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Some Extensions of Johnson's Hierarchical Clustering Algorithms

Published online by Cambridge University Press:  01 January 2025

Lawrence Hubert
Lawrence Hubert*
Affiliation:
University of Wisconsin
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Abstract

Considerable attention has been given in the psychological literature to techniques of data reduction that partition a set of objects into optimally homogeneous groups. This paper is an attempt to extend the hierarchical partitioning algorithms proposed by Johnson and to emphasize a general connection between these clustering procedures and the mathematical theory of lattices. A goodness-of-fit statistic is first proposed that is invariant under monotone increasing transformations of the basic similarity matrix. This statistic is then applied to three illustrative hierarchical clusterings: two obtained by the Johnson algorithms and one obtained by an algorithm that produces the same chain under hypermonotone increasing transformations of the similarity measures.

Keywords

Public PolicyCluster AlgorithmHierarchical ClusterSimilarity MeasureStatistical Theory
Type
Original Paper
Information
Psychometrika , Volume 37 , Issue 3 , September 1972 , pp. 261 - 274
Copyright
Copyright © 1972 The Psychometric Society

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