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Solving Non-Uniqueness in Agglomerative Hierarchical Clustering Using Multidendrograms

Solving Non-Uniqueness in Agglomerative Hierarchical Clustering Using Multidendrograms In agglomerative hierarchical clustering, pair-group methods suffer from a problem of non-uniqueness when two or more distances between different clusters coincide during the amalgamation process. The traditional approach for solving this drawback has been to take any arbitrary criterion in order to break ties between distances, which results in different hierarchical classifications depending on the criterion followed. In this article we propose a variable-group algorithm that consists in grouping more than two clusters at the same time when ties occur. We give a tree representation for the results of the algorithm, which we call a multidendrogram, as well as a generalization of the Lance andWilliams’ formula which enables the implementation of the algorithm in a recursive way. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Classification Springer Journals

Solving Non-Uniqueness in Agglomerative Hierarchical Clustering Using Multidendrograms

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References (16)

Publisher
Springer Journals
Copyright
Copyright © 2008 by Springer Science+Business Media, LLC
Subject
Statistics; Marketing ; Psychometrics; Signal, Image and Speech Processing; Bioinformatics; Pattern Recognition; Statistical Theory and Methods
ISSN
0176-4268
eISSN
1432-1343
DOI
10.1007/s00357-008-9004-x
Publisher site
See Article on Publisher Site

Abstract

In agglomerative hierarchical clustering, pair-group methods suffer from a problem of non-uniqueness when two or more distances between different clusters coincide during the amalgamation process. The traditional approach for solving this drawback has been to take any arbitrary criterion in order to break ties between distances, which results in different hierarchical classifications depending on the criterion followed. In this article we propose a variable-group algorithm that consists in grouping more than two clusters at the same time when ties occur. We give a tree representation for the results of the algorithm, which we call a multidendrogram, as well as a generalization of the Lance andWilliams’ formula which enables the implementation of the algorithm in a recursive way.

Journal

Journal of Classification – Springer Journals

Published: Jun 26, 2008

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