Variational regularized two-dimensional nonnegative matrix factorization with the flexible β-Divergence for single channel source separation

This paper presents an algorithm for nonnegative matrix factorization 2D (NMF-2D) with the flexible β-Divergence. The β-Divergence is a group of cost functions parameterized by a single parameter β. The Least Squares divergence, Kullback-Leibler divergence and the Itakura-Saito divergence are special cases (β=2,1,0).This paper presents a more complete and holistic algorithm which uses a flexible range of β, instead of being limited to the special cases. We describe a maximization minimization (MM) algorithm lead to multiplicative updates. The proposed factorization decomposes an information-bearing matrix into two-dimensional convolution of factor matrices that represent the spectral dictionary and temporal codes with enhanced performance. The method is demonstrated on the separation of audio mixtures recorded from a single channel. The method also enables a generalized criterion for variable sparseness to be imposed onto the solution. Experimental tests and comparisons with other factorization methods have been conducted to verify the efficacy of the proposed method.