Variational Mixture of Bayesian Independent Component Analyzers

There has been growing interest in subspace data modeling over the past few years. Methods such as principal component analysis, factor analysis, and independent component analysis have gained in popularity and have found many applications in image modeling, signal processing, and data compression, to name just a few. As applications and computing power grow, more and more sophisticated analyses and meaningful representations are sought. Mixture modeling methods have been proposed for principal and factor analyzers that exploit local gaussian features in the subspace manifolds. Meaningful representations may be lost, however, if these local features are nongaussian or discontinuous. In this article, we propose extending the gaussian analyzers mixture model to an independent component analyzers mixture model. We employ recent developments in variational Bayesian inference and structure determination to construct a novel approach for modeling nongaussian, discontinuous manifolds. We automatically determine the local dimensionality of each manifold and use variational inference to calculate the optimum number of ICA components needed in our mixture model. We demonstrate our framework on complex synthetic data and illustrate its application to real data by decomposing functional magnetic resonance images into meaningful—and medically useful—features.