Bayesian Non-negative Matrix Factorization

Authors:
Mikkel N. Schmidt;Ole Winther;Lars Kai Hansen
Affiliations:
Department of Engineering, University of Cambridge,;DTU Informatics, Technical University of Denmark,;DTU Informatics, Technical University of Denmark,
Venue:
ICA '09 Proceedings of the 8th International Conference on Independent Component Analysis and Signal Separation
Year:
2009

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Abstract

We present a Bayesian treatment of non-negative matrix factorization (NMF), based on a normal likelihood and exponential priors, and derive an efficient Gibbs sampler to approximate the posterior density of the NMF factors. On a chemical brain imaging data set, we show that this improves interpretability by providing uncertainty estimates. We discuss how the Gibbs sampler can be used for model order selection by estimating the marginal likelihood, and compare with the Bayesian information criterion. For computing the maximum a posteriori estimate we present an iterated conditional modes algorithm that rivals existing state-of-the-art NMF algorithms on an image feature extraction problem.