Calculating Conditions for the Emergence of Structure in Self-Organizing Maps

  • Hans-Ulrich Bauer
  • Maximilian Riesenhuber
  • Theo Geisel

Abstract

The self-organization of sensotopic maps in the brain has been modeled with various approaches, using models with linear [1, 2, 3, 4] and nonlinear [5, 6, 7] lateral interaction functions. In the realm of visual maps, all models are able to generate ocular dominance or orientation structure [8]. Models differ, however, with regard to more subtle effects, like the impact of input correlation on ocular dominance stripe width, the self-organization of oriented receptive fields from non-oriented stimuli or correlation functions, or the preferred angle of intersection between ocular dominance and orientation column systems. For a correct assessment of the behavior of particular models with regard to these or other phenomena, it is dangerous to rely on simulations only. Rather, analytic results on conditions for the pattern formation in map models are desirable. We present here a method for calculating such conditions for a map model with strong lateral nonlinearity, the high-dimensional version of Kohonen’s Self-Organizing Map (SOM). Using this method we then analyze two relevant models, a SOM-model for the development of orientation maps and a SOM-model for the development of ocular dominance maps.

Keywords

Receptive Field Ocular Dominance Oriented Receptive Field Retinal Space Increase Band Width 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    C. von der Malsburg, Kybernetik 14, 85 (1973); Biol. Cyb. 32, 49 (1979).Google Scholar
  2. 2.
    K. D. Miller, J. B. Keller, M. P. Stryker, Science 245, 605 (1989).PubMedCrossRefGoogle Scholar
  3. 3.
    K. D. Miller, J. Neurose. 14, 409 (1994).Google Scholar
  4. 4.
    M. Miyashita, S. Tanaka, NeuroRep. 3, 69 (1992).Google Scholar
  5. 5.
    K. Obermayer, H. Ritter, K. Schulten, Proc. Nat. Acad. Sci. USA 87, 8345 (1990).CrossRefGoogle Scholar
  6. 6.
    R. Durbin, G. Mitchison, Nature 343, 644 (1990).PubMedCrossRefGoogle Scholar
  7. 7.
    F. Wolf, H.-U. Bauer, T. Geisel, Biol. Cyb. 70, 525 (1994).CrossRefGoogle Scholar
  8. 8.
    E. Erwin, K. Obermayer, K. Schulten, Neur. Comp. 7, 425 (1995).CrossRefGoogle Scholar
  9. 9.
    T. Kohonen, Self-Organizing Maps, Springer, Berlin (1995).CrossRefGoogle Scholar
  10. 10.
    M. Riesenhuber, H.-U. Bauer, T. Geisel, Biol. Cyb., in print (1996).Google Scholar
  11. 11.
    K. D. Miller, submitted to Neur. Comp. (1995).Google Scholar
  12. 12.
    E. Erwin, K. Obermayer, K. Schulten, Biol. Cyb. 67, 47 (1992).CrossRefGoogle Scholar
  13. 13.
    K. Obermayer, Adaptive Neuronale Netze und ihre Anwendung als Modelle der Entwicklung kortikaler Karten, infix Verlag, Sankt Augustin (1993).Google Scholar
  14. 14.
    K. Obermayer, G. G. Blasdel, K. Schulten, Phys. Rev. A 45, 7568 (1992).PubMedCrossRefGoogle Scholar
  15. 15.
    G. J. Goodhill, Biol. Cyb. 69, 109 (1993).CrossRefGoogle Scholar
  16. 16.
    S. Löwel, J. Neurosci. 14, 7451 (1994).PubMedGoogle Scholar
  17. 17.
    C. von der Malsburg, Neural and Electronic Networks,Eds. Zornetzer et al., Academic Press. 421 (1994).Google Scholar
  18. 18.
    G. J. Goodhill, D. J. Willshaw, Network 1, 41 (1990);CrossRefGoogle Scholar
  19. P. Dayan, Neur. Comp. 5, 392 (1993).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Hans-Ulrich Bauer
    • 1
  • Maximilian Riesenhuber
    • 1
  • Theo Geisel
    • 1
  1. 1.Institut für Theoretische Physik SFB Nichtlineare DynamikUniversität FrankfurtFrankfurt/MainGermany

Personalised recommendations