Principal component analysis
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| Format: | Buch |
| Sprache: | English |
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New York [u.a.]
Springer
2002
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| Ausgabe: | 2. ed. |
| Schriftenreihe: | Springer series in statistics
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MARC
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| 245 | 1 | 0 | |a Principal component analysis |c I.T. Jolliffe |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2002 | |
| 300 | |a XXIX, 487 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Springer series in statistics | |
| 650 | 4 | |a Analyse en composantes principales | |
| 650 | 7 | |a Análise multivariada |2 larpcal | |
| 650 | 7 | |a Componentes principais |2 larpcal | |
| 650 | 7 | |a Principale-componentenanalyse |2 gtt | |
| 650 | 4 | |a Principal components analysis | |
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Datensatz im Suchindex
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|---|---|
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| DE-BY-TUM_location | LSB 01 |
| DE-BY-TUM_media_number | 040010210252 040020090155 040020107246 |
| _version_ | 1820861347589521408 |
| adam_text | 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 Probability Distributions for Sample Principal Components 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 The Elderly at Home 68
4.3 Spatial and Temporal Variation in Atmospheric Science . 71
4.4 Properties of Chemical Compounds 74
4.5 Stock Market Prices 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 Principal Coordinate Analysis 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
other Methods 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 (Winged Aphids) 145
6.4.2 Crime Rates 147
7 Principal Component Analysis and Factor Analysis 150
7.1 Models for Factor Analysis 151
7.2 Estimation of the Factor Model 152
7.3 Comparisons Between Factor and Principal Component
Analysis 158
7.4 An Example of Factor Analysis 161
7.5 Concluding Remarks 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 Cluster Analysis 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 Other Techniques for Relating Two Sets of Variables 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 Influential Observations in a Principal Component Analysis 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 Coefficients . . 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 Principal Components with Homogeneous, Contrast
and Sparsity Constraints 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
(and POPs) 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—Some 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—Fingerprint 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—Gifi and
Related Approaches 374
14.1.2 Additive Principal Components
and Principal Curves 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 PCs in the Presence of Secondary or Instrumental Variables 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.I Numerical Calculation of Principal Components 408
Index 458
Author Index 478
|
| any_adam_object | 1 |
| author | Jolliffe, Ian T. |
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| author_facet | Jolliffe, Ian T. |
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| bvnumber | BV014380470 |
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| dewey-full | 519.5/3521 519.5/35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-search | 519.5/35 21 519.5/35 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV014380470 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T15:56:08Z |
| institution | BVB |
| isbn | 0387954422 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009847899 |
| oclc_num | 48907152 |
| open_access_boolean | |
| owner | DE-945 DE-739 DE-N2 DE-20 DE-91G DE-BY-TUM DE-521 DE-11 DE-578 DE-83 |
| owner_facet | DE-945 DE-739 DE-N2 DE-20 DE-91G DE-BY-TUM DE-521 DE-11 DE-578 DE-83 |
| physical | XXIX, 487 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in statistics |
| spellingShingle | Jolliffe, Ian T. Principal component analysis Analyse en composantes principales Análise multivariada larpcal Componentes principais larpcal Principale-componentenanalyse gtt Principal components analysis Hauptkomponentenanalyse (DE-588)4129174-8 gnd Multivariate Analyse (DE-588)4040708-1 gnd Faktorenanalyse (DE-588)4016338-6 gnd |
| subject_GND | (DE-588)4129174-8 (DE-588)4040708-1 (DE-588)4016338-6 |
| title | Principal component analysis |
| title_auth | Principal component analysis |
| title_exact_search | Principal component analysis |
| title_full | Principal component analysis I.T. Jolliffe |
| title_fullStr | Principal component analysis I.T. Jolliffe |
| title_full_unstemmed | Principal component analysis I.T. Jolliffe |
| title_short | Principal component analysis |
| title_sort | principal component analysis |
| topic | Analyse en composantes principales Análise multivariada larpcal Componentes principais larpcal Principale-componentenanalyse gtt Principal components analysis Hauptkomponentenanalyse (DE-588)4129174-8 gnd Multivariate Analyse (DE-588)4040708-1 gnd Faktorenanalyse (DE-588)4016338-6 gnd |
| topic_facet | Analyse en composantes principales Análise multivariada Componentes principais Principale-componentenanalyse Principal components analysis Hauptkomponentenanalyse Multivariate Analyse Faktorenanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009847899&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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