Comparison of dendrograms: a multivariate approach

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Abstract
Three new descriptors of dendrogram structure (cluster membership divergence, subtree membership divergence, and partition membership divergence) have been proposed which supplement existing ones (cophenetic difference and topological difference). These enable multivariate comparisons among dendrograms in a manner that minimizes the drawbacks of individual descriptors and emphasizes their agreement. The new descriptors arc illustrated and compared with the existing ones by reference to an artificial data set. The multivariate comparison of dendrograms is further illustrated using two real data sets, one phenetic and one cladistic. These applications demonstrate the ability of this approach to reveal features of dendrograms that may be data dependent, method dependent, or due to the interaction of data and method, and that may not be readily apparent otherwise.