A COUPLED JOINT EIGENVALUE DECOMPOSITION ALGORITHM FOR CANONICAL POLYADIC DECOMPOSITION OF TENSORS

Rémi André (1, 2) , Xavier Luciani (1, 2) , Eric Moreau (1, 2)

1 LIS - Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon)
2 SIIM - Signal et Image

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.

Domaines: Traitement du signal et de l'image [eess.SP]

Rémi André, Xavier Luciani, Eric Moreau. A COUPLED JOINT EIGENVALUE DECOMPOSITION ALGORITHM FOR CANONICAL POLYADIC DECOMPOSITION OF TENSORS. IEEE SAM 2016, Jul 2016, Rio de Janeiro, France. ⟨hal-01862247⟩