Natural Gradient Approach to Blind Separationof over - and under - Complete Mixturesl

In this paper we study natural gradient approaches to blind separation of over-and under-complete mixtures. First we introduce Lie group structures on the mani-folds of the under-and over-complete mixture matrices respectively, and endow Riemannian metrics on the manifolds based on the property of Lie groups. Then we derive the natural gradients on the manifolds using the isometry of the Riemannian metric. Using the natural gradient, we present a new learning algorithm based on the minimization of mutual information. Finally we apply the natural gradient approach to the state-space model and develop a novel learning algorithm for dynamic component analysis.