Faces, Prototypes, and Additive Tree Representations

Abstract

The general purpose of this paper is to present a new method which particularly suits the typicality problem: the additive tree representations. These trees are used to represent objects as leaves on a tree so that the distance on the tree reflects the similarity between them. The problem of constructing these trees is well documented elsewhere, and will not be detailed here (cf. Sattah & Tversky, 1977; Abdi et al., 1984 to appear). If the data to be analyzed are in the form of a rectangular matrix (e.g. crossing objects and their features), the first step is to compute a distance between either the set of objects or the set of features. The additive tree representation is strongly linked with the well-known Tversky’s (1977) contrast model, and is worth interpreting in this light. So, these links are first described, and then applied with an analysis of the data from the Goldstein et al. (1984) study of “bad guys and good guys”.