Practical guide to chemometrics:
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| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC / Taylor & Francis
2006
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 541 S. graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 1574447831 9781574447835 |
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| 245 | 1 | 0 | |a Practical guide to chemometrics |c ed. by Paul Gemperline |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boca Raton [u.a.] |b CRC / Taylor & Francis |c 2006 | |
| 300 | |a 541 S. |b graph. Darst. |e 1 CD-ROM (12 cm) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Chimiométrie | |
| 650 | 7 | |a Chimiométrie |2 ram | |
| 650 | 4 | |a Chemometrics | |
| 700 | 1 | |a Gemperline, Paul |e Sonstige |4 oth | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014817494&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-014817494 | ||
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| adam_text | Contents
Chapter 1
Introduction to Chemometrics 1
Paul J. Gemperline
Chapter 2
Statistical Evaluation of Data 7
Anthony D. Walmsley
Chapter 3
Sampling Theory, Distribution Functions, and the Multivariate
Normal Distribution 41
Paul J. Gemperline and John H. Kalivas
Chapter 4
Principal Component Analysis 69
Paul J. Gemperline
Chapter 5
Calibration 105
John H. Kalivas and Paul J. Gemperline
Chapter 6
Robust Calibration 167
Mia Hubert
Chapter 7
Kinetic Modeling of Multivariate Measurements with
Nonlinear Regression 217
Marcel Maeder and Yorck-Michael Neuhold
Chapter 8
Response-Surface Modeling and Experimental Design 263
Kaiin Stoyanov and Anthony D. Walmsley
Chapter 9
Classification and Pattern Recognition 339
Barry K. Lavine and Charles E. Davidson
Chapter 10
Signal Processing and Digital Filtering 379
Steven D. Brown
Chapter 11
Multivariate Curve Resolution 417
Roma Tauler and Anna de Juan
Chapter 12
Three-Way Calibration with Hyphenated Data 475
Karl S. Booksh
Chapter 13
Future Trends in Chemometrics 509
Paul J. Gemperline
Index 521
1 Introduction to
Chemometrics
Paul J. Gemperline
CONTENTS
1.1 Chemical Measurements — A Basis for Decision
Making 1
1.2 Chemical Measurements — The Three-Legged
Platfbrm 2
1.3 Chemometrics 2
1.4 How to Use This Book 3
1.4.1 Software Applications 4
1.5 General Reading on Chemometrics 5
References 6
O Statistical Evaluation
of Data
Anthony D. Walmsley
CONTENTS
Introduction 8
2.1 Sources of Error 9
2.1.1 Some Common Terms 10
2.2 Precision and Accuracy 12
2.3 Properties of the Normal Distribution 14
2.4 Significance Testing 18
2.4.1 The F-test for Comparison of Variance
(Precision) 19
2.4.2 The Student t-Test 22
2.4.3 One-Tailed or Two-Tailed Tests 24
2.4.4 Comparison of a Sample Mean with a Certified
Value 24
2.4.5 Comparison of the Means from Two Samples 25
2.4.6 Comparison of Two Methods with Different Test Objects
or Specimens 26
2.5 Analysis of Variance 27
2.5.1 ANOVA to Test for Differences Between
Means 28
2.5.2 The Within-Sample Variation (Within-Treatment
Variation) 29
2.5.3 Between-Sample Variation (Between-Treatment
Variation) 29
2.5.4 Analysis of Residuais 30
2.6 Outliers 33
2.7 Robust Estimates of Central Tendency and Spread 36
2.8 Software 38
2.8.1 ANOVA Using Excel 39
Recommended Reading 40
References 40
Q Sampling Theory,
Distribution Functions,
and the Multivariate
Normal Distribution
Paul J. Gemperline and John H. Kalivas
CONTENTS
3.1 Sampling and Sampling Distributions 42
3.1.1 The Normal Distribution 43
3.1.2 Standard Normal Distribution 45
3.2 Central Limit Theorem 45
3.2.1 Implications of the Central Limit Theorem 45
3.3 Small Sample Distributions 46
3.3.1 The t-Distribution 46
3.3.2 Chi-Square Distribution 47
3.4 Univariate Hypothesis Testing 48
3.4.1 Inferences about Means 49
3.4.2 Inferences about Variance and the F-Distribution 51
3.5 The Multivariate Normal Distribution 51
3.5.1 Generalized or Mahalanobis Distances 52
3.5.2 The Variance-Covariance Matrix 53
3.5.3 Estimation of Population Parameters from Small Samples 54
3.5.4 Comments on Assumptions 55
3.5.5 Generalized Sample Variance 55
3.5.6 Graphical Illustration of Selected Bivariate
Normal Distributions 56
3.5.7 Chi-Square Distribution 58
3.6 Hypothesis Test for Comparison of Multivariate Means 59
3.7 Example: Multivariate Distances 59
3.7.1 Step 1: Graphical Review of smx.mat Data File 60
3.7.2 Step 2: Selection of Variables (Wavelengths) 61
3.7.3 Step 3: View Histograms of Selected Variables 61
3.7.4 Step 4: Compute the Training Set Mean and
Variance-Covariance Matrix 62
41
42 Practical Guide to Chemometrics
3.7.5 Step 5: Calculate Mahalanobis Distances and
Probability Densities 64
3.7.6 Step 6: Find Acceptable and
Unacceptable Objects 65
Recommended Reading 66
References 67
A Principal Component
Analysis
Paul J. Gemperline
CONTENTS
4.1 Introduction 70
