Chapter 14 – Proximity Measurement

Publisher Summary This chapter discusses the measurement of proximity. Proximity relations can be inferred from various types of observations, such as rating of similarity or dissimilarity, classification of objects, correlation among variables, frequency of co-occurrences, and errors of substitution. Proximity data are commonly used to infer the structure of the entities under study and to embed them in a suitable formal structure. Formal representations serve two related functions: (1) they provide convenient methods for describing, summarizing, and displaying proximity data; and (2) they are also treated as theories about the data-generating process. Representations of proximity relations can be divided into two general classes: (1) geometrical or spatial, models; and (2) set-theoretical or feature, models. Geometrical models represent the objects under study as points in a space so that the proximity ordering of the objects is represented by the ordering of the metric distances among the respective points. Set-theoretical models of proximity represent each object as a collection of features and express the proximity between objects in terms of the measures of their common and their distinctive features.