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

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References 457regularities in multivariate data. In Food Research and Data Analysis,eds. H. Martens and H. Russwurm, 147–188. London: Applied SciencePublishers.Worton, B.J. (1984). Statistical Aspects of Data Collected in Year 1974–1975 of the Irish Wetlands Enquiry. Unpublished M.Sc. dissertation.University of Kent at Canterbury.Wu, D.-H., Anderson, D.L.T. and Davey, M.K. (1994). ENSO predictionexperiments using a simple ocean-atmosphere model. Tellus,A.Dynam.Meteorol. Oceanog., 46, 465–480.Xie, Y.-L., Wang, J.-H., Liang, Y.-Z., Sun, L.-X., Song, X-H. and Yu, R-Q.(1993). Robust principal component analysis by projection pursuit. J.Chemometrics, 7, 527–541.Xu, L. and Yuille, A. (1995). Robust principal component analysis byself-organizing rules based on statistical physics approach. IEEE Trans.Neural Networks, 6, 131–143.Yanai, H. (1980). A proposition of generalized method for forward selectionof variables. Behaviormetrika, 7, 95–107.Yendle, P.W. and MacFie, H.J.H. (1989). Discriminant principal componentsanalysis. J. Chemometrics, 3, 589–600.Young, G. (1941). Maximum likelihood estimation and factor analysis.Psychometrika, 6, 49–53.Yuan, K.-H. and Bentler, P.M. (1994). Test of linear trend in eigenvaluesof K covariance matrices with applications in common principalcomponents analysis. Commun. Stat.—Theor. Meth., 23, 3141–3156.Yule, W., Berger, M., Butler, S., Newham, V. and Tizard, J. (1969). TheWPPSL. An empirical evaluation with a British sample. Brit. J. Educ.Psychol., 39, 1–13.Zheng, X., Frederiksen, C.S. and Basher, R.E. (2002). EOFs of the potentiallypredictable and weather noise components of seasonal mean fields.Part 1 Methodology. Submitted for publication.Zwick, W.R. and Velicer, W.F. (1986). Comparison of five rules for determiningthe number of components to retain. Psychol. Bull., 99,432–446.Zwiers, F.W. (1999). The detection of climate change. In AnthropogenicClimate Change, eds. H. von Storch and G. Flöser, 161–206. Berlin:Springer.
Indexadditive principal components 377,378agriculture 9, 353, 376carrots 210, 323, 346see also designed experimentsalgebraic derivations of PCs 4–6,10, 11, 13, 21, 30, 39algebraic properties of PCs 10–21,25, 26, 29–34, 86, 139, 158,170, 174, 266, 328, 342, 361,362, 375, 392, 394, 400, 404statistical implications 10, 11,13, 25, 26, 31allometry 344, 345, 374allometric extension 356alternating least squares (ALS)375, 377analysis of variance (ANOVA) 122,351–354, 390blocks and treatments 351, 352two-way models 351, 352, 390see also multivariate analysis ofvarianceanatomical measurements 22, 57,58, 64–68, 81–83, 145–147,458214, 219, 233–236, 242–245,254, 258, 259, 354, 358-359children 233–236criminals 68reflexes 57-58students 64–68, 81–83, 214,242–245, 254, 258, 259,358-359Andrews’ curves 107–110, 242, 253approximations to PCs 269,292–296see also discrete PC coefficients,rounded PC coefficients,truncation of PC coefficientsarchaeology 349, 388artistic qualities 83–85, 97, 98,254-258, 276, 277asymptotic probabilitydistributions, seeprobability distributionsathleticsOlympic track records 42road running 98-101, 298, 316,320–323, 349, 350atmospheric science 70–74, 80, 112,
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Principal ComponentAnalysis,Second
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viPreface to the Second Editionerty
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viiiPreface to the Second EditionA
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xPreface to the First Editionand in
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xiiPreface to the First EditionIn m
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xviAcknowledgmentsthese institution
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xviiiContents3.4.1 Example ........
