Journal of Classification

, Volume 25, Issue 1, pp 43-65

First online:

Solving Non-Uniqueness in Agglomerative Hierarchical Clustering Using Multidendrograms

  • Alberto FernándezAffiliated withUniversitat Rovira i Virgili
  • , Sergio GómezAffiliated withUniversitat Rovira i VirgiliDepartament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili Email author 

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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.


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