Performance analysis of alpha divergence in nonnegative matrix factorization of monaural musical sounds

Abstract

Estimation of original instrument sound signals from complex music signals without any prior information is one of the most challenging problems under the framework of Blind Source Separation (BSS). Due to their effectiveness in other applications of BSS, Nonnegative Matrix Factorization (NMF) based methods have particularly gained attention in the context of musical sound source separation. These techniques are based on decomposing the magnitude or power spectrum of an input signal into a sum of components with time varying gains. This is achieved by using a suitable cost function to determine the optimal factorization. Most work in this field has focused on the use of Euclidean and Kullback-Liebler (KL) divergence. This study looks into the use of α-divergence based non negative factorization in the context of single channel musical sound separation. Simulation experiments were carried on single channel mixtures of randomly mixed pitched musical instrument samples to determine optimal α values for this problem. The paper also looks into the performance of the algorithm as important system parameters are varied.