Principal Component AnalysisPrincipal 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. |
Contents
Introduction | 1 |
Properties of Population Principal Components | 10 |
Properties of Sample Principal Components | 29 |
3 | 68 |
2 | 85 |
4 | 105 |
Choosing a Subset of Principal Components or Variables | 111 |
4 | 145 |
6 | 188 |
Principal Components Used with Other Multivariate | 199 |
Rotation and Interpretation of Principal Components | 269 |
PCA for Time Series and Other NonIndependent Data | 299 |
Principal Component Analysis for Special Types of Data | 338 |
Generalizations and Adaptations of Principal | 373 |
A Computation of Principal Components 407 | 406 |
| 458 | |
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Common terms and phrases
algorithm approximation biplot Chapter coefficients columns compared context correlation matrix correspondence analysis covariance matrix covariance or correlation criteria criterion curves data matrix data set defined deleted derived diagonal discriminant analysis discussed in Section distribution eigenvalues eigenvectors elements equation estimates Euclidean distance example factor analysis give given groups interpretation Jolliffe Krzanowski kth PC last few PCs latent root regression least squares linear functions loadings Mahalanobis distance maximized measurements methods minimized multicollinearities multivariate normal multivariate normal distribution optimal original variables orthogonal outliers PC regression plot population possible prediction predictor variables principal component analysis principal coordinate analysis procedure Property q PCs relationships respect retained rotation rules sample covariance second PC similar simulation singular value decomposition statistical structure subset of variables subspace suggested sum of squares Table techniques tion total variation uncorrelated values variable selection variance vector zero