4.2 Spectroscopic-Chromatographic Data 70
4.2.1 Basis Vectors 71
4.3 The Principal Component Model 73
4.3.1 Eigenvectors and Eigenvalues 74
4.3.2 The Singular-Value Decomposition 76
4.3.3 Alternative Formulations of the Principal
Component Model 77
4.4 Preprocessing Options 77
4.4.1 Mean Centering 78
4.4.2 Variance Scaling 78
4.4.3 Baseline Correction 80
4.4.4 Smoothing and Filtering 81
4.4.5 First and Second Derivatives 82
4.4.6 Normalization 83
4.4.7 Multiplicative Scatter Correction (MSC) and
Standard Normal Variate (SNV) Transforms 83
4.5 PCA Data Exploration Procedure 86
46 Influencing Factors 87
4.6.1 Variance and Residual Variance 89
4.6.2 Distribution of Error in Eigenvalues 93
4.6.3 F-Test for Determining the Number
of Factors 93
4.7 Basis Vectors %
4.7.1 Clustering and Classification with PCA
ScorePlots 98
4.8 Residual Spectra 98
4.8.1 Residual Variance Analysis 100 i
4.9 Conclusions 102 |
Recommended Reading 103
References 103 j
II
C Calibration
John H. Kalivas and Paul J. Gemperline
CONTENTS
5.1 Data Sets 107
5.1.1 Near Infrared Spectroscopy 107
5.1.2 Fundamental Modes of Vibration, Overtones,
and Combinations 108
5.1.3 Water-Methanol Mixtures 108
5.1.4 Solvent Interactions 108
5.2 Introduction to Calibration 109
5.2.1 Univariate Calibration 109
5.2.2 Nonzero Intercepts 110
5.2.3 Multivariate Calibration 111
5.2.4 Curvilinear Calibration 112
5.2.5 Selection of Calibration and Validation Samples 113
5.2.6 Measurement Error and Measures of
Prediction Error 114
5.3 A Practical Calibration Example 116
5.3.1 Graphical Survey of NIR Water-Methanol Data 116
5.3.2 Univariate Calibration 118
5.3.2.1 Without an Intercept Term 118
5.3.2.2 With an Intercept Term 119
5.3.3 Multivariate Calibration 119
5.4 Statistical Evaluation of Calibration Models Obtained by
Least Squares 121
5.4.1 Hypothesis Testing 122
5.4.2 Partitioning of Variance in Least-Squares Solutions 123
5.4.3 Interpreting Regression ANOVA Tables 125
5.4.4 Confidence Interval and Hypothesis Tests for
Regression Coefficients 126
5.4.5 Prediction Confidence Intervals 127
5.4.6 Leverage and Influence 128
5.4.7 Model Departures and Outliers 129
5.4.8 Coefficient of Determination and Multiple
Correlation Coefficient 130
5.4.9 Sensitivity and Limit of Detection 131
5.4.9.1 Sensitivity 131
5.4.9.2 Limit of Detection 132
5.4.10 Interference Effects and Selectivity 134
5.5 Variable Selection 135
5.5.1 Forward Selection 136
5.5.2 Efroymson s Stepwise Regression Algorithm 136
5.5.2.1 Variable-Addition Step 136
5.5.2.2 Variable-Deletion Step 137
5.5.2.3 Convergence of Algorithm 137
5.5.3 Backward Elimination 137
5.5.4 Sequential-Replacement Algorithms 138
5.5.5 All Possible Subsets ...138
5.5.6 Simulated Annealing and Genetic Algorithm 138
5.5.7 Recommendations and Precautions 138
5.6 Biased Methods of Calibration ZZ.ZZ . l39
5.6.1 Principal Component Regression 140
5.6.1.1 Basis Vectors 141
5.6.1.2 Mathematical Procedures 142
5.6.1.3 Number of Basis Vectors 144
5.6.1.4 Example PCR Results [ _ 145
5.6.2 Partial Least Squares 147
5.6.2.1 Mathematical Procedure 148
5.6.2.2 Number of Basis Vectors Selection 149
5.6.2.3 Comparison with PCR ..149
5.6.3 A Few Other Calibration Methods Z....ZZZZZZZZZZZZZZZ 150
5.6.3.1 Common Basis Vectors and a
Generic Model 150
5.6.4 Regularization 151
5.6.5 Example Regularization Results 153
5.7 Standard Addition Method !53
5.7.1 Univariate Standard Addition Method 154
5.7.2 Multivariate Standard Addition Method. 155
5.8 Internal Standards , 156
5.9 Preprocessing Techniques ZZZ 156
5.10 Calibration Standardization ZZZZZZZZ. 157
5.10.1 Standardization of Predicted Values ] 157
5.10.2 Standardization of Instrument ResponseT Z! 158
5.10.3 Standardization with Preprocessing
Techniques , SQ
5.11 Software ZZZZZZZ. 159
Recommended Reading An
References ^
160
£ Robust Calibration j
Mia Hubert j
CONTENTS j
6.1 Introduction 168 |
62 Location and Scale Estimation 169 j
6.2.1 The Mean and the Standard Deviation 169 j
6.2.2 The Mediän and the Mediän Absolute Deviation 171
6.2.3 Other Robust Estimators of Location and Scale 171
6.3 Location and Covariance Estimation in Low Dimensions 173 j
6.3.1 The Empirical Mean and Covariance Matrix 173 (
6.3.2 The Robust MCD Estimator 174
6.3.3 Other Robust Estimators of Location and Covariance 176 j
6-4 Linear Regression in Low Dimensions 176
6.4.1 Linear Regression with One Response Variable 176 1
6.4.1.1 The Multiple Linear Regression Model 176 ;
6.4.1.2 The Classical Least-Squares Estimator 177
6.4.1.3 The Robust LTS Estimator 178
6.4.1.4 An Outlier Map 180
6.4.1.5 Other Robust Regression Estimators 182 ;
6.4.2 Linear Regression with Several Response Variables 183
6.4.2.1 The Multivariate Linear Regression
Model 183
6.4.2.2 The Robust MCD-Regression Estimator 184
6.4.2.3 An Example 185
6.5 Principal Components Analysis 185
