Skip to main content

A Functional-Neural Network for Post-Nonlinear Independent Component Analysis

  • Conference paper
  • First Online:
  • 1411 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2084))

Abstract

In this paper a hybrid approach, based on a functional network and a neural network, for post-nonlinear independent component analysis is presented. In order to obtain the independence among the outputs, it was used as cost function a measure based on Renyi’s quadratic entropy and Cauchy-Sc hw artz inequality. Also, the Kernel method was used for nonparametric estimation of the probability density function. The experimental results corroborated the soundness of the approach and a comparative study with a neural network showed its superior performance.

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

Buying options

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Burel, G.: A non-linear neural algorithm. Meural Networks 5 (1992) 937–947

    Article  Google Scholar 

  2. Castillo, E.: Functional Networks. Neural Processing Letters, 7(3) (1998) 151–159

    Article  MathSciNet  Google Scholar 

  3. Castillo, E., Cobo, A., Gutierrez, J. M., Pruneda, R. E.: Functional Networks with Applications. A Neural-Based Paradigm. Kluwer Academic Publishers, Dordrecht (1998)

    Google Scholar 

  4. Comon, P.: Independent Component Analysis-a new concept?. Signal Processing 36 (1994) 287–314

    Article  MATH  Google Scholar 

  5. Duda, R. O., Hart, P. E.: Pattern Classification and Scene Analysis. John Wiley & Sons, New York (1973)

    MATH  Google Scholar 

  6. Hyvarinen, A., Pajunen, P.: Nonlinear Independent Component Analysis: Existence and Uniqueness results. Neural Networks 12(3) (1999) 429–439

    Article  Google Scholar 

  7. Jutten, C., Herault, J.: Blind separation of sources, part I: An adaptive algorithm based on neuromimetic architecture. Signal Processing 24 (1991) 1–10

    Article  MATH  Google Scholar 

  8. Pajunen, P.: Nonlinear independent component analysis by self-organizing maps. Proceedings ICANN (1996) 815–819

    Google Scholar 

  9. Principe, J. C., Fisher III, J., Xu, D.: Information Theoretic Learning. In S. Haykin (Ed.): Unsupervised Adaptive Filtering, Vol. I. John Wiley & Sons, New York (2000)

    Google Scholar 

  10. Principe, J. C., Xu, D.: Information Theoretic Learning using Renyi’s Quadratic Entropy. Proceedings ICA’99 (1999) 407–412

    Google Scholar 

  11. Schobben, D. W. E., Torkkola, K., Smaragdis, P.: Evaluation of Blind Signal Separation Methods. Proceedings ICA’99 (1999) 261–266

    Google Scholar 

  12. Silverman, B. W.: Density estimation for statistics and data analysis. Chapman & Hall, London (1986)

    MATH  Google Scholar 

  13. Taleb, A., Jutten, C.: Nonlinear source separation: The post-nonlinear mixtures. Proceedings ESANN (1997) 279–284

    Google Scholar 

  14. Taleb, A., Jutten, C.: Source separation in post-nonlinear mixtures. IEEE Trans. on Signal Processing 47(10) (1999) 2807–2820

    Article  Google Scholar 

  15. Xu, D., Principe, J. C., Fisher III, J., Wu, H.-C.: A Novel Measure for Independent Component Analysis (ICA). Proceedings ICASSP, Vol. II (1998) 1161–1164

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Romero, O.F., Berdiñas, B.G., Betanzos, A.A. (2001). A Functional-Neural Network for Post-Nonlinear Independent Component Analysis. In: Mira, J., Prieto, A. (eds) Connectionist Models of Neurons, Learning Processes, and Artificial Intelligence. IWANN 2001. Lecture Notes in Computer Science, vol 2084. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45720-8_34

Download citation

  • DOI: https://doi.org/10.1007/3-540-45720-8_34

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42235-8

  • Online ISBN: 978-3-540-45720-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics