Permutation-Free Cgmm: Complex Gaussian Mixture Model with Inverse Wishart Mixture Model Based Spatial Prior for Permutation-Free Source Separation and Source Counting

Here we propose a permutation-free cGMM (PF-cGMM), a new probabilistic model of observed mixtures, which can resolve permutation ambiguity between frequency bins, and is applicable even when the number of sources is unknown. A recently proposed complex Gaussian mixture model (cGMM) is highly effective for frequency bin-wise clustering when the number of sources is known. However, it cannot resolve the permutation ambiguity, and is inapplicable when the number of sources is unknown. The proposed PF-cGMM is an extension of the cGMM, which resolves these issues. The resolution of the permutation ambiguity can be realized by a spatial prior called a complex inverse Wishart mixture model (cIWMM). The absence of the permutation ambiguity facilitates source counting, which is performed by hierarchical clustering in this paper. Experiments showed that the PF-cGMM was able to (1) resolve the permutation ambiguity and (2) realize source separation even when the number of sources was unknown with little performance degradation compared to when it was known.