Grouping Multidimensional Data

pp 127-160

Clustering with Entropy-Like k-Means Algorithms

  • M. TeboulleAffiliated withSchool of Mathematical Sciences, Tel Aviv University
  • , P. BerkhinAffiliated withYahoo!
  • , I. DhillonAffiliated withDepartment of Computer Science, University of Texas
  • , Y. GuanAffiliated withDepartment of Computer Science, University of Texas
  • , J. KoganAffiliated withDepartment of Mathematics and Statistics, University of MarylandDepartment of Computer Science and Electrical Engineering, University of Maryland

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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.