Geometric Optimisation and FastICA Algorithms

Independent component analysis is a challenging problem in the area of unsupervised adaptive filtering. Recently, there has been an increasing interest in using geometric optimisation for adaptive filtering. The performance of ICA algorithms significantly depends on the choice of the contrast function and the optimisation algorithm used in obtaining the demixing matrix. In this paper we focus on the standard linear ICA problem from an optimisation point of view. It is well known that after a pre-whitening process, the problem can be solved via an optimisation approach on a suitable manifold. We propose an approximate Newton’s method on the unit sphere to solve the one-unit ICA problem. The local convergence properties are discussed. The performance of the proposed algorithm is investigated by numerical experiments. It turns out that the well known FastICA algorithm can be considered as a special case of our algorithm. Moreover, some generalisations of the proposed algorithm are also discussed. Keywords— Geometric optimisation, independent component analysis, FastICA, scalar shift strategy, local convergence