A post-nonlinear mixture model approach to binary matrix factorization

Mamadou Diop (1, 2) , Anthony Larue (3) , Sebastian Miron (2) , David Brie (2)

1 DGDE - CEA Tech Grand-Est
2 CRAN - Centre de Recherche en Automatique de Nancy
3 LOAD (CEA, LIST) - Laboratoire Outils d'Analyse des Données (CEA, LIST)

In this paper, we address the Binary Matrix Factorization (BMF) problem which is the restriction of the nonnegative matrix factorization (NMF) to the binary matrix case. A necessary and sufficient condition for the identifiability for the BFM model is given. We propose to approach the BMF problem by the NMF problem using a nonlinear function which guarantees the binarity of the reconstructed data. Two new algorithms are introduced and compared in simulations with the state of art BMF algorithms.

Mots clés: NMF problem; BFM model; necessary condition; sufficient condition; Matrix decomposition; nonnegative matrix factorization; binary matrix product; Inverse problems; constrained NMF; Mixture models; Cost function; Signal processing algorithms; Europe; Signal processing; post-nonlinear mixture model approach; Binary Matrix Factorization problem; nonlinear function

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

Mamadou Diop, Anthony Larue, Sebastian Miron, David Brie. A post-nonlinear mixture model approach to binary matrix factorization. 25th European Signal Processing Conference, EUSIPCO 2017, Aug 2017, Kos Island, Greece. ⟨10.23919/EUSIPCO.2017.8081221⟩. ⟨hal-01558843⟩