Page 7 - Jolliffe I. Principal Component Analysis

Preface to the Second Edition
vi
erty (A6) has been added to Chapter 2, with Property A6 in Chapter 3
becoming A7.
Chapter 5 has been extended by further discussion of a number of ordina-
tion and scaling methods linked to PCA, in particular varieties of the biplot.
Chapter 6 has seen a major expansion. There are two parts of Chapter 6
concerned with deciding how many principal components (PCs) to retain
and with using PCA to choose a subset of variables. Both of these topics
have been the subject of considerable research in recent years, although a
regrettably high proportion of this research confuses PCA with factor anal-
ysis, the subject of Chapter 7. Neither Chapter 7 nor 8 have been expanded
as much as Chapter 6 or Chapters 9 and 10.
Chapter 9 in the first edition contained three sections describing the
use of PCA in conjunction with discriminant analysis, cluster analysis and
canonical correlation analysis (CCA). All three sections have been updated,
but the greatest expansion is in the third section, where a number of other
techniques have been included, which, like CCA, deal with relationships be-
tween two groups of variables. As elsewhere in the book, Chapter 9 includes
yet other interesting related methods not discussed in detail. In general,
the line is drawn between inclusion and exclusion once the link with PCA
becomes too tenuous.
Chapter 10 also included three sections in first edition on outlier de-
tection, influence and robustness. All have been the subject of substantial
research interest since the first edition; this is reflected in expanded cover-
age. A fourth section, on other types of stability and sensitivity, has been
added. Some of this material has been moved from Section 12.4 of the first
edition; other material is new.
The next two chapters are also new and reflect my own research interests
more closely than other parts of the book. An important aspect of PCA is
interpretation of the components once they have been obtained. This may
not be easy, and a number of approaches have been suggested for simplifying
PCs to aid interpretation. Chapter 11 discusses these, covering the well-
established idea of rotation as well recently developed techniques. These
techniques either replace PCA by alternative procedures that give simpler
results, or approximate the PCs once they have been obtained. A small
amount of this material comes from Section 12.4 of the first edition, but
the great majority is new. The chapter also includes a section on physical
interpretation of components.
My involvement in the developments described in Chapter 12 is less direct
than in Chapter 11, but a substantial part of the chapter describes method-
ology and applications in atmospheric science and reflects my long-standing
interest in that field. In the first edition, Section 11.2 was concerned with
‘non-independent and time series data.’ This section has been expanded
to a full chapter (Chapter 12). There have been major developments in
this area, including functional PCA for time series, and various techniques
appropriate for data involving spatial and temporal variation, such as (mul-