Expectation-maximization algorithms for Itakura-Saito nonnegative matrix factorization

Paul Magron (1) , Tuomas Virtanen (1)

1 Department of Signal Processing [Tampere]

This paper presents novel expectation-maximization (EM) algorithms for estimating the nonnegative matrix factorization model with Itakura-Saito divergence. The commonly-used EM-based approach exploits the space-alternating generalized EM (SAGE) variant of EM and provides poor separation quality at a high computational cost. We propose to explore more exhaustively those algorithms, in particular the choice of the variant (classical EM or SAGE) and the latent variable set (full or reduced). We then derive four EM-based algorithms, among which 3 are novel. Experimental results show that the standard EM algorithm proposed in this paper with a reduced set of latent variables yields better separation quality and a lower computational burden than its SAGE variants.

Mots clés: Expectation-Maximization; nonnegative matrix factorization; Itakura-Saito divergence; audio source separation

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

Paul Magron, Tuomas Virtanen. Expectation-maximization algorithms for Itakura-Saito nonnegative matrix factorization. 2017. ⟨hal-01632082v1⟩