A moment-based approach for guaranteed tensor decomposition

Arthur Marmin (1, 2) , Marc Castella (3, 4, 5) , Jean-Christophe Pesquet (1, 2)

1 CVN - Centre de vision numérique
2 OPIS - OPtimisation Imagerie et Santé
3 TSP - CITI - Communications, Images et Traitement de l'Information
4 IP Paris - Institut Polytechnique de Paris
5 TIPIC-SAMOVAR - Traitement de l'Information Pour Images et Communications

This paper presents a new scheme to perform the canonical polyadic decomposition (CPD) of a symmetric tensor. We first formulate the CPD problem as a truncated moment problem , where a measure has to be recovered knowing some of its moments. The support of the measure is discrete and encodes the CPD. The support is then retrieved by solving a polynomial system. Using algebraic results, our method resorts only to classical linear algebra operations (eigenvalue method and Schur reordered factorization). This new viewpoint offers theoretical guarantees on the retrieved decomposition. Finally experimental results show the validity of our method and a better reconstruction accuracy compared to classic CPD algorithms .

Mots clés: Tensors; Canonical polyadic decomposition; Moment problem

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

Arthur Marmin, Marc Castella, Jean-Christophe Pesquet. A moment-based approach for guaranteed tensor decomposition. ICASSP 2020 - 45th International Conference on Acoustics, Speech and Signal Processing, May 2020, Barcelona, Spain. pp.3927-3931, ⟨10.1109/icassp40776.2020.9054186⟩. ⟨hal-02654329⟩