Multidimensional Scaling and Correspondence Analysis

Abstract

In Chapter 3 we noted in passing that one of the most useful ways of using principal component analysis was to obtain a low-dimensional “map” of the data that preserved as far as possible the Euclidean distances between the observations in the space of the original q variables. In this chapter we will make this aspect of principal component analysis more explicit and also introduce some other, more direct methods, which aim to produce similar maps of data that have a different form from the usual multivariate data matrix, X. We will consider two such techniques The first, multidimensional scaling, is used, essentially, to represent an observed proximity matrix geometrically. Proximity matrices arise either directly from experiments in which subjects are asked to assess the similarity of pairs of stimuli, or indirectly; as a measure of the correlation, covariance, or distance of the pair of stimuli derived from the raw profile data, that is, the variable values in X.