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xxContents10 Outlier Detection, Inf
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xxivList of Figures5.2 Artistic qua
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xxviiiList of Tables6.1 First six e
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2 1. IntroductionFigure 1.1. Plot o
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4 1. IntroductionFigure 1.3. Studen
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1.2. A Brief History of Principal C
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1.2. A Brief History of Principal C
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2.1. Optimal Algebraic Properties o
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2.2. Geometric Properties of Popula
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2.3. Principal Components Using a C
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2.4. Principal Components with Equa
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3Mathematical and StatisticalProper
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where3.1. Optimal Algebraic Propert
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3.2. Geometric Properties of Sample
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3.3. Covariance and Correlation Mat
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3.3. Covariance and Correlation Mat
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3.4. Principal Components with Equa
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show that X = ULA ′ .⎡ULA ′ =
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3.6. Probability Distributions for
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3.7. Inference Based on Sample Prin
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3.7.2 Interval Estimation3.7. Infer
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3.8. Patterned Covariance and Corre
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3.9. Models for Principal Component
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3.9. Models for Principal Component
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4Principal Components as a SmallNum
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4.1. Anatomical Measurements 65Tabl
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4.1. Anatomical Measurements 67spac
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4.2. The Elderly at Home 69Table 4.
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4.3. Spatial and Temporal Variation
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4.3. Spatial and Temporal Variation
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4.4. Properties of Chemical Compoun
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4.5. Stock Market Prices 77Table 4.
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5. Graphical Representation of Data
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Anatomical Measurements5.1. Plottin
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5.1. Plotting Two or Three Principa
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5.2. Principal Coordinate Analysis
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5.3. Biplots 91columns, L is an (r
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5.3. Biplots 93ButandSubstituting i
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5.3. Biplots 95The vector gi ∗ co
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5.3. Biplots 97Figure 5.3. Biplot u
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5.3. Biplots 99Table 5.2. First two
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5.3. Biplots 101Figure 5.5. Biplot
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5.4. Correspondence Analysis 103of
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5.4. Correspondence Analysis 105Fig
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5.6. Displaying Intrinsically High-
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5.6. Displaying Intrinsically High-
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6Choosing a Subset of PrincipalComp
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6.1. How Many Principal Components?
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6.2. Choosing m, the Number of Comp
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6.2. Choosing m, the Number of Comp
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6.3. Selecting a Subset of Variable
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6.4. Examples Illustrating Variable
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7.1. Models for Factor Analysis 151
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7.2. Estimation of the Factor Model
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7.3. Comparisons Between Factor and
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7.4. An Example of Factor Analysis
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7.4. An Example of Factor Analysis
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7.5. Concluding Remarks 165To illus
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8Principal Components in Regression
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8.1. Principal Component Regression
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8.1. Principal Component Regression
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8.2. Selecting Components in Princi
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8.2. Selecting Components in Princi
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8.3. Connections Between PC Regress
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8.4. Variations on Principal Compon
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8.5. Variable Selection in Regressi
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8.5. Variable Selection in Regressi
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8.6. Functional and Structural Rela
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8.7. Examples of Principal Componen
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Table 8.3. Principal component regr
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9Principal Components Used withOthe
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9.1. Discriminant Analysis 201on th
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9.1. Discriminant Analysis 203Figur
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9.1. Discriminant Analysis 205Corbi
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9.1. Discriminant Analysis 207that
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9.1. Discriminant Analysis 209betwe
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9.2. Cluster Analysis 211dimensiona
