Free trees and bidirectional trees as representations of psychological distance

Two types of graph-theoretic representations of psychological distances or dissimilarities are proposed: weighted free trees and weighted bidirectional trees. A weighted free tree is a generalization of the sort of graph representation used in hierarchical clustering. A weighted bidirectional tree is a further generalization which allows for asymmetric dissimilarities. The properties of these structures are discussed and numerical methods are presented that can be used to derive a representation for any given set of dissimilarities. The applicability of these structures is illustrated by using them to represent the data from experiments on the similarities among animal terms and on memory for sentences. An analysis based upon free trees is compared and contrasted with analyses using hierarchical clustering and multidimensional scaling.