This book, the only one of its kind available, presents PCA from its simplest form through its abstract formalism, including applications. Furthermore, it extends the use of PCA far beyond its well-known applications to scalar (e.g. temperature) or vector (e.g. wind) fields. Much of the material is hitherto unpublished, thus greatly extending the realm of applicability of PCA, and many suggestions are made for its future application. The first half of the book provides a comprehensive discussion of PCA, including solved numerical examples, beginning with a simple bivariate data set and progressing to the PCA of multivariate fields. The use of selection rules to establish statistical significance is emphasized. The second half of the book compares PCA with other analysis techniques such as Factor Analysis, Linear Regression Analysis, and Canonical Factor Analysis. The book also discusses the use of PCA in construction of statistical-dynamical models, in the detection of moving patterns in data sets, and in studies of stationary random processes.