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9.2. Cluster Analysis 213Before loo
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9.2. Cluster Analysis 215Figure 9.3
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9.2. Cluster Analysis 217demographi
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9.2. Cluster Analysis 219county clu
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9.2. Cluster Analysis 221choosing a
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9.3. Canonical Correlation Analysis
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10.1. Detection of Outliers Using P
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10.2. Influential Observations in a
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10.3. Sensitivity and Stability 259
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10.3. Sensitivity and Stability 261
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10.4. Robust Estimation of Principa
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11Rotation and Interpretation ofPri
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11.1. Rotation of Principal Compone
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oot of the corresponding eigenvalue
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11.2. Alternatives to Rotation 279w
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11.2. Alternatives to Rotation 281F
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11.2. Alternatives to Rotation 283F
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11.2. Alternatives to Rotation 285T
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11.2. Alternatives to Rotation 287T
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11.2. Alternatives to Rotation 289A
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11.2. Alternatives to Rotation 291
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11.3. Simplified Approximations to
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11.3. Simplified Approximations to
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11.4. Physical Interpretation of Pr
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12Principal Component Analysis forT
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12.1. Introduction 301series is alm
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12.2. PCA and Atmospheric Time Seri
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and a typical row of the matrix is1
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12.3. Functional PCA 317A key refer
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12.3. Functional PCA 319The sample
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12.3. Functional PCA 321speed (mete
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12.3. Functional PCA 323of the data
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12.3. Functional PCA 325subject to
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12.3. Functional PCA 327series than
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12.4. PCA and Non-Independent Data
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13.1. Principal Component Analysis
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13.2. Analysis of Size and Shape 34
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13.2. Analysis of Size and Shape 34
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13.5. Common Principal Components 3
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13.7. PCA in Statistical Process Co
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13.8. Some Other Types of Data 369A
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13.8. Some Other Types of Data 371d
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14Generalizations and Adaptations o
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14.1. Non-Linear Extensions of Prin
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14.1. Additive Principal Components
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14.2. Weights, Metrics, Transformat
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14.3. PCs in the Presence of Second
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14.4. PCA for Non-Normal Distributi
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14.5. Three-Mode, Multiway and Mult
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14.5. Three-Mode, Multiway and Mult
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14.6. Miscellanea 401• Linear App
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14.6. Miscellanea 40314.6.3 Regress
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14.7. Concluding Remarks 405space o
Page 438 and 439: Appendix AComputation of Principal
Page 440 and 441: A.1. Numerical Calculation of Princ
Page 446 and 447: ReferencesAguilera, A.M., Gutiérre
Page 448 and 449: References 417Apley, D.W. and Shi,
Page 450 and 451: References 419Benasseni, J. (1986b)
Page 452 and 453: References 421Boik, R.J. (1986). Te
Page 454 and 455: References 423Castro, P.E., Lawton,
Page 456 and 457: References 425Cook, R.D. (1986). As
Page 458 and 459: References 427Dempster, A.P., Laird
Page 460 and 461: References 429Feeney, G.J. and Hest
Page 462 and 463: References 431in Descriptive Multiv
Page 464 and 465: References 433Gunst, R.F. and Mason
Page 466 and 467: References 435Hocking, R.R., Speed,
Page 468 and 469: References 437Jeffers, J.N.R. (1978
Page 470 and 471: References 439Kazi-Aoual, F., Sabat
Page 472 and 473: References 441Krzanowski, W.J. (200
Page 474 and 475: References 443Mann, M.E. and Park,
Page 476 and 477: References 445Monahan, A.H., Tangan
Page 478 and 479: References 447Pack, P., Jolliffe, I
Page 480 and 481: References 449Richman M.B. (1993).
Page 482 and 483: References 451Soofi, E.S. (1988). P
Page 484 and 485: References 453Tenenbaum, J.B., de S
Page 486 and 487: References 455Vong, R., Geladi, P.,
Page 490 and 491: Index 459116, 127-130, 133, 270, 27
Page 492 and 493: Index 461computationin (PC) regress
Page 494 and 495: Index 463discriminant principal com
Page 496 and 497: Index 465of correlations between va
Page 498 and 499: Index 467see also hypothesis testin
Page 500 and 501: Index 469PC algorithms with noise 4
Page 502 and 503: Index 471in functional and structur
Page 504 and 505: Index 473variance ellipsoids,S-esti
Page 506 and 507: Index 475spatial correlation/covari
Page 508 and 509: Index 477for covariance matrices 26
Page 510 and 511: Author Index 479Belsley, D.A. 169Be
Page 512 and 513: Author Index 481Fowlkes, E.B. 377Fr
Page 514 and 515: Author Index 483Krzanowski, W.J. 46
Page 516 and 517: Author Index 485Rencher, A.C. 64, 1
Page 518: Author Index 487Yaguchi, H. 371Yana
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