Convergence of the symmetrical FastICA algorithm
ABSTRACT The FastICA algorithm is one of the most popular methods to solve problems in independent component analysis (ICA) and blind source separation. It has been shown experimentally that it outperforms most of the commonly used ICA algorithms in convergence speed. A rigorous convergence analysis has been presented only for the so-called one-unit case, in which just one of the rows of the separating matrix is considered. However, in the FastICA algorithm, there is also an explicit normalization step, and it may be questioned whether the extra rotation caused by the normalization will effect the convergence speed. The purpose of this paper is to show that this is not the case and the good convergence properties of the one-unit case are also shared by the full algorithm with symmetrical normalization.
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ABSTRACT: The contrast function optimization based independent component analysis is one of the most widespread methods in separating independent sources from their linear mixtures. The convergence analysis of such algorithms, which has both theoretical and practical value, is a current research focus. In this article, we present a convergence analysis for the separation of complex sources via use of these algorithms. Based on this analysis, we provide the characterization of the stationary points of the algorithms using symmetric orthogonalization.Signal Processing, Communication and Applications Conference, 2008. SIU 2008. IEEE 16th; 05/2008
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ABSTRACT: Many algorithms for independent component analysis (ICA) and blind source separation (BSS) can be considered particular instances of a criterion based on the sum of two terms: C(Y), which expresses the decorrelation of the components and G(Y), which measures their non-Gaussianity. Within this framework, the popular FastICA algorithm can be regarded as a technique that keeps C(Y)=0 by first enforcing the whiteness of Y. Because of this constraint, the standard version of FastICA employs the sample-fourth moment as G(Y), instead of the sample-fourth cumulant. Our work analyzes some of the estimation errors introduced by the use of finite date sets in such a higher-order statistics (HOS) contrast and compares FastICA with an alternative version based on the sample-fourth cumulant, which is shown for different probability distributions having a lower variance in the generalization error in the case in which no whitening is performed, e.g. when orthonormal mixing of sources is present.Neurocomputing 12/2007; 71(1-3):392-399. · 1.63 Impact Factor
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ABSTRACT: 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 resultsSignals, Systems and Computers, 2005. Conference Record of the Thirty-Ninth Asilomar Conference on; 01/2005