A Theoretic Model for Linear Geometric ICA

Abstract

Geometric algorithms for linear ICA have recently received some attention due to their pictorial description and their relative ease of implementation. The geometric approach to ICA has been proposed first by Puntonet and Prieto in order to separate linear mixtures. We will reconsider geometric ICA in a solid theoretic framework showing that fixpoints of geometric ICA fulfill a so called geometric convergence condition, which the mixed images of the unit vectors satisfy, too. This leads to a conjecture claiming that in the supergaussian unimodal symmetric case there is only one stable fixpoint, thus demonstrating uniqueness of geometric ICA after convergence.