Skip to main content

Generalized Clustering via Kernel Embeddings

  • Conference paper
KI 2009: Advances in Artificial Intelligence (KI 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5803))

Included in the following conference series:

Abstract

We generalize traditional goals of clustering towards distinguishing components in a non-parametric mixture model. The clusters are not necessarily based on point locations, but on higher order criteria. This framework can be implemented by embedding probability distributions in a Hilbert space. The corresponding clustering objective is very general and relates to a range of common clustering concepts.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

  • Aghagolzadeh, M., Soltanian-Zadeh, H., Araabi, B., Aghagolzadeh, A.: A hierarchical clustering based on maximizing mutual information. In: ICIP (2007)

    Google Scholar 

  • Arora, S., Kannan, R.: Learning mixtures of arbitrary Gaussians. In: STOC (2001)

    Google Scholar 

  • Chaudhuri, K., Rao, S.: Beyond Gaussians: Spectral methods for learning mixtures of heavy-tailed distributions. In: COLT (2008)

    Google Scholar 

  • Erdogmus, D., Principe, J.C.: From linear adaptive filtering to nonlinear information processing. IEEE Signal Processing Magazine 23(6), 14–33 (2006)

    Article  Google Scholar 

  • Fuglede, B., Topsøe, F.: Jensen-Shannon divergence and Hilbert space embedding. In: Proc. of the Int. Symp. on Information Theory, ISIT (2004)

    Google Scholar 

  • Gokcay, E., Principe, J.C.: Information theoretic clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(2), 158–170 (2002)

    Article  Google Scholar 

  • Gretton, A., Bousquet, O., Smola, A., Schölkopf, B.: Measuring statistical dependence with Hilbert-Schmidt norms. In: Jain, S., Simon, H.U., Tomita, E. (eds.) ALT 2005. LNCS (LNAI), vol. 3734, pp. 63–77. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  • Gretton, A., Borgwardt, K.M., Rasch, M., Schölkopf, B., Smola, A.: A kernel method for the two-sample problem. In: NIPS (2006)

    Google Scholar 

  • Gretton, A., Borgwardt, K., Rasch, M., Schölkopf, B., Smola, A.: A kernel method for the two-sample problem. Tech. Report 157, MPI for Biol. Cyb. (2008)

    Google Scholar 

  • Jenssen, R., Erdogmus, D., Principe, J., Eltoft, T.: The laplacian pdf distance: a cost function for clustering in a kernel feature space. In: NIPS (2004)

    Google Scholar 

  • Lin, J.: Divergence measures based on the Shannon entropy. IEEE Transaction on Information Theory 37(1) (1991)

    Google Scholar 

  • Newman, M.E.J., Girvan, M.: Finding and evaluating community structure in networks. Physical review E 69 (2004)

    Google Scholar 

  • Renyi, A.: On measures of entropy and information. In: Proc. Fourth Berkeley Symp. Math., Statistics and Probability, pp. 547–561 (1960)

    Google Scholar 

  • Rose, K.: A mapping approach to rate-distortion computation and analysis. IEEE Transactions on Information Theory 40(6), 1939–1952 (1994)

    Article  MATH  Google Scholar 

  • Song, L., Smola, A., Gretton, A., Borgwardt, K.: A dependence maximization view of clustering. In: 24th International Conference on Machine Learning, ICML (2007)

    Google Scholar 

  • Sriperumbudur, B.K., Gretton, A., Fukumizu, K., Lanckriet, G., Schölkopf, B.: Injective Hilbert space embeddings of probability measures. In: COLT (2008)

    Google Scholar 

  • Wächter, A., Biegler, L.T.: On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Mathematical Programming 106(1), 25–57 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • Xu, L., Neufeld, J., Larson, B., Schuurmans, D.: Maximum margin clustering. In: NIPS (2005)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Jegelka, S., Gretton, A., Schölkopf, B., Sriperumbudur, B.K., von Luxburg, U. (2009). Generalized Clustering via Kernel Embeddings. In: Mertsching, B., Hund, M., Aziz, Z. (eds) KI 2009: Advances in Artificial Intelligence. KI 2009. Lecture Notes in Computer Science(), vol 5803. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04617-9_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-04617-9_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04616-2

  • Online ISBN: 978-3-642-04617-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics