Soft Competitive Learning for Large Data Sets

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 185)

Abstract

Soft competitive learning is an advanced k-means like clustering approach overcoming some severe drawbacks of k-means, like initialization dependence and sticking to local minima. It achieves lower distortion error than k-means and has shown very good performance in the clustering of complex data sets, using various metrics or kernels. While very effective, it does not scale for large data sets which is even more severe in case of kernels, due to a dense prototype model. In this paper, we propose a novel soft-competitive learning algorithm using core-sets, significantly accelerating the original method in practice with natural sparsity. It effectively deals with very large data sets up to multiple million points. Our method provides also an alternativefastkernelization of soft-competitive learning. In contrast to many other clustering methods the obtained model is based on only few prototypes and shows natural sparsity. It is the first natural sparse kernelized soft competitive learning approach. Numerical experiments on synthetical and benchmark data sets show the efficiency of the proposed method.

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References

  1. 1.
    Badoiu, M., Har-Peled, S., Indyk, P.: Approximate clustering via core-sets. In: STOC, pp. 250–257 (2002)Google Scholar
  2. 2.
    Blake, C., Merz, C.: UCI repository of machine learning databases. Department of Information and Computer Science. University of California, Irvine, CA (1998), http://www.ics.uci.edu/~mlearn/MLRepository.html Google Scholar
  3. 3.
    Camastra, F., Verri, A.: A Novel Kernel Method for Clustering. IEEE TPAMI 27(5), 801–805 (2005)CrossRefGoogle Scholar
  4. 4.
    Filippone, M., Camastra, F., Massulli, F., Rovetta, S.: A survey of kernel and spectral methods for clustering. Pattern Recognition 41, 176–190 (2008)MATHCrossRefGoogle Scholar
  5. 5.
    Frénay, B., Verleysen, M.: Parameter-insensitive kernel in extreme learning for non-linear support vector regression. Neurocomputing 74(16), 2526–2531 (2011)CrossRefGoogle Scholar
  6. 6.
    Frey, B., Dueck, D.: Clustering by message passing between data points. Science 315, 972–976 (2007)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Hammer, B., Hasenfuss, A.: Topographic mapping of large dissimilarity data sets. Neural Computation 22(9), 2229–2284 (2010)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Labusch, K., Barth, E., Martinetz, T.: Soft-competitive learning of sparse codes and its application to image reconstruction. Neurocomputing 74(9), 1418–1428 (2011)CrossRefGoogle Scholar
  9. 9.
    Liang, C., Xiao-Ming, D., Sui-Wu, Z., Yong-Qing, W.: Scaling up kernel grower clustering method for large data sets via core-sets. Acta Automatica Sinica 34(3), 376–382 (2008)MATHGoogle Scholar
  10. 10.
    Martinetz, T., Berkovich, S., Schulten, K.: Neural Gas Network for Vector Quantization and its Application to Time-Series Prediction. IEEE Transactions on Neural Networks 4(4), 558–569 (1993)CrossRefGoogle Scholar
  11. 11.
    Qin, A.K., Suganthan, P.N.: A novel kernel prototype-based learning algorithm. In: Proc. of ICPR 2004, pp. 2621–2624 (2004)Google Scholar
  12. 12.
    Schleif, F.M., Villmann, T., Hammer, B., Schneider, P.: Effcient kernelized prototype-based classification. Journal of Neural Systems 21(6), 443–457 (2011)CrossRefGoogle 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.
    Schölkopf, B., Smola, A.J.: Learning with Kernels. MIT Press (2002)Google Scholar
  15. 15.
    Schölkopf, B., Smola, A.J., Müller, K.R.: Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation 10(5), 1299–1319 (1998)CrossRefGoogle Scholar
  16. 16.
    Smola, A.J., Schölkopf, B.: Sparse greedy matrix approximation for machine learning. In: Langley, P. (ed.) ICML, pp. 911–918. Morgan Kaufmann (2000)Google Scholar
  17. 17.
    Tax, D.M.J., Duin, R.P.W.: Support vector domain description. Pattern Recognition Letters 20(11-13), 1191–1199 (1999)CrossRefGoogle Scholar
  18. 18.
    Tsang, I.W., Kwok, J.T., Cheung, P.M.: Core vector machines: Fast svm training on very large data sets. Journal of Machine Learning Research 6, 363–392 (2005)MathSciNetMATHGoogle Scholar
  19. 19.
    Tzortzis, G., Likas, A.: The global kernel k-means clustering algorithm. In: IJCNN, pp. 1977–1984. IEEE (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Frank-Michael Schleif
    • 1
  • Xibin Zhu
    • 1
  • Barbara Hammer
    • 1
  1. 1.CITEC Centre of ExcellenceBielefeld UniversityBielefeldGermany

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