Bayesian independent component analysis: Variational methods and non-negative decompositions

In this paper we present an empirical Bayesian framework for independent component analysis. The framework provides estimates of the sources, the mixing matrix and the noise parameters, and is flexible with respect to choice of source prior and the number of sources and sensors. Inside the engine of the method are two mean field techniques—the variational Bayes and the expectation consistent framework—and the cost function relating to these methods are optimized using the adaptive overrelaxed expectation maximization (EM) algorithm and the easy gradient recipe. The entire framework, implemented in a Matlab toolbox, is demonstrated for non-negative decompositions and compared with non-negative matrix factorization.