Average convergence behavior of the FastICA algorithm for blind source separation

Authors:
Scott C. Douglas;Zhijian Yuan;Erkki Oja
Affiliations:
Department of Electrical Engineering, Southern Methodist University, Dallas, Texas;Neural Networks Research Centre, Helsinki University of Technology, Espoo, Finland;Neural Networks Research Centre, Helsinki University of Technology, Espoo, Finland
Venue:
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Year:
2006

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Abstract

The FastICA algorithm is a popular procedure for independent component analysis and blind source separation. In this paper, we analyze the average convergence behavior of the single-unit FastICA algorithm with kurtosis contrast for general m-source noiseless mixtures. We prove that this algorithm causes the average inter-channel interference (ICI) to converge exponentially with a rate of (1/3) or -4.77dB at each iteration, independent of the source mixture kurtoses. Explicit expressions for the average ICI for the three- and four-source mixture cases are also derived, along with an exact expression for the average ICI in a particular situation. Simulations verify the accuracy of the analysis.