Canonical Polyadic Decomposition based on joint eigenvalue decomposition

Abstract

A direct algorithm based on Joint EigenValue Decomposition (JEVD) has been proposed to compute the Canonical Polyadic Decomposition (CPD) of multi-way arrays (tensors). The iterative part of our method is thus limited to the JEVD computation. At this occasion we also propose an original JEVD technique. Most of the iterative CPD algorithms such as ALS have been shown by means of practical studies to suffer from convergence problems (local minima, slow convergence or high computational cost per iteration). On the other hand, direct methods seem in practice to confine these disadvantages but impose some restrictive necessary conditions. In this context, our proposed algorithm involves less restrictive necessary conditions than other recent direct approaches and a limited computational complexity. It has been compared to reference (direct and non-direct) algorithms on synthetic arrays and real spectroscopic data. These numerical examples highlight the main advantages of the proposed methods to solve both the JEVD and CPD problems.