# Principal Component Analysis

• I. T. Jolliffe
Book

Part of the Springer Series in Statistics book series (SSS)

1. Front Matter
Pages i-xiii
2. I. T. Jolliffe
Pages 1-7
3. I. T. Jolliffe
Pages 8-22
4. I. T. Jolliffe
Pages 23-49
5. I. T. Jolliffe
Pages 50-63
6. I. T. Jolliffe
Pages 64-91
7. I. T. Jolliffe
Pages 92-114
8. I. T. Jolliffe
Pages 115-128
9. I. T. Jolliffe
Pages 129-155
10. I. T. Jolliffe
Pages 156-172
11. I. T. Jolliffe
Pages 173-198
12. I. T. Jolliffe
Pages 199-222
13. I. T. Jolliffe
Pages 223-234
14. Back Matter
Pages 235-271

### Introduction

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.

### Keywords

Eigenvalue Finite Matrix Statistica computation computer eigenvector factor analysis form principal component analysis regression regression analysis set symmetric relation variable

#### Authors and affiliations

• I. T. Jolliffe
• 1
1. 1.Mathematical InstituteUniversity of KentKentEngland

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4757-1904-8
• Copyright Information Springer-Verlag New York 1986
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4757-1906-2
• Online ISBN 978-1-4757-1904-8
• Series Print ISSN 0172-7397
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