Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-08T12:11:42.091Z Has data issue: false hasContentIssue false
  • English
  • Français

Ultrametric Hierarchical Clustering Algorithms

Published online by Cambridge University Press:  01 January 2025

Glenn W. Milligan
Glenn W. Milligan*
Affiliation:
The Ohio State University
*
Requests for reprints should be sent to Glenn W. Milligan, 356 Hagerty Hall, Faculty of Management Sciences, The Ohio State University, Columbus, Ohio 43210.
Get access Rights & Permissions [Opens in a new window]

Abstract

Johnson has shown that the single linkage and the complete linkage hierarchical clustering algorithms induce a metric on the data known as the ultrametric. Through the use of the Lance and Williams recurrence formula, Johnson's proof is extended to four other common clustering algorithms. It is also noted that two additional methods produce hierarchical structures which can violate the ultrametric inequality.

Type
Notes And Comments
Information
Psychometrika , Volume 44 , Issue 3 , September 1979 , pp. 343 - 346
Copyright
Copyright © 1979 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderberg, M. R. Cluster analysis for applications, 1973, New York: Academic Press.Google Scholar
Cormack, R. M. A review of classification. Journal of the Royal Statistical Society, 1971, 134, 321–367.CrossRefGoogle Scholar
D'Andrade, R. U-statistic hierarchical clustering. Psychometrika, 1978, 43, 59–68.CrossRefGoogle Scholar
Hubert, L. J. Monotone invariant clustering procedures. Psychometrika, 1973, 38, 47–62.CrossRefGoogle Scholar
Jardine, N., & Sibson, R. Mathematical taxonomy, 1971, New York: Wiley.Google Scholar
Johnson, S. C. Hierarchical clustering schemes. Psychometrika, 1967, 32, 241–254.CrossRefGoogle ScholarPubMed
Lance, G. N., & Williams, W. T. A generalized sorting strategy for computer classification. Nature, 1966, 212, 218–218.CrossRefGoogle Scholar
Lance, G. N., & Williams, W. T. A general theory of classificatory sorting strategies: I. Hierarchical systems. Computer Journal, 1967, 9, 373–380.CrossRefGoogle Scholar
Williams, W. T., Lance, G. N., Dale, M. B., & Clifford, H. T. Controversy concerning the criteria for taxonometric strategies. Computer Journal, 1971, 14, 162–165.CrossRefGoogle Scholar