Learning algorithm for independent component analysis by geodesic flows on orthogonal group

Abstract

In this paper we propose a new equivalent learning algorithm for independent component analysis when sensor signals are prewhitened. Since the search for demixing matrix is reduced to finding an orthogonal matrix instead of nonsingular matrix, optimization should be performed on the orthogonal group. We generalize the natural gradient approach to this case based on geodesics on the orthogonal group and the Stiefel manifold. Ordinary algorithms can be regarded as linear approximation of ours. The result of computer simulations demonstrates the effectiveness of our method.