Boolean CP decomposition of binary tensors: Uniqueness and algorithm

Mamadou Diop (1) , Sébastian Miron (1) , Antoine Souloumiac (2) , David Brie (1)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 LS2D (CEA, LIST) - Laboratoire Sciences des Données et de la Décision (CEA, LIST)

We propose an algorithm to perform the low-rank Boolean Canonical Polyadic Decomposition (BCPD) of a binary tensor. The proposed approach is based on the AO-ADMM strategy introduced in [1] and uses a post-nonlinear mixture model for binary sources. We show that this new method is better suited for low-rank approximation of binary tensors compared to other similar methods. We also provide an easy-to-check uniqueness condition for the BCPD. This is the first time that such a condition is derived for Boolean decompositions.

Mots clés: tensor factorization; Data processing; AO-ADMM; uniqueness; binary tensor; Index Terms-binary tensor; Boolean Canonical Polyadic Decomposition

Domaines: Algorithme et structure de données [cs.DS]; Analyse numérique [cs.NA]; Analyse numérique [math.NA]

Mamadou Diop, Sébastian Miron, Antoine Souloumiac, David Brie. Boolean CP decomposition of binary tensors: Uniqueness and algorithm. 44th IEEE International Conference on Acoustics Speech and Signal Processing, ICASSP 2019, May 2019, Brighton, United Kingdom. ⟨10.1109/ICASSP.2019.8683508⟩. ⟨hal-02314551⟩