Factorial Scaled Hidden Markov Model for polyphonic audio representation and source separation

We present a new probabilistic model for polyphonic audio termed factorial scaled hidden Markov model (FS-HMM), which generalizes several existing models, notably the Gaussian scaled mixture model and the Itakura-Saito nonnegative matrix factorization (NMF) model. We describe two expectation-maximization (EM) algorithms for maximum likelihood estimation, which differ by the choice of complete data set. The second EM algorithm, based on a reduced complete data set and multiplicative updates inspired from NMF methodology, exhibits much faster convergence. We consider the FS-HMM in different configurations for the difficult problem of speech/music separation from a single channel and report satisfying results.