6.5.1 Classical PCA 185
6.5.2 Robust PCA Based on a Robust Covariance
Estimator 187
6.5.3 Robust PCA Based on Projection Pursuit 188
6.5.4 Robust PCA Based on Projection Pursuit
and the MCD 189
6.5.5 An Outlier Map 191
6.5.6 Selecting the Number of Principal Components 193
6.5.7 An Example 194
6 6 Principal Component Regression 194
6.6.1 Classical PCR 194
6.6.2 Robust PCR 197
6.6.3 Model Calibration and Validation 198
6.6.4 An Example ino
6.7 Partial Least-Squares Regression 202
6.7.1 Classical PLSR 202
6.7.2 Robust PLSR ZZZZ 203
6.7.3 An Example 204
6.8 Classification „„„
6.8.1 Classification in Low Dimensions 207
6.8.1.1 Classical and Robust Discriminant Rules.. . . . . . . . . . . . . . . 207
6.8.1.2 Evaluating the Discriminant Rules 208
6.8.1.3 An Example 209
6.8.2 Classification in High Dimensions oi,
6.9 Software Availability
References : 2U
212
7 Kinetic Modeling
of Multivariate
Measurements with
Nonlinear Regression
Marcel Maeder and Yorck-Michael Neuhold
CONTENTS
218
7.1 Introduction 910
7.2 Multivariate Data, Beer-Lambert s Law, Matrix Notation
7.3 Calculation of the Concentration Profiles: Case I, ^
Simple Mechanisms 222
7.4 Model-Based Nonlinear Fitting 225
7.4.1 Direct Methods, Simplex 227
7.4.2 Nonlinear Fitting Using Excel s Solver ^
7.4.3 Linear and Nonlinear Parameters - l :: 230
7.4.4 Newton-Gauss-Levenberg/Marquardt (NGL/M) ~Z.2Y1
7.4.5 Nonwhite Noise
7.5 Calculation of the Concentration Profiles: Case 11, ^
Complex Mechanisms . c 242
7.5.1 Fourth-Order Runge-Kutta Method in Excel ¦¦•¦»^
7.5.2 Interesting Kinetic Examples 246
7.5.2.1 Autocatalysis 248
7.5.2.2 Zeroth-Order Reaction.._- •
7 5 2 3 Lotka-Volterra (Sheep and Wolves) £
7 5 214 Tne Belousov-Zhabotinsky (BZ) Reaction 251
7.6 Calculation of the Concentration Profiles: Case III, ^
Very Complex Mechanisms 255
7.7 Related Issues ¦ 256
7.7.1 Measurement Techmques • ¦ • 256
7.7.2 Model Parser 256
7.7.3 Flow Reactors ......-- 256
7.7.4 Globalization of the Analysis
7.7.5 Soft-Modeling Methods 257
7.7.6 Other Methods 258
Appendix 258
References 259
Q Response-Surface
Modeling and
Experimental Design
Kaiin Stoyanov and Anthony D. Walmsley
CONTENTS
264
8.1 Introduction 265
8.2 Response-Surface Modeling 265
8.2.1 The General Scheine of RSM ^^ 268
8.2.2 Factor Spaces 268
8.2.2.1 Process Factor Spaces •¦¦¦¦¦¦¦ 269
8.2.2.2 Mixture Factor Spaces 272
8.2.2.3 Simplex-Lattice Designs —- 2?5
8.2.2.4 Simplex-Centroid Designs .. ........279
8 2 2 5 Constrained Mixture Spaces 2g3
8.2.2.6 Mixture+Process Factor Spaces 2g6
8.2.3 Some Regression-Analysis-Related Notation •¦••••¦¦¦• ^
8.3 One-Variable-at-a-Time vs. Optimal Design 2gg
8.3.1 Bivariate (Multivariate) Exarnple -¦~~^ 290
8.3.2 Advantages of the One-Vanable-at-a-Time Approach ^
8.3.3 Disadvantages 290
8.4 Symmetrie Optimal Designs •• 290
8.4.1 Two-Level Füll Factorial Designs _^ 29Q
8 4 11 Advantages of Factonal D^.8- 291
8.4.3 Central Composite Designs •• — ¦- 294
8.5 The Taguchi Experimental Design Approacn ^
8.6 Nonsymmetric Optimal Designs 298
8.6.1 Optimality Criteria...». ^ ^: j s 299
X zS SZEtt- —£
o c i i Desien Measures
6 3 2 üSptimality and D-Efficiency 04
8.6.3.3 G-Optimality and G-Efficiency 305
k
8.6.3.4 A-Optimality 30g j
8.6.3.5 E-Optimality 306 !
8.7 Algorithms for the Search of Realizable Optimal
Experimental Designs 306
8.7.1 Exact (or N-Point) D-Optimal Designs Z Z Z ZZ307
8.7.1.1 Fedorov s Algorithm 307
8.7.1.2 Wynn-Mitchell and van Schalkwyk Algorithms 308
8.7.1.3 DETMAX Algorithm 308
lJAA The MD Galil and Kiefer s MgonthmZZZ 111.309
8.7.2 Sequential D-Optimal Designs 310
8.7.2.1 Example 3^j
8 8 ™i sTToal Comp°site D^marDe;ignsi::::::::::::3i3
*tOfft *£T * Catal°gS °f D™Z™ of Expenments 316
8.8.1 Off-the-Shelf Software Packages 316
8.8.1.1 MATLAB ,..IZ 316
8.8.1.2 Design Expert 319
8.8.1.3 Other Packages ... 319
*J2 Catf ogs of Experimental Designs . . 320
?97C^TCT?DOE in ^.vanatecäiibrat^ ::::::32i
8.9.1 ConstructionofaCalibration Sample Set .321 !
8 9 12 IT^ °f * Number °f Signet Factors 322
8.9. .2 Idenüfymg the Type of the Regression Model 325
8.91.3 Definmg the Boundsof the Factor Space 327 I
892 In!- ES lmftln8EXtinCtionCoefficients.. 329 I
8.9.2 Improvmg Qualuy from Historical Data... 330
8-9.2.1 Improving the Numerical Stabilitv
of the Data Set.... y „,
8.9.2.2 Prediction Ability. l
8.10 Conclusion * 334
References 337
337
Q Classification and Pattern
Recognition
Barry K. Lavine and Charles E. Davidson
CONTENTS
9.1 Introduction 339
9.2 Data Preprocessing 341
9.3 Mapping and Display 342
9.4 Clustering 347
9.5 Classification 351
9.5.1 K-Nearest Neighbor 352
9.5.2 Partial Least Squares 352
9.5.3 SIMCA 353
9.6 Practical Considerations 354
9.7 Applications of Pattern-Recognition
Techniques 355
9.7.1 Archaeological Artifacts 356
9.7.2 Fuel Spill Identification 358
9.7.3 Sorting Plastics for Recycling 365
