Advertisement

Asymptotic Level Density of the Elastic Net Self-Organizing Feature Map

  • Jens Christian Claussen
  • Heinz Georg Schuster
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2415)

Abstract

Whileas the Kohonen Self Organizing Map shows an asymptotic level density following a power law with a magnification exponent 2/3, it would be desired to have an exponent 1 in order to provide optimal mapping in the sense of information theory. In this paper, we study analytically and numerically the magnification behaviour of the Elastic Net algorithm as a model for self-organizing feature maps. In contrast to the Kohonen map the Elastic Net shows no power law, but for onedimensional maps nevertheless the density follows an universal magnification law, i.e. depends on the local stimulus density only and is independent on position and decouples from the stimulus density at other positions.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    T. Kohonen 1982. Biological Cybernetics 43, 59–69.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    K. Obermayer, G. G. Blasdel, and K. Schulten 1992. Phys. Rev. A 45, 7568–7589.CrossRefGoogle Scholar
  3. 3.
    H. Ritter, T. Martinetz, and K. Schulten 1992. Neural Computation and Self-Organizing Maps. Addison-Wesley.Google Scholar
  4. 4.
    R. Durbin and D. Willshaw 1987. Nature 326, 689–691.CrossRefGoogle Scholar
  5. 5.
    P. D. Simic 1990. Network 1, 89–103.zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    R. Durbin, R. Szeliski, and A. Yuille 1989. Neural Computation 1, 348–358.CrossRefGoogle Scholar
  7. 7.
    M. W. Simmen 1991. Neural Computation 3, 363–374.CrossRefGoogle Scholar
  8. 8.
    J. Hertz, A. Krogh, and R. G. Palmer 1991. Intr. to the Theory of Neural Comp. Addison-Wesley, Reading, MA.Google Scholar
  9. 9.
    J. C. Claussen (born Gruel) 1992. Diploma thesis, KielGoogle Scholar
  10. J.
    C. Claussen (born Gruel) and H. G. Schuster 1994. Preprint.Google Scholar
  11. 10.
    T. Kohonen 1991. in: Artificial Neural Networks, ed. T. Kohonen et al. North-Holland, Amsterdam.Google Scholar
  12. 11.
    R. Linsker 1989. Neural Computation 1, 402–411.CrossRefGoogle Scholar
  13. 12.
    H. Ritter and K. Schulten 1986. Biological Cybernetics 54, 99–106.zbMATHCrossRefGoogle Scholar
  14. 13.
    D. R. Dersch and P. Tavan 1995. IEEE Trans. Neur. Netw. 6, 230–236.CrossRefGoogle Scholar
  15. 14.
    H. Ritter 1991. IEEE Transactions on Neural Networks 2, 173–175.CrossRefMathSciNetGoogle Scholar
  16. 15.
    P. D. Simic 1994. Private communication.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jens Christian Claussen
    • 1
  • Heinz Georg Schuster
    • 1
  1. 1.Institut für Theoretische Physik und AstrophysikUniversität zu KielChristian-AlbrechtsGermany

Personalised recommendations