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

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10.2. Influential Observations in a Principal Component Analysis 255Table 10.2. Artistic qualities of painters: comparisons between estimated (empirical) and actual (sample) influence of individualobservations for the first two PCs, based on the covariance matrix.Component number 1 2InfluenceInfluenceEigenvalue Eigenvector Eigenvalue EigenvectorEstimated Actual Obs. no. Estimated Actual Obs. no. Estimated Actual Obs. no. Estimated Actual Obs. no.2.490 2.486 31 6.791 6.558 34 1.759 1.854 44 11.877 13.767 342.353 2.336 7 5.025 4.785 44 1.757 1.770 48 5.406 5.402 442.249 2.244 28 3.483 4.469 42 1.478 1.491 34 3.559 4.626 422.028 2.021 5 1.405 1.260 48 1.199 1.144 43 2.993 3.650 43............0.248 0.143 44 0.001 0.001 53 −0.073 −0.085 49 0.016 0.017 24−0.108 −0.117 52 0.000 0.000 17 −0.090 −0.082 20 0.009 0.009 1−0.092 −0.113 37 0.000 0.000 24 0.039 0.045 37 0.000 0.001 300.002 −0.014 11 0.000 0.000 21 −0.003 −0.010 10 0.000 0.000 53
256 10. Outlier Detection, Influential Observations and Robust EstimationTable 10.3. Artistic qualities of painters: comparisons between estimated (empirical) and actual (sample) influence of individualobservations for the first two PCs, based on the correlation matrix.Component number 1 2InfluenceInfluenceEigenvalue Eigenvector Eigenvalue EigenvectorEstimated Actual Obs. no. Estimated Actual Obs. no. Estimated Actual Obs. no. Estimated Actual Obs. no.−0.075 −0.084 34 1.406 1.539 26 0.075 0.080 34 5.037 7.546 340.068 0.074 31 1.255 1.268 44 0.064 0.070 44 4.742 6.477 43−0.067 −0.073 43 0.589 0.698 42 0.061 0.062 43 4.026 4.333 260.062 0.067 28 0.404 0.427 22 0.047 0.049 39 1.975 2.395 42............−0.003 −0.003 6 0.001 0.001 33 −0.001 −0.002 45 0.011 0.012 21−0.001 −0.001 32 0.000 0.000 53 −0.001 −0.001 14 0.010 0.012 380.001 0.001 11 0.000 0.000 30 −0.000 −0.001 42 0.001 0.001 300.001 0.001 13 0.000 0.000 21 −0.000 −0.000 11 0.001 0.001 53
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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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Page 248 and 249: 9.2. Cluster Analysis 217demographi
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Page 252 and 253: 9.2. Cluster Analysis 221choosing a
Page 254 and 255: 9.3. Canonical Correlation Analysis
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Page 290 and 291: 10.3. Sensitivity and Stability 259
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Page 300 and 301: 11Rotation and Interpretation ofPri
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Page 332 and 333: 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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