9.7.4 Taxonomy Based on Chemical
Constitution 371
References 374
1 Q Signal Processing and
Digital Filtering
Steven D. Brown
CONTENTS
379
10.1 Introduction ion
10.2 Noise Removal and the Problem of Prior Information ^
10.2.1 Signal Estimation and Signal Detection....
10.3 Reexpressing Data in Alternate Bases to Analyze Structure. .^
10.3.1 Projection-Based Signal Analysis as S.gnal Processmg 383
10.4 Frequency-Domain Signal Processing 386 j
10.4.1 The Fourier Transform 386 |
10.4.2 The Sampüng Theorem and Aliasing.....- . »•- • |
10.4.3 The Bandwidth-Limited, Discrete Founer Transform 388
10.4.4 Properties of the Fourier Transform ZZZ.394
10.5 Frequency Domain Smoothing ...394
10.5.1 Smoothing . 395
10.5.2 Smoothing with Designer Transfer Functions ...........395
10.6 Time-Domain Filtering and Smoothing • • 39g
10.6.1 Smoothing 400
!S: JÄisäss^^^™ ;::Z
10.7 Wavelet-Based Signal Processing 406
10.7.1 The Wavelet Function -^^tf^^™™ons 408
10.7.2 Time and Frequency Localizations ^
10.7.3 The Discrete Wavelet Transform — ••••¦•
10.7.4 Smoothing and Denoismg w* Wavelets................ ^
References 416
Further Reading
A | Multivariate Curve
Resolution
Roma Tauler and Anna de Juan
CONTENTS
11.1 Introduction: General Concept, Ambiguities,
Resolution Theorems 4*°
11.2 Historical Background 422
11.3 Local Rank and Resolution: Evolving Factor Analysis
and Related Techniques 423
11.4 Noniterative Resolution Methods 426
11.4.1 Window Factor Analysis (WFA) 427
11.4.2 Other Techniques: Subwindow Factor Analysis (SFA)
and Heuristic Evolving Latent Projections (HELP) 429
11.5 Iterative Methods
11.5.1 Generation of Initial Estimates 432
11.5.2 Constraints, Definition, Classification: Equality and
Inequality Constraints Based on Chemical or
Mathematical Properties 4^
11.5.2.1 Nonnegativity ^
11.5.2.2 Unimodality *
11.5.2.3 Closure
11.5.2.4 Known Profiles #J3
11.5.2.5 Hard-Modeling Constraints:
Physicochemical Models 4j5
115 2 6 Local-Rank Constraints, Selectivity,
and Zero-Concentration Windows ¦_¦ 433
11.5.3 Iterative Target Transformation Factor Analys.s (ITTFA) 43
11.5.4 Multivariate Curve Resolution-Alternating ^
Least Squares (MCR-ALS) ¦•••••;
11.6 Extension of Self-Modeling Curve Resolution to Multiway
Data: MCR-ALS Simultaneous Analysis of Mutaple ^
Correlated Data Matrices
11.7 Uncertainty in Resolution Results, Range of Feasible ^
Solutions, and Error in Resolution . . . . . .... M%
11.8 Applications 449
11.8.1 Biochemical Processes
11.8.1.1 Study of Changes in the Protein
Secondary Structure 451
11.8.1.2 Study of Changes in the Tertiary Structure 453
11.8.1.3 Global Description of the Protein
Folding Process 453
11.8.2 Environmental Data 454
11.8.3 Spectroscopic Images 461
11.9 Software 465
References 467
1 O Three-Way Calibration
with Hyphenated Data
Karl S. Booksh
CONTENTS
12.1 Introduction 475
12.2 Background 476
12.3 Nomenclature of Three-Way Data 478
12.4 Three-Way Models 478
12.5 Examples 481
12.6 Rank Annihilation Methods 482
12.6.1 Rank Annihilation Factor Analysis 482
12.6.1.1 RAFA Application 483
12.6.2 Generalized Rank Annihilation Method 485
12.6.2.1 GRAM Application 486
12.6.3 Direct Trilinear Decomposition 489
12.6.3.1 DTLD Application 490
12.7 Alternating Least-Squares Methods 491
12.7.1 PARAFAC / CANDECOMP 491
12.7.1.1 Tuckals 493
12.7.1.2 Solution Constraints 493
12.7.1.3 PARAFAC Application 494
12.8 Extensions of Three-Way Methods 495
12.9 Figures of Merit 496
12.10 Caveats 497
References 49^
Appendix 12.1 GRAM Algorithm 502
Appendix 12.2 DTLD Algorithm 503
Appendix 12.3 PARAFAC Algorithm 504
1 Q Future Trends in
Chemometrics
Paul J. Gemperline
CONTENTS
13.1 Historical Development of Chemometrics 510
13.1.1 Chemometrics — a Maturing Discipline 511
13.2 Reviews of Chemometrics and Future Trends 511
13.2.1 Process Analytical Chemistry 512
13.2.2 Spectroscopy 512
13.2.3 Food and Feed Chemistry 512
13.2.4 Other Interesting Application Areas 513
13.3 Drivers of Growth in Chemometrics 513
13.3.1 The Challenge of Large Data Sets 514
13.3.2 Chemometrics at the Interface of Chemical
and Biological Sciences 514
13.4 Concluding Remarks 516
References 516
|
| adam_txt |
Contents
Chapter 1
Introduction to Chemometrics 1
Paul J. Gemperline
Chapter 2
Statistical Evaluation of Data 7
Anthony D. Walmsley
Chapter 3
Sampling Theory, Distribution Functions, and the Multivariate
Normal Distribution 41
Paul J. Gemperline and John H. Kalivas
Chapter 4
Principal Component Analysis 69
Paul J. Gemperline
Chapter 5
Calibration 105
John H. Kalivas and Paul J. Gemperline
Chapter 6
Robust Calibration 167
Mia Hubert
Chapter 7
Kinetic Modeling of Multivariate Measurements with
Nonlinear Regression 217
Marcel Maeder and Yorck-Michael Neuhold
Chapter 8
Response-Surface Modeling and Experimental Design 263
Kaiin Stoyanov and Anthony D. Walmsley
Chapter 9
