HOSVD on Tensors and Its Extensions

Abstract

This chapter describes in detail tensor decomposition for recommender systems. As our running toy example, we will use a tensor with three dimensions (i.e., user–item–tag). The main factorization method that will be presented in this chapter is higher order SVD (HOSVD), which is an extended version of the Singular Value Decomposition (SVD) method. In this chapter, we will present a step-by-step implementation of HOSVD in our toy example. Then we will present how we can update HOSVD when a new user is registered in our recommender system. We will also discuss how HOSVD can be combined with other methods for leveraging the quality of recommendations. Finally, we will study limitations of HOSVD and discuss in detail the problem of non-unique tensor decomposition results and how we can deal with this problem. We also discuss other problems in tensor decomposition, e.g., actualization and scalability.