Comparison of CP and Tucker tensor decomposition algorithms

Abstract

Structured multidimensional data is often expressed in a tensor format. However, due to the large number of terms, it can be difficult to process, store, interpret, or extract patterns from data in a raw tensor format. To alleviate this, various types of tensor decompositions have been developed to reduce the number of terms used to represent multidimensional data, as well as to reveal underlying structure and relationships among the variables. This article will explore variations on two types of tensor decompositions, the CANDECOMP/PARAFAC and the Tucker decompositions, and perform baseline comparisons of their associated algorithms on common datasets with similar choices of parameters. We perform numerical experiments on synthetic and real-world data to directly compare multiple algorithms to approximate the two tensor decomposition types. We also present results comparing the two decomposition models and their algorithms for image denoising and completion examples.