Multi-layer Perceptrons for Functional Data Analysis: A Projection Based Approach

  • Brieuc Conan-Guez
  • Fabrice Rossi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2415)

Abstract

In this paper, we propose a new way to use Functional Multi-Layer Perceptrons (FMLP). In our previous work, we introduced a natural extension of Multi Layer Perceptrons (MLP) to functional inputs based on direct manipulation of input functions. We propose here to rely on a representation of input and weight functions thanks to projection on a truncated base. We show that the proposed model has the universal approximation property. Moreover, parameter estimation for this model is consistent. The new model is compared to the previous one on simulated data: performances are comparable but training time it greatly reduced.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Christophe Abraham, Pierre-André Cornillon, Eric Matzner-Lober, and Nicolas Molinari. Unsupervised curve clustering using b-splines. Technical Report 00-04, ENSAM-INRA-UM 11-Montpellier, October 2001.Google Scholar
  2. 2.
    Andrew R. Barron. Universal Approximation Bounds for Superpositions of a Sigmoidal Function. IEEE Trum. Information Theory, 39(3):930–945, May 1993.Google Scholar
  3. 3.
    Helga Bunke and Olaf Bunke, editors. Nonlinear Regression, Functional Relations and Robust Methods, volume II of Series in Probability and Mathematical Statistics. Wiley, 1989.Google Scholar
  4. 4.
    Brieuc Conan-Guez and Fabrice Rossi. Projection based functional multi layer perceptrons. Technical report, LISE/CEREMADE & INRIA, http://www.ceremade.dauphine.fr/, february 2002.
  5. 5.
    Jim Ramsay and Bernard Silverman. Functional Data Analysis. Springer Series in Statistics. Springer Verlag, June 1997.Google Scholar
  6. 6.
    Fabrice Rossi, Brieuc Conan-Guez, and François Fleuret. Functional data analysis with multi layer perceptrons. In IJCNN 2002/WCCI 2002, volume 3, pages 2843–2848. IEEE/NNS/INNS, May 2002.Google Scholar
  7. 7.
    Fabrice Rossi, Brieuc Conan-Guez, and Fraqois Fleuret. Theoretical properties of functional multi layer perceptrons. In ESANN 2002, April 2002.Google Scholar
  8. 8.
    Maxwell B. Stinchcombe. Neural network approximation of continuous functionals and continuous functions on compactifications. Neural Networks, 12(3):467–477, 1999.CrossRefGoogle Scholar
  9. 9.
    Halbert White. Learning in Artificial Neural Networks: A Statistical Perspective. Neural Computation, 1(4):425–464, 1989.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Brieuc Conan-Guez
    • 1
  • Fabrice Rossi
    • 2
  1. 1.INRIALe Chesnay CedexFrance
  2. 2.LISE/CEREMADE, UMR CNRS 7534Université Paris-IX DauphineParisFrance

Personalised recommendations