Solving non-uniqueness in agglomerative hierarchical clustering using multidendrograms

Details Solving non-uniqueness in agglomerative hierarchical clustering using multidendrograms Solving non-uniqueness in agglomerative hierarchical clustering using multidendrograms

2006-08-08

arxiv.org/abs/cs/0608049v2

Journal of Classification 25 (2008) 43-65

Computer Science

Information Retrieval

Free Software for Agglomerative Hierarchical Clustering using Multidendrograms available at http://deim.urv.cat/~sgomez/mult

Scientific paper

10.1007/s00357-008-9004-x

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 and Williams' formula which enables the implementation of the algorithm in a recursive way.

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