Skip to main content
SpringerLink
Log in

Algorithms with high order convergence speed for blind source extraction

  • Published:
Computational Optimization and Applications Aims and scope Submit manuscript

Abstract

A rigorous convergence analysis for the fixed point ICA algorithm of Hyvärinen and Oja is provided and a generalization of it involving cumulants of an arbitrary order is presented. We consider a specific optimization problem OP(p), p>3, integer, arising from a Blind Source Extraction problem (BSE) and prove that every local maximum of OP(p) is a solution of (BSE) in sense that it extracts one source signal from a linear mixture of unknown statistically independent signals. An algorithm for solving OP(p) is constructed, which has a rate of convergence p−1.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Alekseev, V.M., Tihomirov, V.M., Fomin, S.V.: Optimal Control. Nauka, Moscow (1979) (in Russian)

    Google Scholar 

  2. Amari, S., Cichocki, A.: Adaptive blind signal processing—neural network approaches. Proc. IEEE 86(10), 2016–2048 (1998) (invited paper)

    Article  Google Scholar 

  3. Cichocki, A., Amari, S.: Adaptive Blind Signal and Image Processing. Wiley, Chichester (2002)

    Google Scholar 

  4. Delfosse, N., Loubaton, P.: Adaptive blind separation of independent sources: a deflation approach. Signal Process. 45, 59–83 (1995)

    Article  MATH  Google Scholar 

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

    Google Scholar 

  6. Hyvarinen, A., Oja, E.: A fast fixed-point algorithm for independent component analysis. Neural Comput. 9, 1483–1492 (1997)

    Article  Google Scholar 

  7. Hyvarinen, A.: Blind source separation by nonstationarity of variance: a cumulant based approach. IEEE Trans. Neural Netw. 12(6), 1471–1474 (2001)

    Article  Google Scholar 

  8. Shiryaev, A.N.: Probability. Graduate Texts in Mathematics. Springer, New York (1996)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ECECS Department, University of Cincinnati, ML 0030, Cincinnati, OH, 45221-0030, USA

    Pando Georgiev

  2. Sofia University “St. Kl. Ohridski”, 5 J. Bourchier Blvd., 1164, Sofia, Bulgaria

    Pando Georgiev

  3. Center for Applied Optimization, University of Florida, Florida, USA

    Panos Pardalos

  4. The Institute for Physical and Chemical Research (RIKEN), Brain Science Institute, Wako-shi, Saitama, 351-0198, Japan

    Andrzej Cichocki

Authors
  1. Pando Georgiev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Panos Pardalos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Andrzej Cichocki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pando Georgiev.

Additional information

Research partially supported by NSF and NIH grants.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Georgiev, P., Pardalos, P. & Cichocki, A. Algorithms with high order convergence speed for blind source extraction. Comput Optim Appl 38, 123–131 (2007). https://doi.org/10.1007/s10589-007-9031-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10589-007-9031-2

Keywords

Search

Navigation