Expectation-Maximization Algorithms for Itakura-Saito Nonnegative Matrix Factorization

This paper presents novel expectation-maximization (EM) algorithms for estimating the nonnegative matrix factorization model with Itakura-Saito divergence. Indeed, the common EM-based approach exploits the space-alternating generalized EM (SAGE) variant of EM but it usually performs worse than the conventional multiplicative algorithm. We propose to explore more exhaustively those algorithms, in particular the choice of the methodology (standard EM or SAGE variant) and the latent variable set (full or reduced). We then derive four EM-based algorithms, among which three are novel. Speech separation experiments show that one of those novel algorithms using a standard EM methodology and a reduced set of latent variables outperforms its SAGE variants and competes with the conventional multiplicative algorithm.