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

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Contentsxix6.2 Choosing m, the Number of Components: Examples . . . 1336.2.1 Clinical Trials Blood Chemistry . . . ....... 1336.2.2 Gas Chromatography Data ............. 1346.3 Selecting a Subset of Variables ............... 1376.4 Examples Illustrating Variable Selection . . ....... 1456.4.1 Alate adelges (WingedAphids) .......... 1456.4.2 Crime Rates ..................... 1477 Principal Component Analysis and Factor Analysis 1507.1 ModelsforFactorAnalysis................. 1517.2 Estimation of the Factor Model .............. 1527.3 Comparisons Between Factor and Principal ComponentAnalysis ........................... 1587.4 AnExampleofFactorAnalysis .............. 1617.5 ConcludingRemarks .................... 1658 Principal Components in Regression Analysis 1678.1 Principal Component Regression .............. 1688.2 Selecting Components in Principal Component Regression 1738.3 Connections Between PC Regression and Other Methods 1778.4 Variations on Principal Component Regression ...... 1798.5 Variable Selection in Regression Using Principal Components............................. 1858.6 Functional and Structural Relationships . . ....... 1888.7 Examples of Principal Components in Regression .... 1908.7.1 Pitprop Data .................... 1908.7.2 Household Formation Data ............. 1959 Principal Components Used with Other MultivariateTechniques 1999.1 Discriminant Analysis .................... 2009.2 ClusterAnalysis....................... 2109.2.1 Examples ...................... 2149.2.2 Projection Pursuit ................. 2199.2.3 Mixture Models ................... 2219.3 Canonical Correlation Analysis and Related Techniques . 2229.3.1 Canonical Correlation Analysis . . . ....... 2229.3.2 Example of CCA .................. 2249.3.3 Maximum Covariance Analysis (SVD Analysis),Redundancy Analysis and Principal Predictors . . 2259.3.4 Other Techniques for Relating Two Sets of Variables 228
xxContents10 Outlier Detection, Influential Observations andRobust Estimation 23210.1 Detection of Outliers Using Principal Components .... 23310.1.1 Examples ...................... 24210.2 Influential Observations in a Principal Component Analysis 24810.2.1 Examples ...................... 25410.3 Sensitivity and Stability .................. 25910.4 Robust Estimation of Principal Components ....... 26310.5 Concluding Remarks .................... 26811 Rotation and Interpretation of Principal Components 26911.1 Rotation of Principal Components ............. 27011.1.1 Examples ...................... 27411.1.2 One-step Procedures Using Simplicity Criteria . . 27711.2 Alternatives to Rotation .................. 27911.2.1 Components with Discrete-Valued Coefficients . . 28411.2.2 Components Based on the LASSO . ....... 28611.2.3 Empirical Orthogonal Teleconnections ...... 28911.2.4 Some Comparisons ................. 29011.3 Simplified Approximations to Principal Components . . 29211.3.1 Principal Components with Homogeneous, ContrastandSparsityConstraints.............. 29511.4 Physical Interpretation of Principal Components ..... 29612 PCA for Time Series and Other Non-Independent Data 29912.1 Introduction ......................... 29912.2 PCA and Atmospheric Time Series ............ 30212.2.1 Singular Spectrum Analysis (SSA) . ....... 30312.2.2 Principal Oscillation Pattern (POP) Analysis . . 30812.2.3 Hilbert (Complex) EOFs .............. 30912.2.4 Multitaper Frequency Domain-Singular ValueDecomposition (MTM SVD) ............ 31112.2.5 Cyclo-Stationary and Periodically Extended EOFs(andPOPs) ..................... 31412.2.6 Examples and Comparisons ............ 31612.3 Functional PCA ....................... 31612.3.1 The Basics of Functional PCA (FPCA) ...... 31712.3.2 Calculating Functional PCs (FPCs) . ....... 31812.3.3 Example - 100 km Running Data . . ....... 32012.3.4 Further Topics in FPCA .............. 32312.4 PCA and Non-Independent Data—Some Additional Topics 32812.4.1 PCA in the Frequency Domain . . . ....... 32812.4.2 Growth Curves and Longitudinal Data ...... 33012.4.3 Climate Change—Fingerprint Techniques ..... 33212.4.4 Spatial Data ..................... 33312.4.5 Other Aspects of Non-Independent Data and PCA 335
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: xviiiContents3.4.1 Example ........
Page 25 and 26: xxivList of Figures5.2 Artistic qua
Page 29 and 30: 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
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Page 64 and 65: 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
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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
Page 518:
Author Index 487Yaguchi, H. 371Yana
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