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Hierarchical Clustering Schemes

Published online by Cambridge University Press:  01 January 2025

Stephen C. Johnson
Stephen C. Johnson*
Affiliation:
Bell Telephone Laboratories, Murray Hill, New Jersey
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Abstract

Techniques for partitioning objects into optimally homogeneous groups on the basis of empirical measures of similarity among those objects have received increasing attention in several different fields. This paper develops a useful correspondence between any hierarchical system of such clusters, and a particular type of distance measure. The correspondence gives rise to two methods of clustering that are computationally rapid and invariant under monotonic transformations of the data. In an explicitly defined sense, one method forms clusters that are optimally “connected,” while the other forms clusters that are optimally “compact.”

Type
Original Paper
Information
Psychometrika , Volume 32 , Issue 3 , September 1967 , pp. 241 - 254
Copyright
Copyright © 1967 The Psychometric Society

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Footnotes

*

I am indebted to R. N. Shepard and J. D. Carroll for many stimulating discussions about this work, and for aid in preparing this paper.

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