Agnostic Clustering

  • Maria Florina Balcan
  • Heiko Röglin
  • Shang-Hua Teng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5809)

Abstract

Motivated by the principle of agnostic learning, we present an extension of the model introduced by Balcan, Blum, and Gupta [3] on computing low-error clusterings. The extended model uses a weaker assumption on the target clustering, which captures data clustering in presence of outliers or ill-behaved data points. Unlike the original target clustering property, with our new property it may no longer be the case that all plausible target clusterings are close to each other. Instead, we present algorithms that produce a small list of clusterings with the guarantee that all clusterings satisfying the assumption are close to some clustering in the list, proving both upper and lower bounds on the length of the list needed.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Jain, K., Mahdian, M., Saberi, A.: A new greedy approach for facility location problems. In: STOC (2002)Google Scholar
  2. 2.
    Charikar, M., Guha, S., Tardos, E., Shmoys, D.B.: A constant-factor approximation algorithm for the k-median problem. In: Proceedings of the Thirty-First Annual ACM Symposium on Theory of Computing (1999)Google Scholar
  3. 3.
    Balcan, M.F., Blum, A., Gupta, A.: Approximate clustering without the approximation. In: Proceedings of the ACM-SIAM Symposium on Discrete Algorithms (2009)Google Scholar
  4. 4.
    Balcan, M.F., Blum, A., Vempala, S.: A discrimantive framework for clustering via similarity functions. In: Proceedings of the 40th ACM Symposium on Theory of Computing (2008)Google Scholar
  5. 5.
    Balcan, M.F., Braverman, M.: Finding low error clusterings. In: Proceedings of the 22nd Annual Conference on Learning Theory (2009)Google Scholar
  6. 6.
    Kearns, M.J., Schapire, R.E., Sellie, L.M.: Toward efficient agnostic learning. Machine Learning Journal (1994)Google Scholar
  7. 7.
    Kanungo, T., Mount, D.M., Netanyahu, N.S., Piatko, C.D., Silverman, R., Wu, A.Y.: A local search approximation algorithm for k -means clustering. In: Proceedings of the Eighteenth Annual Symposium on Computational Geometry (2002)Google Scholar
  8. 8.
    Valiant, L.: A theory of the learnable. Commun. ACM 27(11), 1134–1142 (1984)CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Maria Florina Balcan
    • 1
  • Heiko Röglin
    • 2
  • Shang-Hua Teng
    • 3
  1. 1.College of ComputingGeorgia Institute of TechnologyUSA
  2. 2.Department of Quantitative EconomicsMaastricht UniversityNetherlands
  3. 3.Computer Science DepartmentUniversity of Southern CaliforniaUSA

Personalised recommendations