Page 18 - Jolliffe I. Principal Component Analysis

Contents

Preface to the Second Edition v
Preface to the First Edition ix
Acknowledgments xv
List of Figures xxiii
List of Tables xxvii

1 Introduction 1
1.1 Definition and Derivation of Principal Components . . . 1
1.2 A Brief History of Principal Component Analysis .... 6

2 Properties of Population Principal Components 10
2.1 Optimal Algebraic Properties of Population
Principal Components ................... 11
2.2 Geometric Properties of Population Principal Components 18
2.3 Principal Components Using a Correlation Matrix .... 21
2.4 Principal Components with Equal and/or Zero Variances 27
3 Properties of Sample Principal Components 29
3.1 Optimal Algebraic Properties of Sample
Principal Components ................... 30
3.2 Geometric Properties of Sample Principal Components . 33
3.3 Covariance and Correlation Matrices: An Example . . . 39
3.4 Principal Components with Equal and/or Zero Variances 43