Principal Component Analysis

Principal component analysis is probably the oldest and best known of the It was first introduced by Pearson (1901), techniques ofmultivariate analysis. and developed independently by Hotelling (1933). Like many multivariate methods, it was not widely used until the advent of electronic computers, but it is now weIl entrenched in virtually every statistical computer package. The central idea of principal component analysis is to reduce the dimen­ sionality of a data set in which there are a large number of interrelated variables, while retaining as much as possible of the variation present in the data set. This reduction is achieved by transforming to a new set of variables, the principal components, which are uncorrelated, and which are ordered so that the first few retain most of the variation present in all of the original variables. Computation of the principal components reduces to the solution of an eigenvalue-eigenvector problem for a positive-semidefinite symmetrie matrix. Thus, the definition and computation of principal components are straightforward but, as will be seen, this apparently simple technique has a wide variety of different applications, as weIl as a number of different deri­ vations. Any feelings that principal component analysis is a narrow subject should soon be dispelled by the present book; indeed some quite broad topics which are related to principal component analysis receive no more than a brief mention in the final two chapters. Front Matter....Pages i-xiii Introduction....Pages 1-7 Mathematical and Statistical Properties of Population Principal Components....Pages 8-22 Mathematical and Statistical Properties of Sample Principal Components....Pages 23-49 Principal Components as a Small Number of Interpretable Variables: Some Examples....Pages 50-63 Graphical Representation of Data Using Principal Components....Pages 64-91 Choosing a Subset of Principal Components or Variables....Pages 92-114 Principal Component Analysis and Factor Analysis....Pages 115-128 Principal Components in Regression Analysis....Pages 129-155 Principal Components Used with Other Multivariate Techniques....Pages 156-172 Outlier Detection, Influential Observations and Robust Estimation of Principal Components....Pages 173-198 Principal Component Analysis for Special Types of Data....Pages 199-222 Generalizations and Adaptations of Principal Component Analysis....Pages 223-234 Back Matter....Pages 235-271