Controlling the Asymptotic Level Density for Quantization Processes with Self-Organizing Maps

  • Ewa Skubalska-Rafajłowicz
Conference paper
Part of the Advances in Soft Computing book series (AINSC, volume 19)


We analyze different methods of controlling magnification factor in the relation between the density of the input vectors and the asymptotic density of the quantizers. We also propose a new method of modeling the one-dimensional self-organizing process and examine some properties of the method. Empirical studies show strong influence of the learning rate strategies on the observed magnification factor of the vector quantization process.


Learning Rate Magnification Factor Quantization Process Reference Vector Weight Adjustment 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. U. Bauer, R. Der, M. Herman, Controlling the magnification factor of self-organizing feature maps Neural Computation, vol. 8, 757–771, 1996.Google Scholar
  2. 2.
    E. Erwin, K. Obermayer, K.L. Schulten, Self-organizing maps: ordering, convergence properties and energy function, Biol. Cybern., vol. 67, 47–55, 1992.MATHCrossRefGoogle Scholar
  3. 3.
    A. Gersho, R.M. Gray, Vector quantization and Signal Compression, Kluwer Academic Publisher, Boston, 1993.Google Scholar
  4. 4.
    T. Heskes, B. Kappen, Self-organization and parametric regression, Poc. ICANN95, Paris, France, 81–86, 1995.Google Scholar
  5. 5.
    T.Heskes, Transition Times in Self-Organizing Maps, Biological Cybernetics, vol. 75, 49–57, 1996.MATHCrossRefGoogle Scholar
  6. 6.
    T. Kohonen, Self-organizing formation of topologically correct feature maps, Biol. Cyb., vol. 43, 59–69, 1982.MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    T. Kohonen, Self-organizing maps, Proc. of the IEEE 78, 1464–1480 (1990).CrossRefGoogle Scholar
  8. 8.
    T. Kohonen, Self-organizing maps, Berlin, Heidelberg Springer Verlag (1995).Google Scholar
  9. 9.
    Y.Linde, A. Buzo, R.M. Gray, An algorithm for vector quantizer design, IEEE Transactions on Communication, vol. 28, 84–95, 1980.CrossRefGoogle Scholar
  10. 10.
    S.P. Luttrell, Code vector density in topographic mappings: scalar case, IEEE Trans. on Neural Networks, vol. 2, 427–436, 1991.CrossRefGoogle Scholar
  11. 11.
    T.M. Martinetz, S.G. Berkovich, K.J. Schulten, Neural-gas network for vector quantization and its application to time-series prediction IEEE Trans. on Neural Networks, vol.4., 558–559 (1993).Google Scholar
  12. 12.
    H. Ritter, K.L. Schulten, On the stationary state of Kohonen’s self-organizing sensory mapping, Biological Cybernetics, vol. 54, 99–106, 1986.MATHCrossRefGoogle Scholar
  13. 13.
    H. Ritter, K.L. Schulten, Convergence properties of Kohonen’s topology conserving map: Fluctuations, stability, and dimension detection, Biolgical Cybernetics, vol. 60, 59–71, 1988.MathSciNetMATHGoogle Scholar
  14. 14.
    H. Ritter, Asymptotic level density for a class of vector quantization processes, IEEE Trans. on Neural Networks 2, 173–175 (1991).MathSciNetCrossRefGoogle Scholar
  15. 15.
    E. Skubalska-Rafajlowicz, Applications of the Space-Filling Curves with Data Driven MeasurePreserving Property, Nonlinear Analysis, Theory, Methods 6 Applications, vol. 30 (3), pp. 1305–1310, 1997.MATHGoogle Scholar
  16. 16.
    E. Skubalska-Rafajlowicz, Space-Filling Curves and Kohonen’s 1-D SOM as a Method of a Vector Quantization with Known Asymptotic Level Density, Proc. of the 3rd Conf. Neural Networks and Their Applications, Kule 1997, pp. 161–166.Google Scholar
  17. 17.
    E. Yair, K. Zeger, A. Gersho, Competitive learning and soft competition for vector quantizer design, IEEE Trans. on Signal Processing 40, 294–309 (1992).CrossRefGoogle Scholar
  18. 18.
    Y. Zheng, J.F. Greenleaf, The effect of concave and convex weight adjustments on self-organizing maps, IEEE Trans. on Neural Networks 7, 87–96 (1994).CrossRefGoogle Scholar
  19. 19.
    P.L. Zador, Asymptotic Quantization Error of Continuous Signmals and the Quantization Dimension, IEEE Trans. on Information Theory 28, 139–149 (1982).MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Ewa Skubalska-Rafajłowicz
    • 1
  1. 1.Institute of Engineering CybernetisWrocław University of TechnologyWrocławPoland

Personalised recommendations