Skip to main content
Log in

A Novel Measure for Quantifying the Topology Preservation of Self-Organizing Feature Maps

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

Recently, feature maps have been applied to various problem domains. The success of some of these applications critically depends on whether feature maps are topologically ordered. In this paper, we propose a novel measure for quantifying the neighborhood preserving property of feature maps. Two data sets were tested to illustrate the performance of the proposed method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Kohonen, T.: Self-Organization and Associative Memory, 3rd edn, New York, Berlin: Springer-Verlag, 1989.

    Google Scholar 

  2. Kohonen, T., Oja, E., Simula, O., Visa, A. and Kangas, J.: Engineering application of the self-organizing map, Proceedings of the IEEE 84(10) (1996), 1358–1383.

    Article  Google Scholar 

  3. Ritter, H. and Schulten, K.: Kohonen's self-organizing maps: exploring their computational capabilities, in IEEE Int. Conf. on Neural Networks, San Diego, vol. 1, 1988, pp. 109–116.

    Google Scholar 

  4. Bauer, H. U. and Pawelzik, K. R.: Quantifying the neighborhood preservation of self-organizing feature maps, IEEE Trans. on Neural Networks, vol. 3, no. 4, July 1992.

  5. Ritter, H., Martinetz, T. M. and Schulten, K.: Neural Computation and Self-Organizing Maps, Addison Wesley, Reading, MA: 1992.

    Google Scholar 

  6. Der, R. and Villmann, T.: Dynamies of self-organizing feature mapping, In: J. Mira, J. Cabestany and A. Prieto (eds), New Trends in Neural Computation, Lecture Notes in Computer Science 686, Springer-Verlag, Berlin: 1993, pp. 312–315.

    Google Scholar 

  7. Der, R., Herrmann, M. and Villmann, T.: Time behavior of topological ordering in self-organized feature mapping, to appear in Biol. Cybern., 1994.

  8. Demartines, P. and Blayo, F.: Kohonen self-organizing maps: Is the normalization necessary? Complex Syst. 6 (1992), 105–123.

    MATH  Google Scholar 

  9. Zrehen, S.: Analyzing Kohonen maps with geometry, In: S. Gielen and B. Kappen (eds), Proc. Int. Conf. Artificial Neural Networks 1993, Springer-Verlag, Berlin: 1993, pp. 609–612.

    Google Scholar 

  10. Villmann, T., Der, R., Herrmann, M. and Martinetz, T. M.: Topology preservation in self-organizing feature map: exact definition and measurement, IEEE Trans. on Neural Networks, vol. 8, no. 2, March 1997.

  11. Goodhill, G. J. and Sejnowski, T. J.: Quantifying neighbourhood preservation in topographic mappings, The 3rd Symposium on Neural Computation, 1996, pp. 61–82.

  12. Kraaijveld, M. A., Mao, J. and Jain, A. K.: A nonlinear projection method based on Kohonen's topology preserving maps, IEEE Trans. on Neural Networks 6(3) (1995), 548–559.

    Article  Google Scholar 

  13. Mao, J. and Jain, A. K.: Artificial neural networks for feature extraction and multivariate data projection, IEEE Trans. Neural Networks, vol. 6, no. 2, pp. 296–317.

  14. Pal, N. R. and Eluri, V. K.: Two efficient connectionist schemes for structure preserving dimensionality reduction, IEEE Trans. on Neural Networks 9 (1998), 1142–1154.

    Article  Google Scholar 

  15. Su, M. C. and Chang, H. C.: A new model of self-organizing neural networks and its application in data projection, IEEE Trans. on Neural Networks 12(1) (2001), 153–158.

    Article  Google Scholar 

  16. Ultsch, A.: Self organizing feature maps for monitoring and knowledge acquisition of a chemical process, International Conference on Artificial Neural Networks, 1993, pp. 864–867.

  17. Vesanto, J.: Som-based data visualization methods, Intelligent Data Analysis 3 (1999), 111–126.

    Article  MATH  Google Scholar 

  18. Sammon Jr., J. W.: A nonlinear mapping for data structure analysis, IEEE Trans. on Computers 18 (1969), 491–509.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Su, MC., Chang, HT. & Chou, CH. A Novel Measure for Quantifying the Topology Preservation of Self-Organizing Feature Maps. Neural Processing Letters 15, 137–145 (2002). https://doi.org/10.1023/A:1015240802059

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1015240802059

Navigation