Biological Cybernetics

, Volume 44, Issue 2, pp 135–140 | Cite as

Analysis of a simple self-organizing process

  • Teuvo Kohonen


This paper contains mathematical results relating to a recently discovered self-organizing process. In particular, an analysis of two partial processes is presented. In the first one, a set of numerical representations assumes the correct order, and in the second one the final map of the representations converges to its asymptotic form.


Correct Order Asymptotic Form Numerical Representation Mathematical Result Partial Process 
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  1. Albert, A.E., Gardner, L.A., Jr.: Stochastic approximation and nonlinear regression. Cambridge, Mass: MIT Press 1967Google Scholar
  2. Geman, S.: SIAM J. Appl. Math.36, 86–105 (1979)Google Scholar
  3. Grenander, U.: Private communication (1981)Google Scholar
  4. Kohonen, T.: Automatic formation of topological maps of patterns in a self-organizing system. In: Proc. 2nd Scand. Conf. on Image Analysis, Oja, E., Simula, O. (eds) pp. 214–220. Espoo: Suomen Hahmontunnistustutkimuksen Seura 1981Google Scholar
  5. Kohonen, T.: Self-organized formation of topologically correct feature maps. Biol. Cybern.43, 59–69 (1982)Google Scholar
  6. Kohonen, T.: Hierarchical ordering of vectoral data in a self-organizing process. Helsinki University of Technology, Report TKK-F-A461 (1981)Google Scholar
  7. Stewart, G.W.: Introduction to matrix computations. New York: Academic Press 1973Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Teuvo Kohonen
    • 1
  1. 1.Department of Technical PhysicsHelsinki University of TechnologyEspooFinland

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