Application of the cross-entropy method to clustering and vector quantization

Authors:
Dirk P. Kroese;Reuven Y. Rubinstein;Thomas Taimre
Affiliations:
Department of Mathematics, The University of Queensland, Brisbane, Australia 4072;Faculty of Industrial Engineering and Management, Technion, Haifa, Israel;Department of Mathematics, The University of Queensland, Brisbane, Australia 4072
Venue:
Journal of Global Optimization
Year:
2007

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Abstract

We apply the cross-entropy (CE) method to problems in clustering and vector quantization. The CE algorithm for clustering involves the following iterative steps: (a) generate random clusters according to a specified parametric probability distribution, (b) update the parameters of this distribution according to the Kullback---Leibler cross-entropy. Through various numerical experiments, we demonstrate the high accuracy of the CE algorithm and show that it can generate near-optimal clusters for fairly large data sets. We compare the CE method with well-known clustering and vector quantization methods such as K-means, fuzzy K-means and linear vector quantization, and apply each method to benchmark and image analysis data.