An Iterative Deflation Algorithm for Exact CP Tensor Decomposition

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]

The Canonical Polyadic (CP) tensor decomposition has become an attractive mathematical tool these last ten years in various fields. Yet, efficient algorithms are still lacking to compute the full CP decomposition, whereas rank-one approximations are rather easy to compute. We propose a new deflation-based iterative algorithm allowing to compute the full CP decomposition, by resorting only to rank-one approximations. An analysis of convergence issues is included, as well as computer experiments. Our theoretical and experimental results show that the algorithm converges almost surely.

Mots clés: Tensor; Deflation; rank-1 approximations; CanDecomp; Canonical Polyadic; Parafac; tensor decomposition; convergence

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

Alex Pereira da Silva, Pierre Comon, André L. F. de Almeida. An Iterative Deflation Algorithm for Exact CP Tensor Decomposition. ICASSP 2015 - 40th IEEE International Conference on Acoustics, Speech and Signal Processing, Apr 2015, Brisbane, Australia. ⟨hal-01071402v2⟩