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

viPreface to the Second Editionerty (A6) has been added to Chapter 2, with Property A6 in Chapter 3becoming A7.Chapter 5 has been extended by further discussion of a number of ordinationand scaling methods linked to PCA, in particular varieties of the biplot.Chapter 6 has seen a major expansion. There are two parts of Chapter 6concerned with deciding how many principal components (PCs) to retainand with using PCA to choose a subset of variables. Both of these topicshave been the subject of considerable research in recent years, although aregrettably high proportion of this research confuses PCA with factor analysis,the subject of Chapter 7. Neither Chapter 7 nor 8 have been expandedas much as Chapter 6 or Chapters 9 and 10.Chapter 9 in the first edition contained three sections describing theuse of PCA in conjunction with discriminant analysis, cluster analysis andcanonical correlation analysis (CCA). All three sections have been updated,but the greatest expansion is in the third section, where a number of othertechniques have been included, which, like CCA, deal with relationships betweentwo groups of variables. As elsewhere in the book, Chapter 9 includesyet other interesting related methods not discussed in detail. In general,the line is drawn between inclusion and exclusion once the link with PCAbecomes too tenuous.Chapter 10 also included three sections in first edition on outlier detection,influence and robustness. All have been the subject of substantialresearch interest since the first edition; this is reflected in expanded coverage.A fourth section, on other types of stability and sensitivity, has beenadded. Some of this material has been moved from Section 12.4 of the firstedition; other material is new.The next two chapters are also new and reflect my own research interestsmore closely than other parts of the book. An important aspect of PCA isinterpretation of the components once they have been obtained. This maynot be easy, and a number of approaches have been suggested for simplifyingPCs to aid interpretation. Chapter 11 discusses these, covering the wellestablishedidea of rotation as well recently developed techniques. Thesetechniques either replace PCA by alternative procedures that give simplerresults, or approximate the PCs once they have been obtained. A smallamount of this material comes from Section 12.4 of the first edition, butthe great majority is new. The chapter also includes a section on physicalinterpretation of components.My involvement in the developments described in Chapter 12 is less directthan in Chapter 11, but a substantial part of the chapter describes methodologyand applications in atmospheric science and reflects my long-standinginterest in that field. In the first edition, Section 11.2 was concerned with‘non-independent and time series data.’ This section has been expandedto a full chapter (Chapter 12). There have been major developments inthis area, including functional PCA for time series, and various techniquesappropriate for data involving spatial and temporal variation, such as (mul-