A coupled joint eigenvalue decomposition algorithm for canonical polyadic decomposition of tensors

Abstract

In this paper we propose a novel algorithm to compute the joint eigenvalue decomposition of a set of squares matrices. This problem is at the heart of recent direct canonical polyadic decomposition algorithms. Contrary to the existing approaches the proposed algorithm can deal equally with real or complex-valued matrices without any modifications. The algorithm is based on the algebraic polar decomposition which allows to make the optimization step directly with complex parameters. Furthermore, both factorization matrices are estimated jointly. This “coupled” approach allows us to limit the numerical complexity of the algorithm. We then show with the help of numerical simulations that this approach is suitable for tensors canonical polyadic decomposition.