Classification and Pattern Recognition 339
Barry K. Lavine and Charles E. Davidson
Chapter 10
Signal Processing and Digital Filtering 379
Steven D. Brown
Chapter 11
Multivariate Curve Resolution 417
Roma Tauler and Anna de Juan
Chapter 12
Three-Way Calibration with Hyphenated Data 475
Karl S. Booksh
Chapter 13
Future Trends in Chemometrics 509
Paul J. Gemperline
Index 521
1 Introduction to
Chemometrics
Paul J. Gemperline
CONTENTS
1.1 Chemical Measurements — A Basis for Decision
Making 1
1.2 Chemical Measurements — The Three-Legged
Platfbrm 2
1.3 Chemometrics 2
1.4 How to Use This Book 3
1.4.1 Software Applications 4
1.5 General Reading on Chemometrics 5
References 6
O Statistical Evaluation
of Data
Anthony D. Walmsley
CONTENTS
Introduction 8
2.1 Sources of Error 9
2.1.1 Some Common Terms 10
2.2 Precision and Accuracy 12
2.3 Properties of the Normal Distribution 14
2.4 Significance Testing 18
2.4.1 The F-test for Comparison of Variance
(Precision) 19
2.4.2 The Student t-Test 22
2.4.3 One-Tailed or Two-Tailed Tests 24
2.4.4 Comparison of a Sample Mean with a Certified
Value 24
2.4.5 Comparison of the Means from Two Samples 25
2.4.6 Comparison of Two Methods with Different Test Objects
or Specimens 26
2.5 Analysis of Variance 27
2.5.1 ANOVA to Test for Differences Between
Means 28
2.5.2 The Within-Sample Variation (Within-Treatment
Variation) 29
2.5.3 Between-Sample Variation (Between-Treatment
Variation) 29
2.5.4 Analysis of Residuais 30
2.6 Outliers 33
2.7 Robust Estimates of Central Tendency and Spread 36
2.8 Software 38
2.8.1 ANOVA Using Excel 39
Recommended Reading 40
References 40
Q Sampling Theory,
Distribution Functions,
and the Multivariate
Normal Distribution
Paul J. Gemperline and John H. Kalivas
CONTENTS
3.1 Sampling and Sampling Distributions 42
3.1.1 The Normal Distribution 43
3.1.2 Standard Normal Distribution 45
3.2 Central Limit Theorem 45
3.2.1 Implications of the Central Limit Theorem 45
3.3 Small Sample Distributions 46
3.3.1 The t-Distribution 46
3.3.2 Chi-Square Distribution 47
3.4 Univariate Hypothesis Testing 48
3.4.1 Inferences about Means 49
3.4.2 Inferences about Variance and the F-Distribution 51
3.5 The Multivariate Normal Distribution 51
3.5.1 Generalized or Mahalanobis Distances 52
3.5.2 The Variance-Covariance Matrix 53
3.5.3 Estimation of Population Parameters from Small Samples 54
3.5.4 Comments on Assumptions 55
3.5.5 Generalized Sample Variance 55
3.5.6 Graphical Illustration of Selected Bivariate
Normal Distributions 56
3.5.7 Chi-Square Distribution 58
3.6 Hypothesis Test for Comparison of Multivariate Means 59
3.7 Example: Multivariate Distances 59
3.7.1 Step 1: Graphical Review of smx.mat Data File 60
3.7.2 Step 2: Selection of Variables (Wavelengths) 61
3.7.3 Step 3: View Histograms of Selected Variables 61
3.7.4 Step 4: Compute the Training Set Mean and
Variance-Covariance Matrix 62
41
42 Practical Guide to Chemometrics
3.7.5 Step 5: Calculate Mahalanobis Distances and
Probability Densities 64
3.7.6 Step 6: Find "Acceptable" and
"Unacceptable" Objects 65
Recommended Reading 66
References 67
A Principal Component
Analysis
Paul J. Gemperline
CONTENTS
4.1 Introduction 70
4.2 Spectroscopic-Chromatographic Data 70
4.2.1 Basis Vectors 71
4.3 The Principal Component Model 73
4.3.1 Eigenvectors and Eigenvalues 74
4.3.2 The Singular-Value Decomposition 76
4.3.3 Alternative Formulations of the Principal
Component Model 77
4.4 Preprocessing Options 77
4.4.1 Mean Centering 78
4.4.2 Variance Scaling 78
4.4.3 Baseline Correction 80
4.4.4 Smoothing and Filtering 81
4.4.5 First and Second Derivatives 82
4.4.6 Normalization 83
4.4.7 Multiplicative Scatter Correction (MSC) and
Standard Normal Variate (SNV) Transforms 83
4.5 PCA Data Exploration Procedure 86
46 Influencing Factors 87
4.6.1 Variance and Residual Variance 89
4.6.2 Distribution of Error in Eigenvalues 93
4.6.3 F-Test for Determining the Number
of Factors 93
4.7 Basis Vectors %
4.7.1 Clustering and Classification with PCA
ScorePlots 98
4.8 Residual Spectra 98
4.8.1 Residual Variance Analysis 100 i
4.9 Conclusions 102 |
Recommended Reading 103 \
References 103 j
II
C Calibration
John H. Kalivas and Paul J. Gemperline
CONTENTS
5.1 Data Sets 107
5.1.1 Near Infrared Spectroscopy 107
5.1.2 Fundamental Modes of Vibration, Overtones,
and Combinations 108
5.1.3 Water-Methanol Mixtures 108
5.1.4 Solvent Interactions 108
5.2 Introduction to Calibration 109
5.2.1 Univariate Calibration 109
5.2.2 Nonzero Intercepts 110
5.2.3 Multivariate Calibration 111
5.2.4 Curvilinear Calibration 112
5.2.5 Selection of Calibration and Validation Samples 113
5.2.6 Measurement Error and Measures of
Prediction Error 114
5.3 A Practical Calibration Example 116
5.3.1 Graphical Survey of NIR Water-Methanol Data 116
5.3.2 Univariate Calibration 118
5.3.2.1 Without an Intercept Term 118
5.3.2.2 With an Intercept Term 119
