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An Examination of Procedures for Determining the Number of Clusters in a Data Set

Published online by Cambridge University Press:  01 January 2025

Glenn W. Milligan  and
Martha C. Cooper
Glenn W. Milligan*
Affiliation:
The Ohio State University
Martha C. Cooper
Affiliation:
The Ohio State University
*
Requests for reprints should be sent to Glenn W. Milligan, Faculty of Management Sciences, 301 Hagerty Hall, The Ohio State University, Columbus, OH 43210.
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Abstract

A Monte Carlo evaluation of 30 procedures for determining the number of clusters was conducted on artificial data sets which contained either 2, 3, 4, or 5 distinct nonoverlapping clusters. To provide a variety of clustering solutions, the data sets were analyzed by four hierarchical clustering methods. External criterion measures indicated excellent recovery of the true cluster structure by the methods at the correct hierarchy level. Thus, the clustering present in the data was quite strong. The simulation results for the stopping rules revealed a wide range in their ability to determine the correct number of clusters in the data. Several procedures worked fairly well, whereas others performed rather poorly. Thus, the latter group of rules would appear to have little validity, particularly for data sets containing distinct clusters. Applied researchers are urged to select one or more of the better criteria. However, users are cautioned that the performance of some of the criteria may be data dependent.

Keywords

classificationstopping rulesnumerical taxonomy
Type
Original Paper
Information
Psychometrika , Volume 50 , Issue 2 , June 1985 , pp. 159 - 179
Copyright
Copyright © 1985 The Psychometric Society

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Footnotes

The authors would like to express their appreciation to a number of individuals who provided assistance during the conduct of this research. Those who deserve recognition include Roger Blashfield, John Crawford, John Gower, James Lingoes, Wansoo Rhee, F. James Rohlf, Warren Sarle, and Tom Soon.

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