13th Annual Conference of the International Speech Communication Association

Portland, OR, USA
September 9-13, 2012

Hidden Markov Models as Priors for Regularized Nonnegative Matrix Factorization in Single-Channel Source Separation

Emad M. Grais, Hakan Erdogan

Faculty of Engineering and Natural Sciences, Sabanci University, Orhanli Tuzla, Istanbul, Turkey

We propose a new method to incorporate rich statistical priors, modeling temporal gain sequences in the solutions of nonnegative matrix factorization (NMF). The proposed method can be used for single-channel source separation (SCSS) applications. In NMF based SCSS, NMF is used to decompose the spectra of the observed mixed signal as a weighted linear combination of a set of trained basis vectors. In this work, the NMF decomposition weights are enforced to consider statistical and temporal prior information on the weight combination patterns that the trained basis vectors can jointly receive for each source in the observed mixed signal. The Hidden Markov Model (HMM) is used as a lognormalized gain "weights" prior model for the NMF solution. The normalization makes the prior models energy independent. HMM is used as a rich model that characterizes the statistics of sequential data. The NMF solutions for the weights are encouraged to increase the log-likelihood with the trained gain prior HMMs while reducing the NMF reconstruction error at the same time.

Index Terms: Nonnegative matrix factorization, single-channel source separation, Hidden Markov Models

Full Paper

Bibliographic reference.  Grais, Emad M. / Erdogan, Hakan (2012): "Hidden Markov models as priors for regularized nonnegative matrix factorization in single-channel source separation", In INTERSPEECH-2012, 1536-1539.