5.3.3 Multivariate Calibration 119
5.4 Statistical Evaluation of Calibration Models Obtained by
Least Squares 121
5.4.1 Hypothesis Testing 122
5.4.2 Partitioning of Variance in Least-Squares Solutions 123
5.4.3 Interpreting Regression ANOVA Tables 125
5.4.4 Confidence Interval and Hypothesis Tests for
Regression Coefficients 126
5.4.5 Prediction Confidence Intervals 127
5.4.6 Leverage and Influence 128
5.4.7 Model Departures and Outliers 129
5.4.8 Coefficient of Determination and Multiple
Correlation Coefficient 130
5.4.9 Sensitivity and Limit of Detection 131
5.4.9.1 Sensitivity 131
5.4.9.2 Limit of Detection 132
5.4.10 Interference Effects and Selectivity 134
5.5 Variable Selection 135
5.5.1 Forward Selection 136
5.5.2 Efroymson's Stepwise Regression Algorithm 136
5.5.2.1 Variable-Addition Step 136
5.5.2.2 Variable-Deletion Step 137
5.5.2.3 Convergence of Algorithm 137
5.5.3 Backward Elimination 137
5.5.4 Sequential-Replacement Algorithms 138
5.5.5 All Possible Subsets .138
5.5.6 Simulated Annealing and Genetic Algorithm 138
5.5.7 Recommendations and Precautions 138
5.6 Biased Methods of Calibration ZZ.ZZ ."l39
5.6.1 Principal Component Regression 140
5.6.1.1 Basis Vectors 141
5.6.1.2 Mathematical Procedures 142
5.6.1.3 Number of Basis Vectors 144
5.6.1.4 Example PCR Results ['_ 145
5.6.2 Partial Least Squares 147
5.6.2.1 Mathematical Procedure 148
5.6.2.2 Number of Basis Vectors Selection 149
5.6.2.3 Comparison with PCR .149
5.6.3 A Few Other Calibration Methods Z.ZZZZZZZZZZZZZZZ 150
5.6.3.1 Common Basis Vectors and a
Generic Model 150
5.6.4 Regularization 151
5.6.5 Example Regularization Results 153
5.7 Standard Addition Method !53
5.7.1 Univariate Standard Addition Method 154
5.7.2 Multivariate Standard Addition Method. 155
5.8 Internal Standards , 156
5.9 Preprocessing Techniques ZZZ 156
5.10 Calibration Standardization ZZZZZZZZ. 157
5.10.1 Standardization of Predicted Values ] 157
5.10.2 Standardization of Instrument ResponseT'Z! 158
5.10.3 Standardization with Preprocessing
Techniques , SQ
5.11 Software ZZZZZZZ. 159
Recommended Reading An
References ^
160
£ Robust Calibration j
Mia Hubert j
CONTENTS j
6.1 Introduction 168 |
62 Location and Scale Estimation 169 j
6.2.1 The Mean and the Standard Deviation 169 j
6.2.2 The Mediän and the Mediän Absolute Deviation 171
6.2.3 Other Robust Estimators of Location and Scale 171
6.3 Location and Covariance Estimation in Low Dimensions 173 j
6.3.1 The Empirical Mean and Covariance Matrix 173 (
6.3.2 The Robust MCD Estimator 174 \
6.3.3 Other Robust Estimators of Location and Covariance 176 j
6-4 Linear Regression in Low Dimensions 176
6.4.1 Linear Regression with One Response Variable 176 1
6.4.1.1 The Multiple Linear Regression Model 176 ;
6.4.1.2 The Classical Least-Squares Estimator 177
6.4.1.3 The Robust LTS Estimator 178 \
6.4.1.4 An Outlier Map 180
6.4.1.5 Other Robust Regression Estimators 182 ;
6.4.2 Linear Regression with Several Response Variables 183
6.4.2.1 The Multivariate Linear Regression
Model 183
6.4.2.2 The Robust MCD-Regression Estimator 184
6.4.2.3 An Example 185
6.5 Principal Components Analysis 185
6.5.1 Classical PCA 185
6.5.2 Robust PCA Based on a Robust Covariance
Estimator 187
6.5.3 Robust PCA Based on Projection Pursuit 188
6.5.4 Robust PCA Based on Projection Pursuit
and the MCD 189
6.5.5 An Outlier Map 191
6.5.6 Selecting the Number of Principal Components 193
6.5.7 An Example 194
6 6 Principal Component Regression 194
6.6.1 Classical PCR 194
6.6.2 Robust PCR 197
6.6.3 Model Calibration and Validation 198
6.6.4 An Example ino
6.7 Partial Least-Squares Regression 202
6.7.1 Classical PLSR 202
6.7.2 Robust PLSR "ZZZZ 203
6.7.3 An Example 204
6.8 Classification „„„
6.8.1 Classification in Low Dimensions ' ' 207
6.8.1.1 Classical and Robust Discriminant Rules.".'.'.'.'"".'.'.'.'.'.'.'.'."."207
6.8.1.2 Evaluating the Discriminant Rules 208
6.8.1.3 An Example 209
6.8.2 Classification in High Dimensions oi,
6.9 Software Availability \
References : 2U
212
7 Kinetic Modeling
of Multivariate
Measurements with
Nonlinear Regression
Marcel Maeder and Yorck-Michael Neuhold
CONTENTS
218
7.1 Introduction 910
7.2 Multivariate Data, Beer-Lambert's Law, Matrix Notation
7.3 Calculation of the Concentration Profiles: Case I, ^
Simple Mechanisms 222
7.4 Model-Based Nonlinear Fitting 225
7.4.1 Direct Methods, Simplex 227
7.4.2 Nonlinear Fitting Using Excel's Solver ^
7.4.3 Linear and Nonlinear Parameters -"""l":: 230
7.4.4 Newton-Gauss-Levenberg/Marquardt (NGL/M) "~Z.2Y1
7.4.5 Nonwhite Noise " "
7.5 Calculation of the Concentration Profiles: Case 11, ^
Complex Mechanisms ' ".""c \ 242
7.5.1 Fourth-Order Runge-Kutta Method in Excel ¦¦•¦»^
7.5.2 Interesting Kinetic Examples 246
7.5.2.1 Autocatalysis 248
7.5.2.2 Zeroth-Order Reaction._- •
7 5 2 3 Lotka-Volterra (Sheep and Wolves) £"
