Clustering with Entropy-like k-means Algorithms | Center for Big Data Analytics

Abstract: 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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Clustering with Entropy-like k-means Algorithms (pdf, software)
M. Teboulle, P. Berkhin, I. Dhillon, Y. Guan, J. Kogan.
Grouping Multidimensional Data – Recent Advances in Clustering, pp. 127-160, January 2005.

Bibtex:
@book{teboulle2005clustering, author = "M. Teboulle AND P. Berkhin AND Inderjit S. Dhillon AND Yuqiang Guan AND J. Kogan", title = "Clustering with Entropy-like k-means Algorithms", booktitle = "Grouping Multidimensional Data – Recent Advances in Clustering", publisher = "Springer-Verlag", publisher = "Springer-Verlag", page = "127–160", year = "2005", month = "jan", abstract = "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." }