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Relationships Between the FastICA Algorithm and the Rayleigh Quotient Iteration

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Independent Component Analysis and Blind Signal Separation (ICA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 3889))

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.

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Southern Methodist University, Dallas, Texas, 75275, USA

    Scott C. Douglas

Authors
  1. Scott C. Douglas
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Editor information

Editors and Affiliations

  1. Siemens Corporate Research, 755 College Road East, 08540, Princeton, NJ, USA

    Justinian Rosca

  2. Department of CSEE, Oregon Health and Science University, Portland, Oregon, USA

    Deniz Erdogmus

  3. Dep. of Electrical and Computer Engineering, University of Florida, Gainesville, Florida, USA

    José C. Príncipe

  4. McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, Ontario, Canada

    Simon Haykin

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© 2006 Springer-Verlag Berlin Heidelberg

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Douglas, S.C. (2006). Relationships Between the FastICA Algorithm and the Rayleigh Quotient Iteration. In: Rosca, J., Erdogmus, D., Príncipe, J.C., Haykin, S. (eds) Independent Component Analysis and Blind Signal Separation. ICA 2006. Lecture Notes in Computer Science, vol 3889. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11679363_97

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  • DOI: https://doi.org/10.1007/11679363_97

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32630-4

  • Online ISBN: 978-3-540-32631-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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