Page 22 - Jolliffe I. Principal Component Analysis

xxi
Contents
13 Principal Component Analysis for Special Types of Data 338
13.1
13.2 Principal Component Analysis for Discrete Data ..... 339
Analysis of Size and Shape .................
343
13.3 Principal Component Analysis for Compositional Data . 346
13.3.1 Example: 100 km Running Data . . . ....... 349
13.4 Principal Component Analysis in Designed Experiments 351
13.5 Common Principal Components .............. 354
13.6 Principal Component Analysis in the Presence of Missing
Data ............................. 363
13.7 PCA in Statistical Process Control ............ 366
13.8 Some Other Types of Data ................. 369
14 Generalizations and Adaptations of Principal
Component Analysis 373
14.1 Non-Linear Extensions of Principal Component Analysis 374
14.1.1 Non-Linear Multivariate Data Analysis—Gifi and
Related Approaches ................. 374
14.1.2 Additive Principal Components
and Principal Curves ................ 377
14.1.3 Non-Linearity Using Neural Networks ....... 379
14.1.4 Other Aspects of Non-Linearity . . . ....... 381
14.2 Weights, Metrics, Transformations and Centerings .... 382
14.2.1 Weights ....................... 382
14.2.2 Metrics ........................ 386
14.2.3 Transformations and Centering . . . ....... 388
14.3 PCs in the Presence of Secondary or Instrumental Variables 392
14.4 PCA for Non-Normal Distributions ............ 394
14.4.1 Independent Component Analysis . . ....... 395
14.5 Three-Mode, Multiway and Multiple Group PCA .... 397
14.6 Miscellanea ......................... 400
14.6.1 Principal Components and Neural Networks . . . 400
14.6.2 Principal Components for Goodness-of-Fit Statis-
tics .......................... 401
14.6.3 Regression Components, Sweep-out Components
and Extended Components ............. 403
14.6.4 Subjective Principal Components . . ....... 404
14.7 Concluding Remarks .................... 405

A Computation of Principal Components 407
A.1 Numerical Calculation of Principal Components ..... 408

Index 458

Author Index 478