Principal Component Analysis

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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
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