Nonparametric Bayesian Nonnegative Matrix Factorization

Nonnegative Matrix Factorization (NMF) is an important tool in machine learning for blind source separation and latent factor extraction. Most of existing NMF algorithms assume a specific noise kernel, which is insufficient to deal with complex noise in real scenarios. In this study, we present a hierarchical nonparametric nonnegative matrix factorization (NPNMF) model in which the Gaussian mixture model is used to approximate the complex noise distribution. 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. Experimental results on both synthetic data and electroencephalogram (EEG) demonstrate that NPNMF performs better in extracting the latent nonnegative factors in comparison with state-of-the-art methods.