Skip to main content

Average Convergence Behavior of the FastICA Algorithm for Blind Source Separation

  • Conference paper
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. 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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Hyvärinen, A., Oja, E.: A fast fixed-point algorithm for independent component analysis. Neural Computation 9(7), 1483–1492 (1997)

    Article  Google Scholar 

  2. Hyvarinen, A., Karhunen, J., Oja, E.: Independent Component Analysis. Wiley, New York (2001)

    Book  Google Scholar 

  3. Douglas, S.C.: On the convergence behavior of the FastICA algorithm. In: Proc. Fourth Symp. Indep. Compon. Anal. Blind Signal Separation, Kyoto, Japan, pp. 409–414 (April 2003)

    Google Scholar 

  4. Douglas, S.C.: A statistical convergence analysis of the FastICA algorithm for twosource mixtures. In: Proc. 39th Asilomar Conf. Signals, Syst., Comput., Pacific Grove, CA (October 2005)

    Google Scholar 

  5. Douglas, S.C.: Relationships between the FastICA algorithm and the Rayleigh Quotient Iteration. In: Proc. 6th Int. Conf. Indep. Compon. Anal. Blind Source Separation, Charleston, SC (March 2006) (to appear)

    Google Scholar 

  6. David, H.A.: Order Statistics, 2nd edn. Wiley, New York (1980)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Douglas, S.C., Yuan, Z., Oja, E. (2006). Average Convergence Behavior of the FastICA Algorithm for Blind Source Separation. 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_98

Download citation

  • DOI: https://doi.org/10.1007/11679363_98

  • 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)

Publish with us

Policies and ethics