Infinite probabilistic latent component analysis for audio source separation

This paper presents a statistical method of audio source separation based on a nonparametric Bayesian extension of probabilistic latent component analysis (PLCA). A major approach to audio source separation is to use nonnegative matrix factorization (NMF) that approximates the magnitude spectrum of a mixture signal at each frame as the weighted sum of fewer source spectra. Another approach is to use PLCA that regards the magnitude spectrogram as a two-dimensional histogram of “sound quanta” and classifies each quantum into one of sources. While NMF has a physically-natural interpretation, PLCA has been used successfully for music signal analysis. To enable PLCA to estimate the number of sources, we propose Dirichlet process PLCA (DP-PLCA) and derive two kinds of learning methods based on variational Bayes and collapsed Gibbs sampling. Unlike existing learning methods for nonparametric Bayesian NMF based on the beta or gamma processes (BP-NMF and GaP-NMF), our sampling method can efficiently search for the optimal number of sources without truncating the number of sources to be considered. Experimental results showed that DP-PLCA is superior to GaP-NMF in terms of source number estimation.