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Springer Series in Statistics

# Principal Component Analysis

Authors: Jolliffe, I.T.

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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.

• Introduction

Pages 1-7

Jolliffe, I. T.

• Mathematical and Statistical Properties of Population Principal Components

Pages 8-22

Jolliffe, I. T.

• Mathematical and Statistical Properties of Sample Principal Components

Pages 23-49

Jolliffe, I. T.

• Principal Components as a Small Number of Interpretable Variables: Some Examples

Pages 50-63

Jolliffe, I. T.

• Graphical Representation of Data Using Principal Components

Pages 64-91

Jolliffe, I. T.

eBook 67,40 €
price for Spain (gross)
• ISBN 978-1-4757-1904-8
• Digitally watermarked, DRM-free
• Included format: PDF
• ebooks can be used on all reading devices

## Bibliographic Information

Bibliographic Information
Book Title
Principal Component Analysis
Authors
Series Title
Springer Series in Statistics
1986
Publisher
Springer-Verlag New York
Springer-Verlag New York
eBook ISBN
978-1-4757-1904-8
DOI
10.1007/978-1-4757-1904-8
Series ISSN
0172-7397
Edition Number
1
Number of Pages
XIII, 271
Topics

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