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Principle Component Analysis.rar
(3.53 MB, 下载次数: 90, 售价: 5 金钱)
Contents
Preface to the Second Edition v
Preface to the First Edition ix
Acknowledgments xv
List of Figures xxiii
List of Tables xxvii
1 Introduction 1
1.1 Definition and Derivation of Principal Components . . . 1
1.2 A Brief History of Principal Component Analysis .... 6
2 Properties of Population Principal Components 10
2.1 Optimal Algebraic Properties of Population
Principal Components ................... 11
2.2 Geometric Properties of Population Principal Components 18
2.3 Principal Components Using a Correlation Matrix .... 21
2.4 Principal Components with Equal and/or Zero Variances 27
3 Properties of Sample Principal Components 29
3.1 Optimal Algebraic Properties of Sample
Principal Components ................... 30
3.2 Geometric Properties of Sample Principal Components . 33
3.3 Covariance and Correlation Matrices: An Example . . . 39
3.4 Principal Components with Equal and/or Zero Variances 43
xviii Contents
3.4.1 Example ....................... 43
3.5 The Singular Value Decomposition ............ 44
3.6 ProbabilityDistributionsforSamplePrincipalComponents 47
3.7 Inference Based on Sample Principal Components .... 49
3.7.1 Point Estimation .................. 50
3.7.2 Interval Estimation ................. 51
3.7.3 Hypothesis Testing ................. 53
3.8 Patterned Covariance and Correlation Matrices ..... 56
3.8.1 Example ....................... 57
3.9 Models for Principal Component Analysis . ....... 59
4 Interpreting Principal Components: Examples 63
4.1 Anatomical Measurements ................. 64
4.2 TheElderlyatHome.................... 68
4.3 Spatial and Temporal Variation in Atmospheric Science . 71
4.4 Properties of Chemical Compounds ............ 74
4.5 StockMarketPrices..................... 76
5 Graphical Representation of Data Using
Principal Components 78
5.1 Plotting Two or Three Principal Components ...... 80
5.1.1 Examples ...................... 80
5.2 PrincipalCoordinateAnalysis............... 85
5.3 Biplots ............................ 90
5.3.1 Examples ...................... 96
5.3.2 Variations on the Biplot .............. 101
5.4 Correspondence Analysis .................. 103
5.4.1 Example ....................... 105
5.5 Comparisons Between Principal Components and
otherMethods........................ 106
5.6 Displaying Intrinsically High-Dimensional Data ..... 107
5.6.1 Example ....................... 108
6 Choosing a Subset of Principal Components or Variables 111
6.1 How Many Principal Components? ............ 112
6.1.1 Cumulative Percentage of Total Variation .... 112
6.1.2 Size of Variances of Principal Components .... 114
6.1.3 The Scree Graph and the Log-Eigenvalue Diagram 115
6.1.4 The Number of Components with Unequal Eigen-
values and Other Hypothesis Testing Procedures 118
6.1.5 Choice of m Using Cross-Validatory or Computa-
tionally Intensive Methods ............. 120
6.1.6 Partial Correlation ................. 127
6.1.7 Rules for an Atmospheric Science Context .... 127
6.1.8 Discussion ...................... 130
Contents xix
6.2 Choosing m, the Number of Components: Examples . . . 133
6.2.1 Clinical Trials Blood Chemistry . . . ....... 133
6.2.2 Gas Chromatography Data ............. 134
6.3 Selecting a Subset of Variables ............... 137
6.4 Examples Illustrating Variable Selection . . ....... 145
6.4.1 Alate adelges (WingedAphids) .......... 145
6.4.2 Crime Rates ..................... 147
7 Principal Component Analysis and Factor Analysis 150
7.1 ModelsforFactorAnalysis................. 151
7.2 Estimation of the Factor Model .............. 152
7.3 Comparisons Between Factor and Principal Component
Analysis ........................... 158
7.4 AnExampleofFactorAnalysis .............. 161
7.5 ConcludingRemarks .................... 165
8 Principal Components in Regression Analysis 167
8.1 Principal Component Regression .............. 168
8.2 Selecting Components in Principal Component Regression 173
8.3 Connections Between PC Regression and Other Methods 177
8.4 Variations on Principal Component Regression ...... 179
8.5 Variable Selection in Regression Using Principal Compo-
nents............................. 185
8.6 Functional and Structural Relationships . . ....... 188
8.7 Examples of Principal Components in Regression .... 190
8.7.1 Pitprop Data .................... 190
8.7.2 Household Formation Data ............. 195
9 Principal Components Used with Other Multivariate
Techniques 199
9.1 Discriminant Analysis .................... 200
9.2 ClusterAnalysis....................... 210
9.2.1 Examples ...................... 214
9.2.2 Projection Pursuit ................. 219
9.2.3 Mixture Models ................... 221
