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Convexity-based clustering criteria: theory, algorithms, and applications in statistics

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  • Hans-Hermann Bock

    (Aachen University of Technology)

Abstract

. This paper deals with the construction of optimum partitions ${\cal B} = (B_1,...,B_m)$ of $I\hspace{-4.0pt}R^p$ for a clustering criterion which is based on a convex function of the class centroids $E[X\vert X\in B_i]$ as a generalization of the classical SSQ clustering criterion for n data points. We formulate a dual optimality problem involving two sets of variables and derive a maximum-support-plane (MSP) algorithm for constructing a (sub-)optimum partition as a generalized k-means algorithm. We present various modifications of the basic criterion and describe the corresponding MSP algorithm. It is shown that the method can also be used for solving optimality problems in classical statistics (maximizing Csiszár’s $\phi$ -divergence) and for simultaneous classification of the rows and columns of a contingency table.

Suggested Citation

  • Hans-Hermann Bock, 2004. "Convexity-based clustering criteria: theory, algorithms, and applications in statistics," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 12(3), pages 293-317, February.
    • Handle: RePEc:spr:stmapp:v:12:y:2004:i:3:d:10.1007_s10260-003-0069-8
    DOI: 10.1007/s10260-003-0069-8
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    Cited by:

    1. Gérard Govaert & Mohamed Nadif, 2018. "Mutual information, phi-squared and model-based co-clustering for contingency tables," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(3), pages 455-488, September.

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