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Order-Constrained Solutions in K-Means Clustering: Even Better Than Being Globally Optimal

Published online by Cambridge University Press:  01 January 2025

Douglas Steinley  and
Lawrence Hubert
Douglas Steinley*
Affiliation:
University of Missouri-Columbia
Lawrence Hubert
Affiliation:
University of Illinois, Urbana-Champaign
*
Requests for reprints should be sent to Douglas Steinley, Department of Psychological Sciences, University of Missouri-Columbia, 210 McAlester Hall, Columbia, MO 65211, USA. E-mail: steinleyd@missouri.edu
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Abstract

This paper proposes an order-constrained K-means cluster analysis strategy, and implements that strategy through an auxiliary quadratic assignment optimization heuristic that identifies an initial object order. A subsequent dynamic programming recursion is applied to optimally subdivide the object set subject to the order constraint. We show that although the usual K-means sum-of-squared-error criterion is not guaranteed to be minimal, a true underlying cluster structure may be more accurately recovered. Also, substantive interpretability seems generally improved when constrained solutions are considered. We illustrate the procedure with several data sets from the literature.

Keywords

K-means cluster analysisdynamic programmingquadratic assignmentconstrained optimizationmulticriterion optimization
Type
Theory and Methods
Information
Psychometrika , Volume 73 , Issue 4 , December 2008 , pp. 647 - 664
Copyright
Copyright © 2008 The Psychometric Society

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