# Principal Component Analysis

Springer Science & Business Media, Mar 9, 2013 - Mathematics - 271 pages
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.

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### Contents

 CHAPTER 1 CHAPTER 8 CHAPTER 9 Mathematical and Statistical Properties of Sample Principal 23 CHAPTER 4 46 Graphical Representation of Data Using Principal Components 64 Choosing a Subset of Principal Components or Variables 92 CHAPTER 7 115
 Principal Components Used with Other Multivariate Techniques 156 CHAPTER 10 173 CHAPTER 11 199 CHAPTER 12 223 APPENDIX 235 References 247 Index 259 Copyright

 Principal Components in Regression Analysis 129