ABSTRACT
The problem of reconstructing distances among stimuli from some empirical measures of pairwise dissimilarity is old. The measures of dissimilarity are numerous, including numerical ratings of (dis)similarity, classifications of stimuli, correlations among response variables, errors of substitution, and many others (Everitt & Rabe-Hesketh, 1997; Suppes, Krantz, Luce, & Tversky, 1989; Sankoff & Kruskal, 1999; Semple & Steele, 2003). Formal representations of proximity data, like Multidimensional Scaling (MDS; Borg & Groenen, 1997; Kruskal & Wish, 1978) or Cluster Analysis (Corter, 1996; Hartigan, 1975), serve to describe and display data structures by embedding them in low-dimensional spatial or graph-theoretical configurations, respectively. In MDS, one embeds data points in a low-dimensional Minkowskian (usually, Euclidean) space so that distances are monotonically (in the metric version, proportionally) related to pairwise dissimilarities. In Cluster Analysis, one typically represents proximity relations by a series of partitions of the set of stimuli resulting in a graph-theoretic tree structure with ultrametric or additive-tree metric distances.
