, Volume 50, Issue 2, pp 159–179

An examination of procedures for determining the number of clusters in a data set

  • Glenn W. Milligan
  • Martha C. Cooper

DOI: 10.1007/BF02294245

Cite this article as:
Milligan, G.W. & Cooper, M.C. Psychometrika (1985) 50: 159. doi:10.1007/BF02294245


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.

Key words

classification stopping rules numerical taxonomy 

Copyright information

© The Psychometric Society 1985

Authors and Affiliations

  • Glenn W. Milligan
    • 1
  • Martha C. Cooper
    • 1
  1. 1.Faculty of Management SciencesThe Ohio State UniversityColumbus

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