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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.
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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

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