Skip to main content

Wavelet frames based estimator

  • Part III: Learning: Theory and Algorithms
  • Conference paper
  • First Online:
Artificial Neural Networks — ICANN'97 (ICANN 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1327))

Included in the following conference series:

  • 298 Accesses

Abstract

This paper introduces a new wavelet frames-based functional estimation method (i.e. a wavelet-based neural network which works for more than one dimension functions. The use of frames and wavelets in our approach yields to robust decomposition with an interesting parsimonious property: compression of information in few coefficients. This approach is illustrated using the problem of estimating radioactivity in Chernobyl area.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Christopher M. Bishop. Neural Networks for Pattern Recognition. Oxford University Press, 1995.

    Google Scholar 

  2. Leo Breiman. Statistics and nets: Understanding nonlinear models from their linear relatives. NIPS 94, Tutorial 6, November 1994.

    Google Scholar 

  3. Emmanuel J. Candès. Harmonic analysis of neural networks. Technical report, Department of Statistics, University of Stanford, October 1996.

    Google Scholar 

  4. Ingrid Daubechies. Ten Lectures on Wavelets. CBMS-NSF Regional Conference Series on Applied Mathematics, No 61, SIAM, 1992.

    Google Scholar 

  5. Bradley Efron and Robert J. Tibshirani. An Introduction to the Bootstrap, volume 57 of Monographs on statistics and Applied probability. Chapman & Hall, 1993.

    Google Scholar 

  6. Frederico Girosi, Michael Jones, and Tomaso Poggio. Regularization theory and neural networks architectures. Neural Computation, 7(2):219–269, 1995.

    Google Scholar 

  7. Wolfgang Hiirdle. Applied Nonparametric Regression, volume 19. Cambridge University Press, 1990.

    Google Scholar 

  8. Vladimir N. Vapnik. The Nature of Statistical Learning Theory. Springer-Verlag, 1995.

    Google Scholar 

  9. Qinghua Zhang. Wavelets and regression analysis. In Anestis Antoniadis and George Oppenheim, editors, Wavelets and Statistics, volume 103 of Lectures in Statistics, pages 397–407. Springer Verlag, 1995.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Wulfram Gerstner Alain Germond Martin Hasler Jean-Daniel Nicoud

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Soltani, S., Canu, S., Boichu, D., Grandvalet, Y. (1997). Wavelet frames based estimator. In: Gerstner, W., Germond, A., Hasler, M., Nicoud, JD. (eds) Artificial Neural Networks — ICANN'97. ICANN 1997. Lecture Notes in Computer Science, vol 1327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0020174

Download citation

  • DOI: https://doi.org/10.1007/BFb0020174

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63631-1

  • Online ISBN: 978-3-540-69620-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics