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
| 1 | |
Properties of Population Principal Components | 10 |
Properties of Sample Principal Components | 29 |
Examples | 64 |
Graphical Representation of Data Using | 78 |
6 | 111 |
Principal Component Analysis and Factor Analysis | 150 |
Principal Components in Regression Analysis | 167 |
Principal Components Used with Other Multivariate | 199 |
10 | 232 |
11 | 269 |
18 | 285 |
PCA for Time Series and Other NonIndependent Data | 300 |
21 | 315 |
Functional | 316 |
PCA and NonIndependent DataSome Additional Topics | 328 |
Other Aspects of NonIndependent Data and | 335 |
Principal Component Analysis for Special Types of Data | 338 |
27 | 350 |
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Common terms and phrases
ˆβ algorithm approximation biplot Chapter cluster analysis coefficients columns compared context correlation matrix correspondence analysis covariance matrix covariance or correlation criterion curves data matrix data set defined deleted derived diagonal discriminant analysis discussed in Section distribution eigenvalues eigenvectors elements EOFs equation estimate Euclidean distance example factor analysis given gives groups influence function interpretation Jolliffe Krzanowski kth PC last few PCs least squares linear functions loadings Mahalanobis distance maximize measurements methods minimized multicollinearities multivariate normal multivariate normal distribution optimal original variables orthogonal outliers PC regression plot population prediction predictor variables principal component analysis procedure projection pursuit Property q PCs q-dimensional relationships respect robust rotated PCs 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 weights zero