Skip to main content

Kernel Methods for Clustering

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3931))

Abstract

Kernel Methods are algorithms that implicitly perform, by replacing the inner product with an appropriate Mercer Kernel, a nonlinear mapping of the input data to a high dimensional Feature Space. In this paper, we describe a Kernel Method for clustering. The algorithm compares better with popular clustering algorithms, namely K-Means, Neural Gas, Self Organizing Maps, on a synthetic dataset and three UCI real data benchmarks, IRIS data, Wisconsin breast cancer database, Spam database.

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

Buying options

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ben-Hur, A., Horn, D., Siegelmann, H.T., Vapnik, V.: Support Vector Clustering. Journal of Machine Learning Research 2, 125–137 (2001)

    MATH  Google Scholar 

  2. Berg, C., Christensen, J.P.R., Ressel, P.: Harmonic analysis on semigroups. Springer, New York (1984)

    Book  MATH  Google Scholar 

  3. Bishop, C.: Neural Networks for Pattern Recognition. Cambridge University Press, Cambridge (1995)

    MATH  Google Scholar 

  4. Camastra, F., Verri, A.: A novel Kernel Method for Clustering. IEEE Transaction on Pattern Analysis and Machine Intelligence 27(5), 801–805 (2005)

    Article  Google Scholar 

  5. Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  6. Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum Likelihood from Incomplete Data via the EM algorithm. Journal Royal Statistical Society 39(1), 1–38 (1977)

    MathSciNet  MATH  Google Scholar 

  7. Fisher, R.A.: The Use of Multiple Measurements in Taxonomic Problems. Annals of Eugenics 7, 179–188 (1936)

    Article  Google Scholar 

  8. Girolami, M.: Mercer kernel based clustering in feature space. IEEE Transactions on Neural Networks 13(3), 780–784 (2002)

    Article  Google Scholar 

  9. Gray, R.M.: Vector Quantization and Signal Compression. Kluwer Academic Press, Dordrecht (1992)

    MATH  Google Scholar 

  10. Jain, A.K., Murty, M.N., Flynn, P.J.: Data Clustering: A review. ACM Comput. Surveys 31(3), 264–323 (1999)

    Article  Google Scholar 

  11. Kohonen, T.: Self-Organized formation of topologically correct feature maps. Biological Cybernetics 43(1), 59–69 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kohonen, T.: Self-Organizing Map. Springer, New York (1997)

    Book  MATH  Google Scholar 

  13. Lloyd, S.P.: An algorithm for vector quantizer design. IEEE Transaction on Communications 28(1), 84–95 (1982)

    Google Scholar 

  14. Mangasarian, O.L., Wolberg, W.H.: Cancer diagnosis via linear programming. SIAM News 23(5), 1–18 (1990)

    Google Scholar 

  15. Martinetz, T.E., Schulten, K.J.: A neural gas network learns topologies. Artificial Neural Networks, 397–402 (1991)

    Google Scholar 

  16. Martinetz, T.E., Schulten, K.J.: Neural-gas network for vector quantization and its application to time-series prediction. IEEE Transaction on Neural Networks 4(4), 558–569 (1993)

    Article  Google Scholar 

  17. Meila, M.: Comparing Clusterings, UW Technical Report 418 (2003)

    Google Scholar 

  18. Ng, A.Y., Jordan, M.I., Weiss, Y.: On Spectral Clustering: Analysis and an algorithm. Advances in Neural Information Processing Systems 14, 849–856 (2001)

    Google Scholar 

  19. Schölkopf, B., Smola, A.J., Müller, K.-R.: Nonlinear component analysis as a kernel eigenvalue problem, Technical Report No. 44, Max Planck Institut für biologische Kybernetik, Tübingen (1996)

    Google Scholar 

  20. Schölkopf, B., Williamson, R.C., Smola, A.J., Shawe-Taylor, J., Platt, J.: Support vector method for novelty detection. Advances in Neural Information Processing Systems 12, 526–532 (1999)

    Google Scholar 

  21. Tax, D.M.J., Duin, R.P.W.: Support Vector domain description. Pattern Recognition Letters 20(11-13), 1191–1199 (1999)

    Article  Google Scholar 

  22. Vapnik, V.: Statistical Learning Theory. Wiley, New York (1998)

    MATH  Google Scholar 

  23. Wolberg, W.H., Mangasarian, O.L.: Multisurface method of pattern separation for medical diagnosis applied to breast citology. In: Proceedings of the National Academy of Sciences, USA, vol. 87, pp. 9193–9196 (1990)

    Google Scholar 

  24. Wu, C.F.J.: On the convergence properties of the em algorithm. The Annals of Statistics 11(1), 95–103 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  25. Yu, K., Ji, L., Zhang, X.: Kernel Nearest-Neighbor Algorithm. Neural Processing Letters 15(2), 147–156 (2002)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Camastra, F. (2006). Kernel Methods for Clustering. In: Apolloni, B., Marinaro, M., Nicosia, G., Tagliaferri, R. (eds) Neural Nets. WIRN NAIS 2005 2005. Lecture Notes in Computer Science, vol 3931. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11731177_1

Download citation

  • DOI: https://doi.org/10.1007/11731177_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-33183-4

  • Online ISBN: 978-3-540-33184-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics