Clustering with Entropy-Like k-Means Algorithms

  • M. Teboulle
  • P. Berkhin
  • I. Dhillon
  • Y. Guan
  • J. Kogan

Summary

The aim of this chapter is to demonstrate that many results attributed to the classical k-means clustering algorithm with the squared Euclidean distance can be extended to many other distance-like functions. We focus on entropy-like distances based on Bregman [88] and Csiszar [119] divergences, which have previously been shown to be useful in various optimization and clustering contexts. Further, the chapter reviews various versions of the classical k-means and BIRCH clustering algorithms with squared Euclidean distance and considers modifications of these algorithms with the proposed families of distance-like functions. Numerical experiments with some of these modifications are reported.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • M. Teboulle
    • 1
  • P. Berkhin
    • 2
  • I. Dhillon
    • 3
  • Y. Guan
    • 3
  • J. Kogan
    • 4
    • 5
  1. 1.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael
  2. 2.Yahoo!SunnyvaleUSA
  3. 3.Department of Computer ScienceUniversity of TexasAustinUSA
  4. 4.Department of Mathematics and StatisticsUniversity of MarylandBaltimore County, BaltimoreUSA
  5. 5.Department of Computer Science and Electrical EngineeringUniversity of MarylandBaltimore County, BaltimoreUSA

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