A Statistical Convergence Analysis of the FastICA Algorithm for Two-Source Mixtures

While the FastICA algorithm is a popular procedure for independent component analysis (ICA) and blind source separation, its average convergence behavior has yet to be studied. This paper provides several statistical convergence analyses of the kurtosis-based FastICA algorithm for two-source noiseless mixtures. We derive explicit and approximate expressions for the evolutions of the average value and the p.d.f. of the inter-channel interference (ICI) under arbitrary and uniform priors for the initial separating system vector. Our results support the observation in S.C. Douglas 2003: this version of the FastICA algorithm reduces the average ICI by 1/3 or 4.77 dB at each iteration, independent of the source distributions and initial system state. Simulations verify the analytical results