Investigation of Topographical Stability of the Concave and Convex Self-Organizing Map Variant

  • Fabien Molle
  • Jens Christian Claussen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4131)


We investigate, by a systematic numerical study, the parameter dependence of the stability of the Kohonen Self-Organizing Map and the Zheng and Greenleaf concave and convex learning with respect to different input distributions, input and output dimensions.

Topical groups: Advances in Neural Network Learning Methods, Neural and hybrid architectures and learning algorithms, Self-organization.


Neural Computation Input Distribution Invariant Density Topology Preservation Neural Layer 
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.


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  1. 1.
    Kohonen, T.: Self-Organized Formation of Toplogically Correct Feature Maps. Biological Cybernetics 43, 59–69 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Zheng, Y., Greenleaf, J.F.: The effect of concave and convex weight adjustments on self-organizing maps. IEEE Transactions on Neural Networks 7, 87–96 (1996)CrossRefGoogle Scholar
  3. 3.
    Villmann, T., Claussen, J.C.: Investigation of Magnification Control in Self-Organizing Maps and Neural Gas. Neural Computation 18, 449–469 (2006)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Kohonen, T.: Comparison of SOM point densities based on different criteria. Neural Computation 11, 2081–2095 (1999)CrossRefGoogle Scholar
  5. 5.
    Villmann, T., Der, R., Herrmann, M., Martinetz, T.: Topology Preservation in Self-Organizing Feature Maps: Exact Definition and Measurement. IEEE Transactions on Neural Networks 8, 256–266 (1997)CrossRefGoogle Scholar
  6. 6.
    Zrehen, S.: Analyzing Kohonen maps with geometry. In: Gielen, S., Kappen, B. (eds.) Proc. ICANN 1993, pp. 609–612. Springer, London (1993)Google Scholar
  7. 7.
    Ritter, H., Schulten, K.: On the Stationary State of Kohonen’s Self-Organizing Sensory Mapping. Biological Cybernetics 54, 99–106 (1986)zbMATHCrossRefGoogle Scholar
  8. 8.
    Ritter, H., Schulten, K.: Convergence Properties of Kohonen’s Topology Conserving Maps: Fluctuations, Stability and Dimension Selection. Biological Cybernetics 60, 59–71 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Ritter, H., Martinetz, T., Schulten, K.: Neural Computation and Self-Organizing Maps: An Introduction. Addison-Wesley, Reading (1992)zbMATHGoogle Scholar
  10. 10.
    Linsker, R.: How to generate maps by maximizing the mutual information between input and output signals. Neural Computation 1, 402–411 (1989)CrossRefGoogle Scholar
  11. 11.
    Heskes, T.: Energy functions for self-organizing maps. In: Oja, E., Kaski, S. (eds.) Kohonen Maps, pp. 303–316. Elsevier, Amsterdam (1999)CrossRefGoogle Scholar
  12. 12.
    Erwin, E., Obermayer, K., Schulten, K.: Self-organizing maps: Ordering, convergence properties and energy functions. Biol. Cyb. 67, 47–55 (1992)zbMATHCrossRefGoogle Scholar
  13. 13.
    Claussen, J.C.: Generalized Winner Relaxing Kohonen Feature Maps. Neural Computation 17, 996–1009 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Claussen, J.C., Villmann, T.: Magnification Control in Winner Relaxing Neural Gas. Neurocomputing 63, 125–137 (2005)CrossRefGoogle Scholar
  15. 15.
    Martinetz, T.M., Berkovich, S.G., Schulten, K.J.: Neural-gas network for vector quantization and its application to time-series prediction. IEEE Trans. on Neural Networks 4, 558–569 (1993)CrossRefGoogle Scholar
  16. 16.
    Villmann, T.: PhD thesis, Leipzig, Verlag Harri Deutsch, Frankfurt (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Fabien Molle
    • 1
    • 2
  • Jens Christian Claussen
    • 2
  1. 1.Theoretical PhysicsChalmers Tekniska HögskolaGöteborg
  2. 2.Institut für Theoretische Physik und AstrophysikChristian-Albrechts-Universität zu KielGermany

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