Related Work on Tensor Factorization

Abstract

In this chapter, we provide a preliminary knowledge overview of tensors. Moreover, we provide the related work on tensor decomposition methods. The first method that is discussed is the Tucker Decomposition (TD) method, which is the underlying tensor factorization model of Higher Order Singular Value Decomposition. TD decomposes a tensor into a set of matrices and one small core tensor. The second one is the PARAFAC method (PARAllel FACtor analysis), which is the same as the TD method with the restriction that the core tensor should be diagonal. The third method is the Pairwise Interaction Tensor Factorization method, which is a special case of the TD method with linear runtime both for learning and prediction. The last method that is analyzed is the low-order tensor decomposition (LOTD) method. This method has low functional complexity, is uniquely capable of enhancing statistics, and avoids overfitting compared with traditional tensor decompositions such as TD and PARAFAC.