Skip to main content

Dynamics of ICA for High- Dimensional Data

  • Conference paper
  • First Online:
  • 117 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2415))

Abstract

The learning dynamics close to the initial conditions of an on-line Hebbian ICA algorithm has been studied. For large input dimension the dynamics can be described by a diffusion equation.A surprisingly large number of examples and unusually low initial learning rate are required to avoid a stochastic trapping state near the initial conditions. Escape from this state results in symmetry breaking and the algorithm therefore avoids trapping in plateau-like fixed points which have been observed in other learning algorithms.

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   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
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. Hyvärinen, A.: Survey on independent component analysis. Neural Computing Surveys 2 (1999) 94–128

    Google Scholar 

  2. Saad, D. and Solla, S. A.: Exact solution for on-line learning in multilayer neural networks. Physical Review Letters E 74 (1995) 4337–4340.

    Article  Google Scholar 

  3. Biehl, M., Schlosser, E.: The dynamics of on-line principal component analysis. Journal of Physics A31 (1998) L97

    Google Scholar 

  4. Rattray, M.: Stochastic trapping in a solvable model of on-line independent component analysis. Neural Computation 14,2 (2002) 421–435

    Article  MATH  Google Scholar 

  5. Rattray, M., Basalyga, G.: Scaling laws and local minima in Hebbian ICA. To appear in Proceedings of Neural Information Processing Systems (NIPS*2001), Vancouver (2002)

    Google Scholar 

  6. Hyvärinen A., Oja, E.: Signal Processing, 64 (1998) 301–313

    Article  MATH  Google Scholar 

  7. Gardiner, C.W.: Handbook of Stochastic Methods. Springer-Verlag, NewYork(1985)

    Google Scholar 

  8. Van Kampen, N.G.: Stochastic processes in physics and chemistry. Elsevier, Amsterdam(1992)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Basalyga, G., Rattray, M. (2002). Dynamics of ICA for High- Dimensional Data. In: Dorronsoro, J.R. (eds) Artificial Neural Networks — ICANN 2002. ICANN 2002. Lecture Notes in Computer Science, vol 2415. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46084-5_180

Download citation

  • DOI: https://doi.org/10.1007/3-540-46084-5_180

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44074-1

  • Online ISBN: 978-3-540-46084-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics