Principal Component Analysis

by I.T. Jolliffe

Overview

Principal component analysis is central to the study of multivariate data. Although one of the earliest multivariate techniques, it continues to be the subject of much research, ranging from new model-based approaches to algorithmic ideas from neural networks. It is extremely versatile, with applications in many disciplines.

The first edition of this book was the first comprehensive text written solely on principal component analysis. The second edition updates and substantially expands the original version, and is once again the definitive text on the subject. It includes core material, current research and a wide range of applications. Its length is nearly double that of the first edition.

Researchers in statistics, or in other fields that use principal component analysis, will find that the book gives an authoritative yet accessible account of the subject. It is also a valuable resource for graduate courses in multivariate analysis. The book requires some knowledge of matrix algebra.

Ian Jolliffe is Professor of Statistics at the University of Aberdeen. He is author or co-author of over 60 research papers and three other books. His research interests are broad, but aspects of principal component analysis have fascinated him and kept him busy for over 30 years.

Product Details

ISBN-13:	9781441929990
Publisher:	Springer New York
Publication date:	12/01/2010
Series:	Springer Series in Statistics , #1
Edition description:	Second Edition 2002
Pages:	488
Product dimensions:	6.10(w) x 9.20(h) x 1.10(d)

Table of Contents

Mathematical and Statistical Properties of Population Principal Components.- Mathematical and Statistical Properties of Sample Principal Components.- Principal Components as a Small Number of Interpretable Variables: Some Examples.- Graphical Representation of Data Using Principal Components.- Choosing a Subset of Principal Components or Variables.- Principal Component Analysis and Factor Analysis.- Principal Components in Regression Analysis.- Principal Components Used with Other Multivariate Techniques.- Outlier Detection, Influential Observations, Stability, Sensitivity, and Robust Estimation of Principal Components.- Rotation and Interpretation of Principal Components.- Principal Component Analysis for Time Series and Other Non-Independent Data.- Principal Component Analysis for Special Types of Data.- Generalizations and Adaptations of Principal Component Analysis.

Editorial Reviews

From the reviews of the second edition:

TECHNOMETRICS

"Bringing the 1E up to date has added more than 200 pages of additional text. Anyone seriously involved with the application of PCA will certainly want to purchase a copy…Seldom has such a wealth of material on a single topic in statistics appeared in one book…All that material has gotten a whole lot more comprehensive here in this new edition. Goodall (1988) also labeled the book ‘a good read.’ Now it may be a little heavy for that purpose, but it certainly is a fantastic reference book."

ISI SHORT BOOK REVIEWS

"This is the bible of principal component analysis (PCA). This second edition of the book is nearly twice the length of the first. [Short Book Reviews, Vol.6, p.45] New material includes discussion of ordination methods linked to PCA, including biplots, determining the number of components to retain, extended discussion of outlier detection, stability, and sensitivity, simplifying PCAs to aid interpretation, time series data, size/shape data, and nonlinear PCA, including the Gifi system and neural networks, and other topics. As can be seen from this, the book is not a narrow discussion of PCA, but links it effectively and in an illuminating way to a wide variety of other multivariate statistical tools.

Principal component analysis is the empirical manifestation of the eigen value-decomposition of a correlation or covariance matrix. The fact that a book of nearly 500 pages can be written on this, and noting the author's comment that 'it is certain that I have missed some topics, and my coverage of others will be too brief for the taste of some readers' drives home the extent to whch statistics exceeds mere mathematics.

This book is an invaluable reference work and I am pleased to have it on my shelves. My only regret is that I probably will not have time to read it from cover to cover with the attention it deserves."

JOURNAL OFCLASSIFICATION

"This revised edition presents much new information on methods developed since the 1986 edition. Some of these newer parts include the expanded discussion of ordination and scaling methods (e.g., biplots), selection of the number of components to retain, canonical correlation for comparing groups of variables, independent correlation analysis for non-normal data, and principal curves."

"This book is one of the very few texts entirely devoted to principal component analysis (PCA). The second edition is usefully expanded and updated from the first edition; thus it is very well worth considering this edition, even if one is familiar with the first. … Very nice features are the carefully discussed links between PCA and related techniques … . Throughout, numerous references to relevant literature are provided. This book will be useful as an introduction to PCA as well as a reference." (Marieke E. Timmerman, Journal of the American Statistical Association, 2004)

"This is another volume in the Springer Series in Statistics … which has consistently produced books of high quality and generally advanced treatment of the topic. This revised edition presents much new information on methods developed since the 1986 edition, and these are well described … ." (William Shannon, Journal of Classification, Vol. 21 (1), 2004)

"The first edition of this book (IE), published in 1986, was the first book devoted entirely to principal component analysis (PCA). … Bringing the IE up to date has added more than 200 pages of additional text. Anyone seriously involved with the application of PCA will certainly want to purchase a copy. … Seldom has such a wealth of material on a single topic in statistics appeared in one book. … it certainly is a fantastic reference book." (Technometrics, Vol. 45 (3), 2003)

"This is the Bible of principle components analysis (PCA). This second edition of the book is nearly twice the length of the first. … The book is an invaluable reference work and I am pleased to have it on my shelves." (D. J. Hand, Short Book Reviews, Issue 2, 2003)

From the Publisher