A new Bayesian approach to nonnegative matrix factorization: uniqueness and model order selection

Abstract

NMF is a blind source separation technique decomposing multivariate non-negative data sets into meaningful non-negative basis components and non-negative weights.There are still open problems to be solved: uniqueness and model order selection as well as developing efficient NMF algorithms for large scale problems. Addressing uniqueness issues,we propose a Bayesian optimality criterion(BOC)for NMF solutions which can be derived in the absence of prior knowledge.Furthermore,we present a new Variational Bayes NMF algorithm VBNMF which is a straightforward generalization of the canonical Lee–Seung method for the Euclidean NMF problem and demonstrate its ability to automatically detect the actual number of components in non-negative data.