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

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List of Tablesxxix10.2 Artistic qualities of painters: comparisons between estimated(empirical) and actual (sample) influence of individualobservations for the first two PCs, based on thecovariance matrix. ...................... 25510.3 Artistic qualities of painters: comparisons between estimated(empirical) and actual (sample) influence of individualobservations for the first two PCs, based on thecorrelation matrix. ...................... 25611.1 Unrotated and rotated loadings for components 3 and 4:artistic qualities data. .................... 27711.2 Hausmann’s 6-variable example: the first two PCs andconstrainedcomponents. .................. 28511.3 Jeffers’ pitprop data - coefficients and variance for thefirstcomponent. ....................... 28711.4 Jeffers’ pitprop data - coefficients and cumulative varianceforthefourthcomponent................... 28713.1 First two PCs: 100 km compositional data. . ....... 35013.2 First two PCs: Aitchison’s (1983) technique for 100 kmcompositional data. ..................... 350
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Page 1: Principal ComponentAnalysis,Second
Page 7 and 8: viPreface to the Second Editionerty
Page 9 and 10: viiiPreface to the Second EditionA
Page 11 and 12: xPreface to the First Editionand in
Page 13 and 14: xiiPreface to the First EditionIn m
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Page 17 and 18: xviAcknowledgmentsthese institution
Page 19 and 20: xviiiContents3.4.1 Example ........
Page 21 and 22: xxContents10 Outlier Detection, Inf
Page 25 and 26: xxivList of Figures5.2 Artistic qua
Page 29: xxviiiList of Tables6.1 First six e
Page 33 and 34: 2 1. IntroductionFigure 1.1. Plot o
Page 35: 4 1. IntroductionFigure 1.3. Studen
Page 38 and 39: 1.2. A Brief History of Principal C
Page 40 and 41: 1.2. A Brief History of Principal C
Page 42 and 43: 2.1. Optimal Algebraic Properties o
Page 50 and 51: 2.2. Geometric Properties of Popula
Page 52 and 53: 2.3. Principal Components Using a C
Page 58 and 59: 2.4. Principal Components with Equa
Page 60 and 61: 3Mathematical and StatisticalProper
Page 62 and 63: where3.1. Optimal Algebraic Propert
Page 64 and 65: 3.2. Geometric Properties of Sample
Page 70 and 71: 3.3. Covariance and Correlation Mat
Page 72 and 73: 3.3. Covariance and Correlation Mat
Page 74 and 75: 3.4. Principal Components with Equa
Page 76 and 77: show that X = ULA ′ .⎡ULA ′ =
Page 78 and 79: 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
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Appendix AComputation of Principal
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A.1. Numerical Calculation of Princ
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ReferencesAguilera, A.M., Gutiérre
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References 417Apley, D.W. and Shi,
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References 419Benasseni, J. (1986b)
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References 421Boik, R.J. (1986). Te
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References 423Castro, P.E., Lawton,
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References 425Cook, R.D. (1986). As
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References 427Dempster, A.P., Laird
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References 429Feeney, G.J. and Hest
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References 431in Descriptive Multiv
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References 433Gunst, R.F. and Mason
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References 435Hocking, R.R., Speed,
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References 437Jeffers, J.N.R. (1978
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References 439Kazi-Aoual, F., Sabat
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References 441Krzanowski, W.J. (200
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References 443Mann, M.E. and Park,
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References 445Monahan, A.H., Tangan
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References 447Pack, P., Jolliffe, I
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References 449Richman M.B. (1993).
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References 451Soofi, E.S. (1988). P
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References 453Tenenbaum, J.B., de S
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References 455Vong, R., Geladi, P.,
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References 457regularities in multi
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Index 459116, 127-130, 133, 270, 27
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Index 461computationin (PC) regress
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Index 463discriminant principal com
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Index 465of correlations between va
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Index 467see also hypothesis testin
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Index 469PC algorithms with noise 4
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Index 471in functional and structur
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Index 473variance ellipsoids,S-esti
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Index 475spatial correlation/covari
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Index 477for covariance matrices 26
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Author Index 479Belsley, D.A. 169Be
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Author Index 481Fowlkes, E.B. 377Fr
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Author Index 483Krzanowski, W.J. 46
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Author Index 485Rencher, A.C. 64, 1
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Author Index 487Yaguchi, H. 371Yana
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Jolliffe I. Principal Component Analysis (2ed., Springer, 2002)(518s)

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