9.3 Canonical Correlation Analysis and Related Techniques . 222
9.3.1 Canonical Correlation Analysis . . . ....... 222
9.3.2 Example of CCA .................. 224
9.3.3 Maximum Covariance Analysis (SVD Analysis),
Redundancy Analysis and Principal Predictors . . 225
9.3.4 OtherTechniquesforRelatingTwoSetsofVariables 228
xx Contents
10 Outlier Detection, Influential Observations and
Robust Estimation 232
10.1 Detection of Outliers Using Principal Components .... 233
10.1.1 Examples ...................... 242
10.2 InfluentialObservationsinaPrincipalComponentAnalysis 248
10.2.1 Examples ...................... 254
10.3 Sensitivity and Stability .................. 259
10.4 Robust Estimation of Principal Components ....... 263
10.5 Concluding Remarks .................... 268
11 Rotation and Interpretation of Principal Components 269
11.1 Rotation of Principal Components ............. 270
11.1.1 Examples ...................... 274
11.1.2 One-step Procedures Using Simplicity Criteria . . 277
11.2 Alternatives to Rotation .................. 279
11.2.1 Components with Discrete-Valued Coe?cients . . 284
11.2.2 Components Based on the LASSO . ....... 286
11.2.3 Empirical Orthogonal Teleconnections ...... 289
11.2.4 Some Comparisons ................. 290
11.3 Simplified Approximations to Principal Components . . 292
11.3.1 PrincipalComponentswithHomogeneous,Contrast
andSparsityConstraints.............. 295
11.4 Physical Interpretation of Principal Components ..... 296
12 PCA for Time Series and Other Non-Independent Data 299
12.1 Introduction ......................... 299
12.2 PCA and Atmospheric Time Series ............ 302
12.2.1 Singular Spectrum Analysis (SSA) . ....... 303
12.2.2 Principal Oscillation Pattern (POP) Analysis . . 308
12.2.3 Hilbert (Complex) EOFs .............. 309
12.2.4 Multitaper Frequency Domain-Singular Value
Decomposition (MTM SVD) ............ 311
12.2.5 Cyclo-Stationary and Periodically Extended EOFs
(andPOPs) ..................... 314
12.2.6 Examples and Comparisons ............ 316
12.3 Functional PCA ....................... 316
12.3.1 The Basics of Functional PCA (FPCA) ...... 317
12.3.2 Calculating Functional PCs (FPCs) . ....... 318
12.3.3 Example - 100 km Running Data . . ....... 320
12.3.4 Further Topics in FPCA .............. 323
12.4 PCA and Non-Independent Data¡ªSome Additional Topics 328
12.4.1 PCA in the Frequency Domain . . . ....... 328
12.4.2 Growth Curves and Longitudinal Data ...... 330
12.4.3 Climate Change¡ªFingerprint Techniques..... 332
12.4.4 Spatial Data ..................... 333
12.4.5 Other Aspects of Non-Independent Data and PCA 335
Contents xxi
13 Principal Component Analysis for Special Types of Data 338
13.1 Principal Component Analysis for Discrete Data ..... 339
13.2 Analysis of Size and Shape ................. 343
13.3 Principal Component Analysis for Compositional Data . 346
13.3.1 Example: 100 km Running Data . . . ....... 349
13.4 Principal Component Analysis in Designed Experiments 351
13.5 Common Principal Components .............. 354
13.6 Principal Component Analysis in the Presence of Missing
Data ............................. 363
13.7 PCA in Statistical Process Control ............ 366
13.8 Some Other Types of Data ................. 369
14 Generalizations and Adaptations of Principal
Component Analysis 373
14.1 Non-Linear Extensions of Principal Component Analysis 374
14.1.1 Non-Linear Multivariate Data Analysis¡ªGifi and
Related Approaches ................. 374
14.1.2 Additive Principal Components
andPrincipalCurves................ 377
14.1.3 Non-Linearity Using Neural Networks ....... 379
14.1.4 Other Aspects of Non-Linearity . . . ....... 381
14.2 Weights, Metrics, Transformations and Centerings .... 382
14.2.1 Weights ....................... 382
14.2.2 Metrics ........................ 386
14.2.3 Transformations and Centering . . . ....... 388
14.3 PCsinthePresenceofSecondaryorInstrumentalVariables 392
14.4 PCA for Non-Normal Distributions ............ 394
14.4.1 Independent Component Analysis . . ....... 395
14.5 Three-Mode, Multiway and Multiple Group PCA .... 397
14.6 Miscellanea ......................... 400
14.6.1 Principal Components and Neural Networks . . . 400
14.6.2 Principal Components for Goodness-of-Fit Statis-
tics.......................... 401
14.6.3 Regression Components, Sweep-out Components
and Extended Components ............. 403
14.6.4 Subjective Principal Components . . ....... 404
14.7 Concluding Remarks .................... 405
A Computation of Principal Components 407
A.1 Numerical Calculation of Principal Components ..... 408
Index 458
Author Index 478
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发表于 2010-12-17 14:31:41
发表于 2011-3-10 17:39:06
好书啊~~