Page 499 - Jolliffe I. Principal Component Analysis

Index
464
first few (high variance) PCs
320–323, 331, 384, 387
computation 408–411, 413
dominated by single variables functional PCA (FPCA) 274,
316-327, 384, 402
22, 24, 41, 56 bivariate FPCA 324
in canonical correlation analysis estimating functional PCs 316,
223, 224, 362 318–320, 327
in climate change detection 332, prediction of time series 316,
333 326, 327
in cluster analysis 211–219 robust FPCA 266, 316, 327
in discriminant analysis 200–202, see also rotation
207, 208
in factor analysis 157–162
gamma distribution
in independent component
probability plots 237, 239, 245
analysis 396 gas chromatography, see chemistry
in outlier detection 234–236,
Gaussian distribution, see normal
238, 239, 263, 367
distribution
in projection pursuit 221
generalizations of PCA 60, 189,
in regression 171–174, 186–188,
210, 220, 342, 360, 361,
191
373–401
in variable selection 138,
generalized linear models 61, 185
186-188, 191, 197
see also cumulative percentage of bilinear models 61
generalized SVD, see singular
total variation, descriptive
use of PCs, dimensionality value decomposition
reduction, dominant PCs, generalized variance 16, 20
genetics 9, 336, 413
interpretation of PCs,
residuals after fitting first gene shaving 213
few PCs, rotation, rules geology 9, 42, 346, 389, 390
for selecting PCs, size and trace element concentrations 248
shape PCs, two-dimensional geometric derivation of PCs 7, 8,
PC plots 10, 36, 59, 87, 189
fixed effects model for PCA 59–61, geometric properties of PCs 7, 8,
86, 96, 124, 125, 131, 158, 10, 18–21, 27, 29, 33–40, 46,
220, 267, 330, 376, 386 53, 78, 80, 87, 113, 189, 212,
Fourier analysis/transforms 311, 320, 340, 347, 372
329, 370 statistical implications 18, 33
frequency domain PCs 299, 310, Gini’s measure of dispersion 340
328-330, 370 Givens transformation 410
multitaper frequency goodness-of-fit tests 317, 373, 401,
domain singular value 402
decomposition (MTM-SVD) lack-of-fit test 379
303, 311, 314 graphical representation
functional and structural comparing covariance matrices
relationships 168, 188–190 360
functional data 61, 266, 302, dynamic graphics 79