Page 442 - Jolliffe I. Principal Component Analysis

Appendix A

Computation of Principal Components

This Appendix is the only part of the book that has shrunk compared to the
first edition, where it consisted of two sections. The first described efficient
methods for deriving PCs, that is efficient techniques from numerical anal-
ysis for calculating eigenvectors and eigenvalues of positive semi-definite
matrices; the second section discussed the facilities for computing PCs,
and performing related analyses, which were then available in five of the
best known statistical computer packages.
The first topic has been updated in this edition and some general com-
ments on the second topic are included. However much of the detail on
the latter topic has been removed from this edition, mainly because such
material rapidly becomes out of date. This is readily illustrated by two
quotations from the first edition.

Despite the likelihood that personal computers will become the
main tool for ...users of PCA ...[it] is still usually carried out
on mainframe computers ...[T]he author has no experience yet
of PCA on personal computers.

MINITAB does not have any direct instructions for finding PCs.
Five packages were described in the first edition—BMDP, GENSTAT,
MINITAB, SAS and SPSS . Since then a number a new packages or lan-
X
guages have appeared. Perhaps the biggest change is the greatly expanded
use by statisticians of S-PLUS and its ‘open source’ relative R. The MAT-
LAB software should also be mentioned. Although it is not primarily a
statistical package, it has found increasing favour among statisticians as a