Jolliffe I. Principal Component Analysis (2ed., Springer, 2002)(518s)

464 Indexfirst few (high variance) PCscomputation 408–411, 413dominated by single variables22, 24, 41, 56in canonical correlation analysis223, 224, 362in climate change detection 332,333in cluster analysis 211–219in discriminant analysis 200–202,207, 208in factor analysis 157–162in independent componentanalysis 396in outlier detection 234–236,238, 239, 263, 367in projection pursuit 221in regression 171–174, 186–188,191in variable selection 138,186-188, 191, 197see also cumulative percentage oftotal variation, descriptiveuse of PCs, dimensionalityreduction, dominant PCs,interpretation of PCs,residuals after fitting firstfew PCs, rotation, rulesfor selecting PCs, size andshape PCs, two-dimensionalPC plotsfixed effects model for PCA 59–61,86, 96, 124, 125, 131, 158,220, 267, 330, 376, 386Fourier analysis/transforms 311,329, 370frequency domain PCs 299, 310,328-330, 370multitaper frequencydomain singular valuedecomposition (MTM-SVD)303, 311, 314functional and structuralrelationships 168, 188–190functional data 61, 266, 302,320–323, 331, 384, 387functional PCA (FPCA) 274,316-327, 384, 402bivariate FPCA 324estimating functional PCs 316,318–320, 327prediction of time series 316,326, 327robust FPCA 266, 316, 327see also rotationgamma distributionprobability plots 237, 239, 245gas chromatography, see chemistryGaussian distribution, see normaldistributiongeneralizations of PCA 60, 189,210, 220, 342, 360, 361,373–401generalized linear models 61, 185bilinear models 61generalized SVD, see singularvalue decompositiongeneralized variance 16, 20genetics 9, 336, 413gene shaving 213geology 9, 42, 346, 389, 390trace element concentrations 248geometric derivation of PCs 7, 8,10, 36, 59, 87, 189geometric properties of PCs 7, 8,10, 18–21, 27, 29, 33–40, 46,53, 78, 80, 87, 113, 189, 212,320, 340, 347, 372statistical implications 18, 33Gini’s measure of dispersion 340Givens transformation 410goodness-of-fit tests 317, 373, 401,402lack-of-fit test 379graphical representationcomparing covariance matrices360dynamic graphics 79