@CONFERENCE\{IMM2009-05734, author = "M. N. Schmidt and O. Winther and L. K. Hansen", title = "Bayesian non-negative matrix factorization", year = "2009", booktitle = "International Conference on Independent Component Analysis and Signal Separation", volume = "", series = "", editor = "", publisher = "Informatics and Mathematical Modelling, Technical University of Denmark, {DTU}", organization = "", address = "Richard Petersens Plads, Building 321, {DK-}2800 Kgs. Lyngby", url = "http://www2.compute.dtu.dk/pubdb/pubs/5734-full.html", 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." }