Efficient algorithms for multichannel extensions of Itakura-Saito nonnegative matrix factorization

This paper proposes new algorithms for multichannel extensions of nonnegative matrix factorization (NMF) with the Itakura-Saito (IS) divergence. We employ Hermitian positive definite matrices for modeling the covariance matrix of a multivariate complex Gaussian distribution. Such matrices are basically estimated for NMF bases, but a source separation task can be performed by introducing variables that relate NMF bases and sources. The new algorithms are derived by using a majorization scheme with properly designed auxiliary functions. The algorithms are in the form of multiplicative updates, and exhibit good convergence behavior. We have succeeded in separating a professionally produced music recording into its vocal and guitar components.