Metrics on spaces of finite trees

With the increasing popularity of hierarchical clustering methods in behavioral science, there is a need for ways of quantitatively comparing different tree structures on the same set of items. We employ lattice-theoretic methods to construct a variety of metrics on spaces of trees and to analyze their properties. Certain of these metrics are applied to data from Fillenbaum and Rapoport (1971) on the semantic structure of common English kin terms. This application shows that tree metrics can be used to select a componential analysis which is maximally consistent with an empirically derived set of trees.