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