Choosing a Subset of Principal Components or Variables

Abstract

In this chapter two separate, but related, topics are considered, both of which are concerned with choosing a subset of variables. In the first section, the choice to be examined is how many PCs adequately account for the total variation in x. The major objective in many applications of PCA is to replace the p elements of x by a much smaller number, m, of PCs, which nevertheless discard very little information. It is crucial to know how small m can be taken without serious information loss. Various rules, mostly ad hoc, have been proposed for determining a suitable value of m, and these are discussed in Section 6.1. Examples of their use are given in Section 6.2.