7 5 214 Tne Belousov-Zhabotinsky (BZ) Reaction 251
7.6 Calculation of the Concentration Profiles: Case III, ^
Very Complex Mechanisms "" ' 255
7.7 Related Issues ¦ 256
7.7.1 Measurement Techmques • ¦ • 256
7.7.2 Model Parser 256
7.7.3 Flow Reactors .-- 256
7.7.4 Globalization of the Analysis
7.7.5 Soft-Modeling Methods 257
7.7.6 Other Methods 258
Appendix 258
References 259
Q Response-Surface
Modeling and
Experimental Design
Kaiin Stoyanov and Anthony D. Walmsley
CONTENTS
264
8.1 Introduction 265
8.2 Response-Surface Modeling 265
8.2.1 The General Scheine of RSM ^^ 268
8.2.2 Factor Spaces 268
8.2.2.1 Process Factor Spaces "•¦¦¦¦¦¦¦ 269
8.2.2.2 Mixture Factor Spaces 272
8.2.2.3 Simplex-Lattice Designs —- 2?5
8.2.2.4 Simplex-Centroid Designs .'.279
8 2 2 5 Constrained Mixture Spaces 2g3
8.2.2.6 Mixture+Process Factor Spaces 2g6
8.2.3 Some Regression-Analysis-Related Notation •¦••••¦¦¦• ^
8.3 One-Variable-at-a-Time vs. Optimal Design 2gg
8.3.1 Bivariate (Multivariate) Exarnple -¦~~^ 290
8.3.2 Advantages of the One-Vanable-at-a-Time Approach ^
8.3.3 Disadvantages 290
8.4 Symmetrie Optimal Designs •• 290
8.4.1 Two-Level Füll Factorial Designs _^ 29Q
8 4 11 Advantages of Factonal D^.8-"" 291
8.4.3 Central Composite Designs ••"—"¦- 294
8.5 The Taguchi Experimental Design Approacn ^
8.6 Nonsymmetric Optimal Designs 298
8.6.1 Optimality Criteria.». ^"^:"j""s""' 299
X zS SZEtt- —£
o c i i Desien Measures
6 3 2 üSptimality and D-Efficiency 04
8.6.3.3 G-Optimality and G-Efficiency 305
k
8.6.3.4 A-Optimality 30g j
8.6.3.5 E-Optimality 306 !
8.7 Algorithms for the Search of Realizable Optimal
Experimental Designs 306
8.7.1 Exact (or N-Point) D-Optimal Designs "Z"Z""Z""ZZ307
8.7.1.1 Fedorov's Algorithm 307
8.7.1.2 Wynn-Mitchell and van Schalkwyk Algorithms 308
8.7.1.3 DETMAX Algorithm 308
lJAA The MD Galil and Kiefer's MgonthmZZZ 111.309
8.7.2 Sequential D-Optimal Designs 310
8.7.2.1 Example 3^j
8 8 ™i sTToal Comp°site D^marDe;ignsi::::::::::::3i3
*tOfft *£T "* Catal°gS °f D™Z™ of Expenments 316
8.8.1 Off-the-Shelf Software Packages 316
8.8.1.1 MATLAB ,.IZ 316
8.8.1.2 Design Expert 319
8.8.1.3 Other Packages . 319
*J2 Catf ogs of Experimental Designs'.'".' 320
?97C^TCT?DOE in ^.vanatecäiibrat^ ::::::32i
8.9.1 ConstructionofaCalibration Sample Set .321 !
8 9 12 IT^ °f *' Number °f Signet Factors 322
8.9. .2 Idenüfymg the Type of the Regression Model 325
8.91.3 Definmg the Boundsof the Factor Space 327 I
892 In!- ES'lmftln8EXtinCtionCoefficients. 329 I
8.9.2 Improvmg Qualuy from Historical Data. 330
8-9.2.1 Improving the Numerical Stabilitv
of the Data Set. y „,
8.9.2.2 Prediction Ability. l"
8.10 Conclusion * 334
References 337
337
Q Classification and Pattern
Recognition
Barry K. Lavine and Charles E. Davidson
CONTENTS
9.1 Introduction 339
9.2 Data Preprocessing 341
9.3 Mapping and Display 342
9.4 Clustering 347
9.5 Classification 351
9.5.1 K-Nearest Neighbor 352
9.5.2 Partial Least Squares 352
9.5.3 SIMCA 353
9.6 Practical Considerations 354
9.7 Applications of Pattern-Recognition
Techniques 355
9.7.1 Archaeological Artifacts 356
9.7.2 Fuel Spill Identification 358
9.7.3 Sorting Plastics for Recycling 365
9.7.4 Taxonomy Based on Chemical
Constitution 371
References 374
1 Q Signal Processing and
Digital Filtering
Steven D. Brown
CONTENTS
379
10.1 Introduction ion
10.2 Noise Removal and the Problem of Prior Information ^
10.2.1 Signal Estimation and Signal Detection.
10.3 Reexpressing Data in Alternate Bases to Analyze Structure. .^
10.3.1 Projection-Based Signal Analysis as S.gnal Processmg 383
10.4 Frequency-Domain Signal Processing 386 j
10.4.1 The Fourier Transform 386 |
10.4.2 The Sampüng Theorem and Aliasing.-". »•-"• |
10.4.3 The Bandwidth-Limited, Discrete Founer Transform 388
10.4.4 Properties of the Fourier Transform ZZZ.394
10.5 Frequency Domain Smoothing .394
10.5.1 Smoothing ""'"' ''.'""' 395
10.5.2 Smoothing with Designer Transfer Functions .395
10.6 Time-Domain Filtering and Smoothing •"• 39g
10.6.1 Smoothing 400
!S:" JÄisäss^^^™" ;::Z
10.7 Wavelet-Based Signal Processing 406
10.7.1 The Wavelet Function -^^tf^^™™ons 408
10.7.2 Time and Frequency Localizations ^
10.7.3 The Discrete Wavelet Transform — ••••¦•
10.7.4 Smoothing and Denoismg w* Wavelets. ^
References 416
Further Reading
A "| Multivariate Curve
