Derivation of Update Rules for Convolutive NMF Based on Squared Euclidean Distance, KL Divergence, and IS Divergence

Abstract

In this paper, we present update rules for convolutive nonnegative matrix factorization (NMF) in which cost functions are based on the squared Euclidean distance, the Kullback-Leibler (KL) divergence and the Itakura-Saito (IS) divergence. We define an auxiliary function for each cost function and derive the update rule. We also apply this method to the single-channel signal separation in speech signals. Experimental results showed that the convergence of our KL divergence-based method was better than that in the conventional method, and our method achieved single-channel signal separation successfully.