Skip to main content
SpringerLink
Log in

Fuzzy Neural Gas for Unsupervised Vector Quantization

  • Conference paper
Artificial Intelligence and Soft Computing (ICAISC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7267))

Included in the following conference series:

Abstract

In this paper we propose the combination of fuzzy c-means for clustering with neighborhood cooperativeness from the neural gas vector quantizer. The new approach avoids the sensitivity of fuzzy c-means with respect to initialization as it is known from neural gas compared to crisp c-means. Thereby, the neural gas paradigm of neighborhood offers a greater flexibility than those of the self-organizing map, which was combined with fuzzy c-means before. However, a careful reformulation of neighborhood has to be done to keep the validity of the convergence proof of this previous approach. We demonstrate the properties for an artificial as well as for real world data.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Backhaus, A., Bollenbeck, F., Seiffert, U.: High-throughput quality control of coffee varieties and blends by artificial neural networks and hyperspectral imaging. In: Proceedings of the 1st International Congress on Cocoa, Coffee and Tea, CoCoTea 2011, accepted for publication (2011)

    Google Scholar 

  2. Backhaus, A., Bollenbeck, F., Seiffert, U.: Robust classification of the nutrition state in crop plants by hyperspectral imaging and artificial neural networks. In: Proceedings of the 3rd IEEE Workshop on Hyperspectral Imaging and Signal Processing: Evolution in Remote Sensing WHISPERS 2011, p. 9. IEEE Press (2011)

    Google Scholar 

  3. Bezdek, J.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum, New York (1981)

    MATH  Google Scholar 

  4. Bezdek, J., Hathaway, R., Windham, M.: Numerical comparison of RFCM and AP algorithms for clustering relational data. Pattern Recognition 24, 783–791 (1991)

    Google Scholar 

  5. Bezdek, J.C., Pal, N.R.: A note on self-organizing semantic maps. IEEE Transactions on Neural Networks 6(5), 1029–1036 (1995)

    Article  Google Scholar 

  6. Bezdek, J.C., Pal, N.R.: Two soft relatives of learning vector quantization. Neural Networks 8(5), 729–743 (1995)

    Article  Google Scholar 

  7. Bezdek, J.C., Tsao, E.C.K., Pal, N.R.: Fuzzy Kohonen clustering networks. In: Proc. IEEE International Conference on Fuzzy Systems, pp. 1035–1043. IEEE Service Center, Piscataway (1992)

    Chapter  Google Scholar 

  8. Duda, R., Hart, P.: Pattern Classification and Scene Analysis. Wiley, New York (1973)

    MATH  Google Scholar 

  9. Dunn, J.: A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters. Journal of Cybernetics 3, 32–57 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  10. Geweniger, T., Zühlke, D., Hammer, B., Villmann, T.: Median fuzzy c-means for clustering dissimilarity data. Neurocomputing 73(7-9), 1109–1116 (2010)

    Article  Google Scholar 

  11. Ghorbani, M.: Maximum entropy-based fuzzy clustering by using L 1 norm space. Turkish Journal of Mathematics 29(4), 431–438 (2005)

    MathSciNet  MATH  Google Scholar 

  12. Graepel, T., Burger, M., Obermayer, K.: Self-organizing maps: generalizations and new optimization techniques. Neurocomputing 21(1-3), 173–190 (1998)

    Article  MATH  Google Scholar 

  13. Grahn, H., Geladi, P. (eds.): Techniques and Applications of Hyperspectral Image Analysis. Wiley (2007)

    Google Scholar 

  14. Hammer, B., Villmann, T.: Generalized relevance learning vector quantization. Neural Networks 15(8-9), 1059–1068 (2002)

    Article  Google Scholar 

  15. Ichihashi, H., Honda, K.: Application of kernel trick to fuzzy c-means with regularization by K-L information. Journal of Advanced Computational Intelligence and Intelligent Informatics 8(6), 566–572 (2004)

    Google Scholar 

  16. Inokuchi, R., Miyamoto, S.: Fuzzy c-means algorithms using Kullback-Leibler divergence and Hellinger distance based on multinomial manifold. Journal of Advanced Computational Intelligence and Intelligent Informatics 12(5), 443–447 (2008)

    Google Scholar 

  17. Kohonen, T.: Self-Organizing Maps. Springer Series in Information Sciences, vol. 30. Springer, Heidelberg (1995) (Second Extended Edition 1997)

    Google Scholar 

  18. Krishnapuram, R., Keller, J.: A possibilistic approach to clustering. IEEE Transactions on Fuzzy Systems 1(4), 98–110 (1993)

    Article  Google Scholar 

  19. Linde, Y., Buzo, A., Gray, R.: An algorithm for vector quantizer design. IEEE Transactions on Communications 28, 84–95 (1980)

