A Generalization of Laplace Nonnegative Matrix Factorization and Its Multichannel Extension

Abstract

The aim of this paper is to generalize the statistical models of nonnegative matrix factorization (NMF) and multichannel NMF (MNMF). For the NMF and its multichannel extensions, various statistical models have been proposed to improve the model flexibility in the literature on signal separation. However, few studies have been done on the generalization which includes the model based on the Laplace distribution. Thus, we propose the generalized models of the NMF and the MNMF, which include the models based on the Gaussian distribution and the two types of the Laplace distributions, using the Bessel function distribution. To estimate unknown model parameters, we derive the update rules based on the majorization-minimization algorithm. The performances of the proposed NMF and MNMF are evaluated in fitting synthetic data and music signal separation, respectively.