Fuzzy Supervised Self-Organizing Map for Semi-supervised Vector Quantization

  • Marika Kästner
  • Thomas Villmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7267)

Abstract

In this paper we propose a new approach to combine unsupervised and supervised vector quantization for clustering and fuzzy classification using the framework of neural vector quantizers like self-organizing maps or neural gas. For this purpose the original cost functions are modified in such a way that both aspects, unsupervised vector quantization and supervised classification, are incorporated. The theoretical justification of the convergence of the new algorithm is given by an adequate redefinition of the underlying dissimilarity measure now interpreted as a dissimilarity in the data space combined with the class label space. This allows a gradient descent learning as known for the original algorithms. Thus a semi-supervised learning scheme is achieved. We apply this method for a spectra image cube of remote sensing data for landtype classification. The obtained fuzzy class visualizations allow a better understanding and interpretation of the spectra.

Keywords

Class Label Vector Quantization Dissimilarity Measure Learn Vector Quantizer Local Cost 
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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References

  1. 1.
    Bauer, H.-U., Herrmann, M., Villmann, T.: Neural maps and topographic vector quantization. Neural Networks 12(4-5), 659–676 (1999)CrossRefGoogle Scholar
  2. 2.
    Geweniger, T., Zühlke, D., Hammer, B., Villmann, T.: Median fuzzy c-means for clustering dissimilarity data. Neurocomputing 73(7-9), 1109–1116 (2010)CrossRefGoogle Scholar
  3. 3.
    Hammer, B., Villmann, T.: Generalized relevance learning vector quantization. Neural Networks 15(8-9), 1059–1068 (2002)CrossRefGoogle Scholar
  4. 4.
    Heskes, T.: Energy functions for self-organizing maps. In: Oja, E., Kaski, S. (eds.) Kohonen Maps, pp. 303–316. Elsevier, Amsterdam (1999)CrossRefGoogle Scholar
  5. 5.
    Kästner, M., Villmann, T.: Functional relevance learning in generalized learning vector quantization. Machine Learning Reports 5(MLR-01-2011), 81–89 (2011), http://www.techfak.uni-bielefeld.de/~fschleif/mlr/mlr_01_2011.pdf ISSN:1865-3960Google Scholar
  6. 6.
    Kästner, M., Villmann, T.: Fuzzy supervised neural gas for semi-supervised vector quantization – theoretical aspects. Machine Learning Reports 5(MLR-02-2011), 1–16 (2011), http://www.techfak.uni-bielefeld.de/~fschleif/mlr/mlr__011.pdf ISSN:1865-3960Google Scholar
  7. 7.
    Kohonen, T.: Self-Organizing Maps. Springer Series in Information Sciences, vol. 30. Springer, Heidelberg (1995) (Second Extended Edition 1997)CrossRefGoogle Scholar
  8. 8.
    Lee, J., Verleysen, M.: Generalization of the l p norm for time series and its application to self-organizing maps. In: Cottrell, M. (ed.) Proc. of Workshop on Self-Organizing Maps, WSOM 2005, Paris, Sorbonne, pp. 733–740 (2005)Google Scholar
  9. 9.
    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(4), 558–569 (1993)CrossRefGoogle Scholar
  10. 10.
    Midenet, S., Grumbach, A.: Learning associations by self-organizatiom: the LASSO model. Neurocomputing 6, 343–361 (1994)CrossRefGoogle Scholar
  11. 11.
    Pekalska, E., Duin, R.: The Dissimilarity Representation for Pattern Recognition: Foundations and Applications. World Scientific (2006)Google Scholar
  12. 12.
    Sato, A., Yamada, K.: Generalized learning vector quantization. In: Touretzky, D.S., Mozer, M.C., Hasselmo, M.E. (eds.) Proceedings of the 1995 Conference on Advances in Neural Information Processing Systems, vol. 8, pp. 423–429. MIT Press, Cambridge (1996)Google Scholar
  13. 13.
    Schleif, F.-M., Villmann, T., Hammer, B., Schneider, P., Biehl, M.: Generalized Derivative Based Kernelized Learning Vector Quantization. In: Fyfe, C., Tino, P., Charles, D., Garcia-Osorio, C., Yin, H. (eds.) IDEAL 2010. LNCS, vol. 6283, pp. 21–28. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  14. 14.
    Schneider, P., Hammer, B., Biehl, M.: Adaptive relevance matrices in learning vector quantization. Neural Computation 21, 3532–3561 (2009)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    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(2), 256–266 (1997)CrossRefGoogle Scholar
  16. 16.
    Villmann, T., Haase, S.: Divergence based vector quantization. Neural Computation 23(5), 1343–1392 (2011)MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Villmann, T., Hammer, B., Schleif, F.-M., Geweniger, T., Herrmann, W.: Fuzzy classification by fuzzy labeled neural gas. Neural Networks 19, 772–779 (2006)MATHCrossRefGoogle Scholar
  18. 18.
    Villmann, T., Merényi, E., Hammer, B.: Neural maps in remote sensing image analysis. Neural Networks 16(3-4), 389–403 (2003)CrossRefGoogle Scholar
  19. 19.
    Villmann, T., Schleif, F.-M.: Functional vector quantization by neural maps. In: Chanussot, J. (ed.) Proceedings of First Workshop on Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS 2009), pp. 1–4. IEEE Press (2009) ISBN: 978-1-4244-4948-4Google Scholar
  20. 20.
    Villmann, T., Schleif, F.-M., Merenyi, E., Hammer, B.: Fuzzy Labeled Self-Organizing Map for Classification of Spectra. In: Sandoval, F., Prieto, A.G., Cabestany, J., Graña, M. (eds.) IWANN 2007. LNCS, vol. 4507, pp. 556–563. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  21. 21.
    Villmann, T., Seiffert, U., Schleif, F.-M., Brüß, C., Geweniger, T., Hammer, B.: Fuzzy Labeled Self-Organizing Map with Label-Adjusted Prototypes. In: Schwenker, F., Marinai, S. (eds.) ANNPR 2006. LNCS (LNAI), vol. 4087, pp. 46–56. Springer, Heidelberg (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Marika Kästner
    • 1
  • Thomas Villmann
    • 1
  1. 1.Computational Intelligence group at the Department for Mathematics/Natural & Computer SciencesUniversity of Applied Sciences MittweidaMittweidaGermany

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