Bayesian Nonnegative Matrix Factorization With Dirichlet Process Mixtures

Abstract

Nonnegative Matrix Factorization (NMF) is valuable in many applications of blind source separation, signal processing and machine learning. A number of algorithms that can infer nonnegative latent factors have been developed, but most of these assume a specific noise kernel. This is insufficient to deal with complex noise in real scenarios. In this paper, we present a hierarchical Dirichlet process nonnegative matrix factorization (DPNMF) model in which the Gaussian mixture model is used to approximate the complex noise distribution. Moreover, the model is cast in the nonparametric Bayesian framework by using Dirichlet process mixture to infer the necessary number of Gaussian components. We derive a mean-field variational inference algorithm for the proposed nonparametric Bayesian model. We first test the model on synthetic data sets contaminated by Gaussian, sparse and mixed noise. We then apply it to extract muscle synergies from the electromyographic (EMG) signal and to select discriminative features for motor imagery single-trial electroencephalogram (EEG) classification. Experimental results demonstrate that DPNMF performs better in extracting the latent nonnegative factors in comparison with state-of-the-art methods.