Bayesian Inference for Nonnegative Matrix Factorisation Models. (27th May 2009)

• Record Type: Journal Article
• Authors: Cemgil, Ali Taylan
• Other Names: Cruces-Alvarez S. Academic Editor.
• Is Part Of: Computational intelligence and neuroscience. Volume 2009(2009)
• Publication Date: 2009-05-27
• Subjects: Neurosciences -- Data processing -- Periodicals; Computational intelligence -- Periodicals; Computational neuroscience -- Periodicals; 612.80285
• DOI: 10.1155/2009/785152
• Languages: English
• ISSNs: 1687-5265

Abstract

Abstract : 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.