Solving Non-Uniqueness in Agglomerative Hierarchical Clustering Using Multidendrograms

Journal of Classification volume 25, pages43–65(2008)Cite this article

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.

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Author information

Affiliations

  1. Universitat Rovira i Virgili, Tarragona, Spain

    Alberto Fernández & Sergio Gómez

  2. Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Campus Sescelades, Avinguda dels Països Catalans 26, E–43007, Tarragona, Spain

    Sergio Gómez

Authors
  1. Alberto Fernández
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  2. Sergio Gómez
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Corresponding author

Correspondence to Sergio Gómez.

Additional information

The authors thank A. Arenas for discussion and helpful comments. This work was partially supported by DGES of the Spanish Government Project No. FIS2006–13321–C02–02 and by a grant of Universitat Rovira i Virgili.

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Fernández, A., Gómez, S. Solving Non-Uniqueness in Agglomerative Hierarchical Clustering Using Multidendrograms. J Classif 25, 43–65 (2008). https://doi.org/10.1007/s00357-008-9004-x

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Keywords

  • Agglomerative methods
  • Cluster analysis
  • Hierarchical classification
  • Lance and Williams’ formula
  • Ties in proximity