cSTMM: A Unified Complex Spherical Student's $t$ Mixture Model for Directional Statistics in Mask-Based Blind Speech Separation

Mask-based blind speech separation (BSS) estimates source-wise time-frequency (TF) masks by clustering multichannel observations using spatial information. The directional statistical approach clusters normalized multichannel observations on the complex unit sphere, without explicitly extracting phase and level difference features based on the plane-wave or spherical-wave assumptions. However, prior studies have mostly compared a small number of separately defined directional statistical mixture models, whereas a broader distribution family would enable a more systematic study of how density profiles affect separation performance. We propose the complex spherical Student's t mixture model (cSTMM), a directional mixture model that connects the complex angular central Gaussian mixture model (cACGMM), complex Bingham mixture model (cBMM), and complex Watson mixture model (cWMM) through the degrees-of-freedom parameter $ν$. We also derive a generalized minorization-maximization (MM) based procedure for parameter estimation. A no-restart evaluation on noise-free LibriSpeech mixtures reverberated with measured room impulse responses shows that a single development-selected value $ν^\ast=1$ achieved higher test-set mean signal-to-distortion ratio improvements (SDRi) than the cACGMM-equivalent setting $ν=M$ in all acoustic conditions, with an average condition-wise gain of 0.25dB. The experiments also numerically verify that the proposed formulation numerically recovers the cACGMM, cBMM, and cWMM cases.