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

4Principal Components as a SmallNumber of Interpretable Variables:Some ExamplesThe original purpose of PCA was to reduce a large number (p) of variablesto a much smaller number (m) of PCs whilst retaining as much as possibleof the variation in the p original variables. The technique is especially usefulif m ≪ p and if the m PCs can be readily interpreted.Although we shall see in subsequent chapters that there are many otherways of applying PCA, the original usage as a descriptive, dimensionreducingtechnique is probably still the most prevalent single application.This chapter simply introduces a number of examples from several differentfields of application where PCA not only reduces the dimensionality of theproblem substantially, but has PCs which are easily interpreted. Graphicalrepresentations of a set of observations with respect to the m retained PCsand discussion of how to choose an appropriate value of m are deferreduntil Chapters 5 and 6, respectively.Of course, if m is very much smaller than p, then the reduction of dimensionalityalone may justify the use of PCA, even if the PCs have no clearmeaning, but the results of a PCA are much more satisfying if intuitivelyreasonable interpretations can be given to some or all of the m retainedPCs.Each section of this chapter describes one example in detail, but otherexamples in related areas are also mentioned in most sections. Some of theexamples introduced in this chapter are discussed further in subsequentchapters; conversely, when new examples are introduced later in the book,an attempt will be made to interpret the first few PCs where appropriate.The examples are drawn from a variety of fields of application, demonstratingthe fact that PCA has been found useful in a very large number