Jolliffe I. Principal Component Analysis (2ed., Springer, 2002)(518s)

9Principal Components Used withOther Multivariate TechniquesPrincipal component analysis is often used as a dimension-reducing techniquewithin some other type of analysis. For example, Chapter 8 describedthe use of PCs as regressor variables in a multiple regression analysis. Thepresent chapter discusses three classes of multivariate techniques, namelydiscriminant analysis, cluster analysis and canonical correlation analysis;for each these three there are examples in the literature that use PCA asa dimension-reducing technique.Discriminant analysis is concerned with data in which each observationcomes from one of several well-defined groups or populations. Assumptionsare made about the structure of the populations, and the main objectiveis to construct rules for assigning future observations to one of the populationsso as to minimize the probability of misclassification or some similarcriterion. As with regression, there can be advantages in replacing the variablesin a discriminant analysis by their principal components. The useof PCA in this way in linear discriminant analysis is discussed in Section9.1. In addition, the section includes brief descriptions of other discriminanttechniques that use PCs, and discussion of links between PCA andcanonical discriminant analysis.Cluster analysis is one of the most frequent contexts in which PCs arederived in order to reduce dimensionality prior to the use of a differentmultivariate technique. Like discriminant analysis, cluster analysis dealswith data sets in which the observations are to be divided into groups.However, in cluster analysis little or nothing is known a priori about thegroups, and the objective is to divide the given observations into groups orclusters in a ‘sensible’ way. There are two main ways in which PCs are em-