Average Convergence Behavior of the FastICA Algorithm for Blind Source Separation

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.

[1]  H. A. David,et al.  Order Statistics (2nd ed). , 1981 .

[2]  S. Douglas.  A Statistical Convergence Analysis of the FastICA Algorithm for Two-Source Mixtures , 2005, Conference Record of the Thirty-Ninth Asilomar Conference onSignals, Systems and Computers, 2005..

[3]  Scott C. Douglas.  Relationships Between the FastICA Algorithm and the Rayleigh Quotient Iteration , 2006, ICA.

[4]  D. Chakrabarti,et al.  A fast fixed - point algorithm for independent component analysis , 1997 .

[5]  Changyuan Fan,et al.  On the Convergence Behavior of the FastICA Algorithm with the Kurtosis Cost Function , 2007, Third International Conference on Intelligent Information Hiding and Multimedia Signal Processing (IIH-MSP 2007).