Supervised Batch Neural Gas

  • Barbara Hammer
  • Alexander Hasenfuss
  • Frank-Michael Schleif
  • Thomas Villmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4087)


Recently, two extensions of neural gas have been proposed: a fast batch version of neural gas for data given in advance, and extensions of neural gas to learn a (possibly fuzzy) supervised classification. Here we propose a batch version for supervised neural gas training which allows to efficiently learn a prototype-based classification, provided training data are given beforehand. The method relies on a simpler cost function than online supervised neural gas and leads to simpler update formulas. We prove convergence of the algorithm in a general framework, which also incorporates supervised k-means and supervised batch-SOM, and which opens the way towards metric adaptation as well as application to proximity data not embedded in a real-vector space.


Cost Function Class Label Learning Vector Quantization Stochastic Gradient Descent Batch Optimization 
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.
    Bottou, L., Bengio, Y.: Convergence properties of the k-means algorithm. In: Tesauro, G., Touretzky, D.S., Leen, T.K. (eds.) NIPS 1994, pp. 585–592. MIT, Cambridge (1994)Google Scholar
  2. 2.
    Conan-Guez, B., Rossi, F., El Golli, A.: A fast algorithm for the self-organizing map on dissimilarity data. In: Workshop on Self-Organizing Maps, pp. 561–568 (2005)Google Scholar
  3. 3.
    Cottrell, M., Hammer, B., Hasenfuss, A., Villmann, T.: Batch and median neural gas. Neural Networks (to appear, 2006)Google Scholar
  4. 4.
    Crammer, K., Gilad-Bachrach, R., Navot, A., Tishby, N.: Margin analysis of the LVQ algorithm. In: NIPS 2002 (2002)Google Scholar
  5. 5.
    Gath, I., Geva, A.B.: Unsupervised optimal fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence 11(7), 773–781 (1989)CrossRefGoogle Scholar
  6. 6.
    Hammer, B., Strickert, M., Villmann, T.: Supervised neural gas with general similarity measure. Neural Processing Letters 21(1), 21–44 (2005)CrossRefGoogle Scholar
  7. 7.
    Hammer, B., Villmann, T.: Generalized relevance learning vector quantization. Neural Networks 15, 1059–1068 (2002)CrossRefGoogle Scholar
  8. 8.
    Heskes, T.: Self-organizing maps, vector quantization, and mixture modeling. IEEE Transactions on Neural Networks 12, 1299–1305 (2001)CrossRefGoogle Scholar
  9. 9.
    Kaski, S., Sinkkonen, J.: Principle of learning metrics for data analysis. Journal of VLSI Signal Processing, special issue on Machine Learning for Signal Processing 37: 177–188 (2004)Google Scholar
  10. 10.
    Kohonen, T.: Self-Organizing Maps. Springer, Heidelberg (1995)Google Scholar
  11. 11.
    Kohonen, T., Somervuo, P.: How to make large self-organizing maps for nonvectorial data. Neural Networks 15, 945–952 (2002)CrossRefGoogle Scholar
  12. 12.
    Martinetz, T., Berkovich, S.G., Schulten, K.J.: Neural-gas network for vector quantization and its application to time-series prediction. IEEE Transactions on Neural Networks 4, 558–569 (1993)CrossRefGoogle Scholar
  13. 13.
    Newman, D.J., Hettich, S., Blake, C.L., Merz, C.J.: UCI Repository of machine learning databases. University of California, Department of Information and Computer Science, Irvine, CA (1998),
  14. 14.
    Peltonen, J., Klami, A., Kaski, S.: Improved learning of Riemannian metrics for exploratory analysis. Neural Networks 17, 1087–1100 (2004)MATHCrossRefGoogle Scholar
  15. 15.
    Seo, S., Obermayer, K.: Self-organizing maps and clustering methods for matrix data. Neural Networks 17, 1211–1230 (2004)MATHCrossRefGoogle Scholar
  16. 16.
    Villmann, T., Hammer, B., Schleif, F., Geweniger, T., Herrmann, W.: Fuzzy classification by fuzzy labeled neural gas. Neural Networks (accepted, 2006)Google Scholar
  17. 17.
    Zhong, S., Ghosh, J.: A unified framework for model-based clustering. Journal of Machine Learning Research 4, 1001–1037 (2003)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Barbara Hammer
    • 1
  • Alexander Hasenfuss
    • 1
  • Frank-Michael Schleif
    • 2
  • Thomas Villmann
    • 3
  1. 1.Institute of Computer ScienceClausthal University of TechnologyClausthal-ZellerfeldGermany
  2. 2.Institute of Computer ScienceUniversity of LeipzigGermany
  3. 3.Clinic for PsychotherapyUniversity of LeipzigLeipzigGermany

Personalised recommendations