Formulations and algorithms for multichannel complex NMF

This paper studies some formulations and algorithms for the multichannel extension of nonnegative matrix factorization (NMF). We model the inter-channel characteristics of each NMF basis, including both the amplitude ratios and the phase differences on a channel pair. The learned inter-channel characteristics provide useful information for binding each NMF basis to each source component in such a situation that multiple sources are mixed in a convolutive manner and observed at multiple microphones. Effective optimization algorithms based on majorization are derived by using properly designed auxiliary functions. Experimental results show that the algorithms converged favorably regardless of the initialization.