Relationships between the fastICA algorithm and the rayleigh quotient iteration

Abstract

The FastICA algorithm is a popular procedure for independent component analysis and blind source separation. Recently, several of its convergence properties have been elucidated, including its average convergence performance and its finite-sample behavior. In this paper, we examine the kurtosis-based algorithm version for two-source mixtures with equal-kurtosis sources, proving that the single-unit FastICA algorithm has dynamical behavior that is identical to the Newton-based Rayleigh Quotient Iteration for finding an eigenvector of a symmetric matrix. We also derive a bound on the average inter-channel interference indicating that the initial convergence rate of FastICA is linear with a rate of (1/3). A simulation indicates its convergence performance. © Springer-Verlag Berlin Heidelberg 2006.