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Clustering N Objects into K Groups under Optimal Scaling of Variables

Published online by Cambridge University Press:  01 January 2025

Stef van Buuren  and
Willem J. Heiser
Stef van Buuren*
Affiliation:
Department of Psychonomy, University of Utrecht
Willem J. Heiser
Affiliation:
Department of Data Theory, University of Leiden
*
Requests for reprints should be sent to Stef van Buuren, Department of Psychonomy, Trans II 17.25, Heidelberglaan 2, 3584 CS Utrecht, THE NETHERLANDS.
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Abstract

We propose a method to reduce many categorical variables to one variable with k categories, or stated otherwise, to classify n objects into k groups. Objects are measured on a set of nominal, ordinal or numerical variables or any mix of these, and they are represented as n points in p-dimensional Euclidean space. Starting from homogeneity analysis, also called multiple correspondence analysis, the essential feature of our approach is that these object points are restricted to lie at only one of k locations. It follows that these k locations must be equal to the centroids of all objects belonging to the same group, which corresponds to a sum of squared distances clustering criterion. The problem is not only to estimate the group allocation, but also to obtain an optimal transformation of the data matrix. An alternating least squares algorithm and an example are given.

Keywords

homogeneity analysiscluster analysisvariable importanceGROUPALS
Type
Original Paper
Information
Psychometrika , Volume 54 , Issue 4 , December 1989 , pp. 699 - 706
Copyright
Copyright © 1989 The Psychometric Society

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Footnotes

The authors thank Eveline Kroezen and Teije Euverman for their comments on a previous draft of this paper.

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