Super-Gaussian Mixture Source Model for ICA

We propose an extension of the mixture of factor (or independent component) analyzers model to include strongly super-gaussian mixture source densities. This allows greater economy in representation of densities with (multiple) peaked modes or heavy tails than using several Gaussians to represent these features. We derive an EM algorithm to find the maximum likelihood estimate of the model, and show that it converges globally to a local optimum of the actual non-gaussian mixture model without needing any approximations. This extends considerably the class of source densities that can be used in exact estimation, and shows that in a sense super-gaussian densities are as natural as Gaussian densities. We also derive an adaptive Generalized Gaussian algorithm that learns the shape parameters of Generalized Gaussian mixture components. Experiments verify the validity of the algorithm.