Nonnegative Matrix Factorization With Transform Learning

Dylan Fagot (1) , Herwig Wendt (2, 3) , Cédric Févotte (1, 3)

1 IRIT-SC - Signal et Communications
2 IRIT-MINDS - CoMputational imagINg anD viSion
3 CNRS - Centre National de la Recherche Scientifique

Traditional NMF-based signal decomposition relies on the factor-ization of spectral data, which is typically computed by means of short-time frequency transform. In this paper we propose to relax the choice of a pre-fixed transform and learn a short-time orthogonal transform together with the factorization. To this end, we formulate a regularized optimization problem reminiscent of conventional NMF, yet with the transform as additional unknown parameters, and design a novel block-descent algorithm enabling to find stationary points of this objective function. The proposed joint transform learning and factorization approach is tested for two audio signal processing ex-periments, illustrating its conceptual and practical benefits.

Mots clés: Nonnegative matrix factorization (NMF); Single-channel source separation; Transform learning

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

Dylan Fagot, Herwig Wendt, Cédric Févotte. Nonnegative Matrix Factorization With Transform Learning. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2018), Apr 2018, Calgary, Canada. pp.1-5, ⟨10.1109/ICASSP.2018.8461803⟩. ⟨hal-02289988⟩