Newton-Like Methods for Parallel Independent Component Analysis

Independent component analysis (ICA) can be studied from different angles. 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 algorithmic point of view. It is well known that after a pre-whitening process, linear ICA problem can be solved via an optimisation approach on a suitable manifold. FastICA is one prominent linear ICA algorithm for solving the so-called one-unit ICA problem, which was recently shown by the authors to be an approximate Newton's method on the real projective space. To extract multiple components in parallel, in this paper, we propose an approximate Ne.wton-like ICA algorithm on the orthogonal group. The local quadratic convergence properties are discussed. The performance of the proposed algorithms is compared with several existing parallel ICA algorithms by numerical experiments..