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Inferential summaries of tree estimates are useful in the setting ofevolutionary biology, where phylogenetic trees have been built from DNA datasince the 1960's. In bioinformatics, psychometrics and data mining,hierarchical clustering techniques output the same mathematical objects, andpractitioners have similar questions about the stability and `generalizability'of these summaries. This paper provides an implementation of the geometricdistance between trees developed by Billera, Holmes and Vogtmann (2001) [BHV]equally applicable to phylogenetic trees and hieirarchical clustering trees,and shows some of the applications in statistical inference for which thisdistance can be useful. In particular, since BHV have shown that the space oftrees is negatively curved (a CAT(0) space), a natural representation of acollection of trees is a tree. We compare this representation to the Euclideanapproximations of treespace made available through Multidimensional Scaling ofthe matrix of distances between trees. We also provide applications of thedistances between trees to hierarchical clustering trees constructed frommicroarrays. Our method gives a new way of evaluating the influence both ofcertain columns (positions, variables or genes) and of certain rows (whetherspecies, observations or arrays).

Computational Tools for Evaluating Phylogenetic and Hierarchical Clustering Trees