Resolution
Roma Tauler and Anna de Juan
CONTENTS
11.1 Introduction: General Concept, Ambiguities,
Resolution Theorems 4*°
11.2 Historical Background 422
11.3 Local Rank and Resolution: Evolving Factor Analysis
and Related Techniques 423
11.4 Noniterative Resolution Methods 426
11.4.1 Window Factor Analysis (WFA) 427
11.4.2 Other Techniques: Subwindow Factor Analysis (SFA)
and Heuristic Evolving Latent Projections (HELP) 429
11.5 Iterative Methods
11.5.1 Generation of Initial Estimates 432
11.5.2 Constraints, Definition, Classification: Equality and
Inequality Constraints Based on Chemical or
Mathematical Properties 4^
11.5.2.1 Nonnegativity ^
11.5.2.2 Unimodality *
11.5.2.3 Closure
11.5.2.4 Known Profiles #J3
11.5.2.5 Hard-Modeling Constraints:
Physicochemical Models 4j5
115 2 6 Local-Rank Constraints, Selectivity,
and Zero-Concentration Windows ¦_¦ 433
11.5.3 Iterative Target Transformation Factor Analys.s (ITTFA) 43
11.5.4 Multivariate Curve Resolution-Alternating ^
Least Squares (MCR-ALS) ¦•••••;
11.6 Extension of Self-Modeling Curve Resolution to Multiway
Data: MCR-ALS Simultaneous Analysis of Mutaple ^
Correlated Data Matrices ""
11.7 Uncertainty in Resolution Results, Range of Feasible ^
Solutions, and Error in Resolution "".'.'.'.'.'. M%
11.8 Applications 449
11.8.1 Biochemical Processes
11.8.1.1 Study of Changes in the Protein
Secondary Structure 451
11.8.1.2 Study of Changes in the Tertiary Structure 453
11.8.1.3 Global Description of the Protein
Folding Process 453
11.8.2 Environmental Data 454
11.8.3 Spectroscopic Images 461
11.9 Software 465
References 467
1 O Three-Way Calibration
with Hyphenated Data
Karl S. Booksh
CONTENTS
12.1 Introduction 475
12.2 Background 476
12.3 Nomenclature of Three-Way Data 478
12.4 Three-Way Models 478
12.5 Examples 481
12.6 Rank Annihilation Methods 482
12.6.1 Rank Annihilation Factor Analysis 482
12.6.1.1 RAFA Application 483
12.6.2 Generalized Rank Annihilation Method 485
12.6.2.1 GRAM Application 486
12.6.3 Direct Trilinear Decomposition 489
12.6.3.1 DTLD Application 490
12.7 Alternating Least-Squares Methods 491
12.7.1 PARAFAC / CANDECOMP 491
12.7.1.1 Tuckals 493
12.7.1.2 Solution Constraints 493
12.7.1.3 PARAFAC Application 494
12.8 Extensions of Three-Way Methods 495
12.9 Figures of Merit 496
12.10 Caveats 497
References 49^
Appendix 12.1 GRAM Algorithm 502
Appendix 12.2 DTLD Algorithm 503
Appendix 12.3 PARAFAC Algorithm 504
1 Q Future Trends in
Chemometrics
Paul J. Gemperline
CONTENTS
13.1 Historical Development of Chemometrics 510
13.1.1 Chemometrics — a Maturing Discipline 511
13.2 Reviews of Chemometrics and Future Trends 511
13.2.1 Process Analytical Chemistry 512
13.2.2 Spectroscopy 512
13.2.3 Food and Feed Chemistry 512
13.2.4 Other Interesting Application Areas 513
13.3 Drivers of Growth in Chemometrics 513
13.3.1 The Challenge of Large Data Sets 514
13.3.2 Chemometrics at the Interface of Chemical
and Biological Sciences 514
13.4 Concluding Remarks 516
References 516 |
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| spelling | Practical guide to chemometrics ed. by Paul Gemperline 2. ed. Boca Raton [u.a.] CRC / Taylor & Francis 2006 541 S. graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Chimiométrie Chimiométrie ram Chemometrics Gemperline, Paul Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014817494&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Practical guide to chemometrics Chimiométrie Chimiométrie ram Chemometrics |
| title | Practical guide to chemometrics |
| title_auth | Practical guide to chemometrics |
| title_exact_search | Practical guide to chemometrics |
| title_exact_search_txtP | Practical guide to chemometrics |
| title_full | Practical guide to chemometrics ed. by Paul Gemperline |
| title_fullStr | Practical guide to chemometrics ed. by Paul Gemperline |
| title_full_unstemmed | Practical guide to chemometrics ed. by Paul Gemperline |
| title_short | Practical guide to chemometrics |
| title_sort | practical guide to chemometrics |
| topic | Chimiométrie Chimiométrie ram Chemometrics |
| topic_facet | Chimiométrie Chemometrics |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014817494&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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