Infinite Positive Semidefinite Tensor Factorization for Source Separation of Mixture Signals

Abstract

This paper presents a new class of tensor fac-torization called positive semidefinite tensor factorization (PSDTF) that decomposes a set of positive semidefinite (PSD) matrices into the convex combinations of fewer PSD basis matrices. PSDTF can be viewed as a natu-ral extension of nonnegative matrix factoriza-tion. One of the main problems of PSDTF is that an appropriate number of bases should be given in advance. To solve this problem, we propose a nonparametric Bayesian model based on a gamma process that can instanti-ate only a limited number of necessary bases from the infinitely many bases assumed to exist. We derive a variational Bayesian algo-rithm for closed-form posterior inference and a multiplicative update rule for maximum-likelihood estimation. We evaluated PSDTF on both synthetic data and real music record-ings to show its superiority. 1.