Performance Evaluation of Selected Cost Functions in Non Negative Matrix Factorization Based Decomposition of Acoustic Mixture

Interaction of acoustic signals when several audio sources are active simultaneously results in the disturbance of estimation of an individual source by co-occurring sounds. Data decomposition therefore constitutes one of the core tasks in monaural source separation.  Particularly, in semi-supervised learning approach, viable means of achieving this is through the application of Non-negative Matrix Factorization (NMF). Owing to a paucity of information on the application of this method, especially in a speech system, evaluation of some cost functions in NMF-based monaural speech decomposition was investigated in this study. A generalized gradient descent algorithm is derived for the minimization while three cost functions: Euclidean Distance, Kullback-Leibler Divergence and Itakura-Saito divergences are applied to the derived separation NMF algorithm.  These divergences are evaluated using experimental data while the performance of each of these is evaluated based on the cost values and convergence rate. Itakura-Saito divergence yields optimal performance over the other two divergences for given number of iterations and number of channels. Keywords— Cost functions, non-negative matrix factorization, speech separation, evaluation