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

Preface to the Second Editionviitichannel) singular spectrum analysis, complex PCA, principal oscillationpattern analysis, and extended empirical orthogonal functions (EOFs).Many of these techniques were developed by atmospheric scientists andare little known in many other disciplines.The last two chapters of the first edition are greatly expanded and becomeChapters 13 and 14 in the new edition. There is some transfer ofmaterial elsewhere, but also new sections. In Chapter 13 there are threenew sections, on size/shape data, on quality control and a final ‘odds-andends’section, which includes vector, directional and complex data, intervaldata, species abundance data and large data sets. All other sections havebeen expanded, that on common principal component analysis and relatedtopics especially so.The first section of Chapter 14 deals with varieties of non-linear PCA.This section has grown substantially compared to its counterpart (Section12.2) in the first edition. It includes material on the Gifi system ofmultivariate analysis, principal curves, and neural networks. Section 14.2on weights, metrics and centerings combines, and considerably expands,the material of the first and third sections of the old Chapter 12. Thecontent of the old Section 12.4 has been transferred to an earlier part inthe book (Chapter 10), but the remaining old sections survive and areupdated. The section on non-normal data includes independent componentanalysis (ICA), and the section on three-mode analysis also discussestechniques for three or more groups of variables. The penultimate sectionis new and contains material on sweep-out components, extended components,subjective components, goodness-of-fit, and further discussion ofneural nets.The appendix on numerical computation of PCs has been retainedand updated, but, the appendix on PCA in computer packages hasbeen dropped from this edition mainly because such material becomesout-of-date very rapidly.The preface to the first edition noted three general texts on multivariateanalysis. Since 1986 a number of excellent multivariate texts have appeared,including Everitt and Dunn (2001), Krzanowski (2000), Krzanowski andMarriott (1994) and Rencher (1995, 1998), to name just a few. Two largespecialist texts on principal component analysis have also been published.Jackson (1991) gives a good, comprehensive, coverage of principal componentanalysis from a somewhat different perspective than the presentbook, although it, too, is aimed at a general audience of statisticians andusers of PCA. The other text, by Preisendorfer and Mobley (1988), concentrateson meteorology and oceanography. Because of this, the notationin Preisendorfer and Mobley differs considerably from that used in mainstreamstatistical sources. Nevertheless, as we shall see in later chapters,especially Chapter 12, atmospheric science is a field where much developmentof PCA and related topics has occurred, and Preisendorfer andMobley’s book brings together a great deal of relevant material.