Single microphone speech separation by diffusion-based HMM estimation

We present a novel non-iterative and rigorously motivated approach for estimating hidden Markov models (HMMs) and factorial hidden Markov models (FHMMs) of high-dimensional signals. Our approach utilizes the asymptotic properties of a spectral, graph-based approach for dimensionality reduction and manifold learning, namely the diffusion framework. We exemplify our approach by applying it to the problem of single microphone speech separation, where the log-spectra of two unmixed speakers are modeled as HMMs, while their mixture is modeled as an FHMM. We derive two diffusion-based FHMM estimation schemes. One of which is experimentally shown to provide separation results that compare with contemporary speech separation approaches based on HMM. The second scheme allows a reduced computational burden.