Robust Non-negative Matrix Factorization with β-Divergence for Speech Separation
Yinan Li, Xiongwei Zhang, Meng Sun · ETRI Journal · 2016
This paper addresses the problem of unsupervised speech separation based on robust non-negative matrix factorization (RNMF) with β-divergence, when neither speech nor noise training data is available beforehand. We propose a robust version of non-negative matrix factorization, inspired by the recently developed sparse and low-rank decomposition, in which the data matrix is decomposed into the sum of a low-rank matrix and a sparse matrix. Efficient multiplicative update rules to minimize the β-divergence-based cost function are derived. A convolutional extension of the proposed algorithm is also proposed, which considers the time dependency of the non-negative noise bases. Experimental speech separation results show that the proposed convolutional RNMF successfully separates the repeating time-varying spectral structures from the magnitude spectrum of the mixture, and does so without any prior training.