Rank-1 Tensor Approximation Methods and Application to Deflation

Alex Pereira da Silva (1) , Pierre Comon (1) , André L. F. de Almeida (2)

1 GIPSA-CICS - GIPSA - Communication Information and Complex Systems
2 GTEL - Wireless Telecom Research Group [Fortaleza]

Because of the attractiveness of the canonical polyadic (CP) tensor decomposition in various applications, several algorithms have been designed to compute it, but efficient ones are still lacking. Iterative deflation algorithms based on successive rank-1 approximations can be used to perform this task, since the latter are rather easy to compute. We first present an algebraic rank-1 approximation method that performs better than the standard higher-order singular value decomposition (HOSVD) for three-way tensors. Second, we propose a new iterative rank-1 approximation algorithm that improves any other rank-1 approximation method. Third, we describe a geometric framework allowing to study the convergence of deflation CP decomposition (DCPD) algorithms based on successive rank-1 approximations. A set of computer experiments then validates theoretical results and demonstrates the efficiency of DCPD algorithms compared to other ones.

Mots clés: rank-1 approximation; tensor; decomposition; iterative deflation; blind source separation

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

Alex Pereira da Silva, Pierre Comon, André L. F. de Almeida. Rank-1 Tensor Approximation Methods and Application to Deflation. [Research Report] GIPSA-lab. 2015. ⟨hal-01186615⟩