Three-Way Procrustean Models

Abstract

In this chapter, we look at some varieties of generalized Procrustes analysis. The simplest task is to fit several given coordinate matrices X _k (k = 1,..., K) to each other in such a way that uninformative differences are eliminated. We also consider generalizations of the Procrustean problem that first find an optimal average configuration for all X _k and then attempt to explain each individual X _k in turn by some simple transformation of the average configuration. One important case is to admit different weights on the dimensions of the average configuration. This case defines an interesting model for individual differences scaling: if the fit is good, then the perceptual space of individual k corresponds to the group’s perceptual space, except that k weights the space’s dimensions in his or her own idiosyncratic way.