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Nonmetric Grouping: Clusters and Cliques

Published online by Cambridge University Press:  01 January 2025

Edmund R. Peay
Edmund R. Peay*
Affiliation:
The Flinders University of South Australia
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Abstract

A class of related nonmetric (“monotone invariant”) hierarchical grouping methods is presented. The methods are defined in terms of generalized cliques, based on a systematically varying specification of the degree of indirectness of permitted relationships (i.e., degree of “chaining”). This approach to grouping is shown to provide a useful framework for grouping methods based on an a priori specification of the properties of the desired subsets, and includes a natural generalization for “complete linkage” and “single linkage” clustering, such as the methods of Johnson [1967]. The central feature of the class of methods is a simple iterative matrix operation on the original disparities (“inverse-proximities” or “dissimilarities”) matrix, and one of the methods also constitutes a very efficient single linkage clustering procedure.

Type
Original Paper
Information
Psychometrika , Volume 40 , Issue 3 , September 1975 , pp. 297 - 313
Copyright
Copyright © 1975 The Psychometric Society

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Footnotes

†

Part of the substantive work for this paper was done while the author was a graduate student at the University of Michigan and was supported by U.S.P.H.S. Grant NIH GM-01231-06. Some of the material was presented at the Meetings of the Midwestern Psychological Association, April, 1970. Gratitude for their helpful comments on an earlier version is expressed to C. H. Coombs and D. Cartwright.

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