge was a competition for the best recommender system algorithm to predict user ratings for movies. The competition was held by Netflix (https://www.netflixprize.com/), an on-line DVD-rental service. In this chapter we describe matrix and tensor factorization techniques (i.e., SVD on matrices and HOSVD on tensors) in recommender systems and social tagging systems, respectively. In addition, we present a real-world recommender system for Location-Based Social Networks, which employs tensor decomposition techniques.