    Article  Google Scholar 

  20. 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)

    Article  Google Scholar 

  21. Miyamoto, S., Ichihashi, H., Honda, K.: Algorithms for Fuzzy Clustering. Studies in Fuzziness and Soft Computing, vol. 229. Springer, Heidelberg (2008)

    MATH  Google Scholar 

  22. Pal, N., Pal, K., Keller, J., Bezdek, J.: A possibilistic fuzzy c-means clustering algorithm. IEEE Transactions on Fuzzy Systems 13(4), 517–530 (2005)

    Article  MathSciNet  Google Scholar 

  23. Pal, N.R., Bezdek, J.C., Tsao, E.C.K.: Generalized clustering networks and Kohonen’s self-organizing scheme. IEEE Transactions on Neural Networks 4(4), 549–557 (1993)

    Article  Google Scholar 

  24. Pal, N.R., Bezdek, J.C., Tsao, E.C.K.: Errata to Generalized clustering networks and Kohonen’s self-organizing scheme. IEEE Transactions on Neural Networks 6(2), 521–521 (1995)

    Google Scholar 

  25. Pekalska, E., Duin, R.: The Dissimilarity Representation for Pattern Recognition: Foundations and Applications. World Scientific (2006)

    Google Scholar 

  26. Seiffert, U., Bollenbeck, F., Mock, H.-P., Matros, A.: Clustering of crop phenotypes by means of hyperspectral signatures using artificial neural networks. In: Proceedings of the 2nd IEEE Workshop on Hyperspectral Imaging and Signal Processing: Evolution in Remote Sensing WHISPERS 2010, pp. 31–34. IEEE Press (2010)

    Google Scholar 

  27. Tsao, E., Bezdek, J., Pal, N.: Fuzzy Kohonen clustering networks. Pattern Recognition 27(5), 757–764 (1994)

    Article  Google Scholar 

  28. 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)

    Article  Google Scholar 

  29. Villmann, T., Geweniger, T., Kästner, M., Lange, M.: Theory of fuzzy neural gas for unsupervised vector quantization. Machine Learning Reports 5(MLR-06-2011), 27–46 (2011), http://www.techfak.uni-bielefeld.de/~fschleif/mlr/mlr_06_2011.pdf ISSN:1865-3960

    Google Scholar 

  30. Villmann, T., Haase, S.: Divergence based vector quantization. Neural Computation 23(5), 1343–1392 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  31. Villmann, T., Hammer, B., Biehl, M.: Some Theoretical Aspects of the Neural Gas Vector Quantizer. In: Biehl, M., Hammer, B., Verleysen, M., Villmann, T. (eds.) Similarity-Based Clustering. LNCS (LNAI), vol. 5400, pp. 23–34. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  32. Xie, X., Beni, G.: A validity measure for fuzzy clustering. IEEE Transactions on Pat 13(8), 841–847 (1991)

    Article  Google Scholar 

  33. Yasuda, M., Furuhashi, T.: Fuzzy entropy based fuzzy-c-means clustering with deterministic and simulated annealing methods. IEICE Transactions on Information and Systems E92-D, 1232–1239 (2009)

    Article  Google Scholar 

  34. Zalik, K., Zalik, B.: Validity index for clusters of different sizes and densities. Pattern Recognition Letters 32, 221–2234 (2011)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computational Intelligence Group at the Department for Mathematics/Natural & Computer Sciences, University of Applied Sciences Mittweida, Mittweida, Germany

    Thomas Villmann, Tina Geweniger, Marika Kästner & Mandy Lange

Authors
  1. Thomas Villmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tina Geweniger
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marika Kästner
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mandy Lange
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Częstochowa University of Technology, Armii Krajowej 36, 42-200, Częstochowa, Poland

    Leszek Rutkowski , Marcin Korytkowski  & Rafał Scherer ,  & 

  2. AGH University of Science and Technology, Mickiewicza 30, 30-059, Kraków, Poland

    Ryszard Tadeusiewicz

  3. Department of Electrical Engineering and Computer Sciences, Computer Science Division, University of California Berkeley, 94720-1776, Berkeley, CA, USA

    Lotfi A. Zadeh

  4. Computational Intelligence Laboratory, Electrical and Computer Engineering, University of Louisville, 405 Lutz Hall, 40292, Louisville, KY, USA

    Jacek M. Zurada

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Villmann, T., Geweniger, T., Kästner, M., Lange, M. (2012). Fuzzy Neural Gas for Unsupervised Vector Quantization. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2012. Lecture Notes in Computer Science(), vol 7267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29347-4_41

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-29347-4_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29346-7

  • Online ISBN: 978-3-642-29347-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation