Bayesian Inference for Nonnegative Matrix Factorisation Models

We describe nonnegative matrix factorisation (NMF) with a Kullback-Leibler (KL) error measure in a statistical framework, with a hierarchical generative model consisting of an observation and a prior component. Omitting the prior leads to the standard KL-NMF algorithms as special cases, where maximum likelihood parameter estimation is carried out via the Expectation-Maximisation (EM) algorithm. Starting from this view, we develop full Bayesian inference via variational Bayes or Monte Carlo. Our construction retains conjugacy and enables us to develop more powerful models while retaining attractive features of standard NMF such as monotonic convergence and easy implementation. We illustrate our approach on model order selection and image reconstruction.

• Publication year

  2009

• Venue

  Computational Intelligence and Neuroscience

• Publication date

  2009-05-27

• Fields of study

  Mathematics, Computer Science, Medicine

• Identifiers
  DOI 10.1155/2009/785152PMID 19536273PMCID 2688815
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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