Multi-channel Non-negative Matrix Factorization Initialized with Full-rank and Rank-1 Spatial Correlation Matrix for Speech Recognition

Abstract

Multi-channel non-negative matrix factorization (MNMF) is one of the most effective blind source separation techniques. This paper proposes a stable initialization method of MNMF by accurately estimating a full-rank spatial correlation matrix. Alternative initialization can be a rank-1 spatial correlation matrix to be obtained as an outer product of a steering vector, which is an eigenvector that corresponds to the maximum eigenvalue of a spatial correlation matrix. This paper compares full-rank and rank-1 types of initialization. On the other hand, independent low-rank matrix analysis (ILRMA) accelerates the matrix factorization by using a rank-1 demixing matrix instead of a spatial correlation matrix. The above-mentioned initialization method can be applied to ILRMA. The drawback of ILRMA is an overdetermined situation where the number of observations is greater than that of sources. In such cases, special treatments are necessary for ILRMA to match the number of observations to the number of sources, whereas MNMF can deal with such cases naturally. Experiments on a noisy speech recognition task showed the effectiveness of the proposed initialization method both for MNMF and ILRMA. For determined cases, ILRMA was faster and better than MNMF, but for overdetermined cases, even with special treatments, ILRMA was inferior to MNMF.