Sách Chemometrics Data Analysis for the Laboratory and Chemical Plant

Contents

Preface . . . . . . . . ix

Supplementary Information . . . . . xii

Acknowledgements . . . . . . . xiii

1 Introduction . . . . . . . . 1

1.1 Points of View . . . . . . . 1

1.2 Software and Calculations . . . . . 6

1.3 Further Reading . . . . . . 8

1.3.1 General . . . . . . . 8

1.3.2 Specific Areas. . . . . . . 10

1.3.3 Internet Resources . . . . . . 11

1.4 References . . . . . . . 12

2 Experimental Design. . . . . . . 15

2.1 Introduction . . . . . . . . 15

2.2 Basic Principles . . . . . . 19

2.2.1 Degrees of Freedom . . . . . 19

2.2.2 Analysis of Variance and Comparison of Errors . . . 23

2.2.3 Design Matrices and Modelling . . . . . 30

2.2.4 Assessment of Significance . . . . 36

2.2.5 Leverage and Confidence in Models . . . . 47

2.3 Factorial Designs. . . . . . . 53

2.3.1 Full Factorial Designs. . . . . . 54

2.3.2 Fractional Factorial Designs . . . . 60

2.3.3 Plackett–Burman and Taguchi Designs . . . 66

2.3.4 Partial Factorials at Several Levels: Calibration Designs . . . 69

2.4 Central Composite or Response Surface Designs . . . . 76

2.4.1 Setting Up the Design. . . . . . 76

2.4.2 Degrees of Freedom . . . . . 79

2.4.3 Axial Points . . . . . . 80

2.4.4 Modelling . . . . . . 83

2.4.5 Statistical Factors . . . . . 84

2.5 Mixture Designs . . . . . . . 84

2.5.1 Mixture Space. . . . . . . 85

2.5.2 Simplex Centroid . . . . . 85

2.5.3 Simplex Lattice . . . . . . 88

2.5.4 Constraints. . . . . . . 90

2.5.5 Process Variables . . . . . 96

2.6 Simplex Optimisation . . . . . . 97

2.6.1 Fixed Sized Simplex. . . . . . . 97

2.6.2 Elaborations . . . . . . 99

2.6.3 Modified Simplex. . . . . . . 100

2.6.4 Limitations . . . . . . . 101

Problems . . . . . . . . . 102

3 Signal Processing . . . . . . . 119

3.1 Sequential Signals in Chemistry . . . . . 119

3.1.1 Environmental and Geological Processes . . . . . 119

3.1.2 Industrial Process Control . . . . . 120

3.1.3 Chromatograms and Spectra. . . . . . 120

3.1.4 Fourier Transforms . . . . . . 120

3.1.5 Advanced Methods . . . . . . 121

3.2 Basics . . . . . . . . 122

3.2.1 Peakshapes . . . . . . . 122

3.2.2 Digitisation . . . . . . . 125

3.2.3 Noise . . . . . . . 128

3.2.4 Sequential Processes. . . . . . . 131

3.3 Linear Filters. . . . . . . . 131

3.3.1 Smoothing Functions . . . . . . 131

3.3.2 Derivatives . . . . . . . 138

3.3.3 Convolution . . . . . . 138

3.4 Correlograms and Time Series Analysis . . . . 142

3.4.1 Auto-correlograms . . . . . . 142

3.4.2 Cross-correlograms . . . . . . 145

3.4.3 Multivariate Correlograms . . . . . 146

3.5 Fourier Transform Techniques . . . . . . 147

3.5.1 Fourier Transforms . . . . . . 147

3.5.2 Fourier Filters. . . . . . . 156

3.5.3 Convolution Theorem . . . . . . 161

3.6 Topical Methods . . . . . . . 163

3.6.1 Kalman Filters. . . . . . . 163

3.6.2 Wavelet Transforms . . . . . . . 167

3.6.3 Maximum Entropy (Maxent) and Bayesian Methods. . . . 168

Problems . . . . . . . . . 173

4 Pattern Recognition . . . . . . . 183

4.1 Introduction . . . . . . . . 183

4.1.1 Exploratory Data Analysis . . . . . 183

4.1.2 Unsupervised Pattern Recognition . . . . 183

4.1.3 Supervised Pattern Recognition. . . . . . 184

4.2 The Concept and Need for Principal Components Analysis . . . 184

4.2.1 History. . . . . . . . 185

4.2.2 Case Studies . . . . . . 186

4.2.3 Multivariate Data Matrices . . . . . 188

4.2.4 Aims of PCA . . . . . . . 190

4.3 Principal Components Analysis: the Method . . . 191

4.3.1 Chemical Factors . . . . . 191

4.3.2 Scores and Loadings . . . . . 192

4.3.3 Rank and Eigenvalues. . . . . . 195

4.3.4 Factor Analysis . . . . . . 204

4.3.5 Graphical Representation of Scores and Loadings . . 205

4.3.6 Preprocessing . . . . . . . 210

4.3.7 Comparing Multivariate Patterns. . . . . 219

4.4 Unsupervised Pattern Recognition: Cluster Analysis . . . . 224

4.4.1 Similarity . . . . . . 224

4.4.2 Linkage . . . . . . . 227

4.4.3 Next Steps . . . . . . . 229

4.4.4 Dendrograms . . . . . . 229

4.5 Supervised Pattern Recognition. . . . . . 230

4.5.1 General Principles . . . . . . 231

4.5.2 Discriminant Analysis. . . . . . 233

4.5.3 SIMCA . . . . . . . 243

4.5.4 Discriminant PLS . . . . . 248

4.5.5KNearest Neighbours . . . . . 249

4.6 Multiway Pattern Recognition . . . . . 251

4.6.1 Tucker3 Models . . . . . . 252

4.6.2 PARAFAC . . . . . . . 253

4.6.3 Unfolding . . . . . . 254

Problems . . . . . . . 255

5 Calibration . . . . . . . 271

5.1 Introduction . . . . . . . . 271

5.1.1 History and Usage . . . . . . 271

5.1.2 Case Study. . . . . . . 273

5.1.3 Terminology . . . . . . 273

5.2 Univariate Calibration . . . . . . 276

5.2.1 Classical Calibration . . . . . 276

5.2.2 Inverse Calibration. . . . . . 279

5.2.3 Intercept and Centring. . . . . . 280

5.3 Multiple Linear Regression . . . . . . 284

5.3.1 Multidetector Advantage . . . . . . 284

5.3.2 Multiwavelength Equations . . . . 284

5.3.3 Multivariate Approaches . . . . . . 288

5.4 Principal Components Regression . . . . 292

5.4.1 Regression . . . . . . . 292

5.4.2 Quality of Prediction . . . . . . 295

5.5 Partial Least Squares. . . . . . . 297

5.5.1 PLS1 . . . . . . . 298

5.5.2 PLS2 . . . . . . . 303

5.5.3 Multiway PLS. . . . . . . 307

5.6 Model Validation. . . . . . . 313

5.6.1 Autoprediction. . . . . . . 313

5.6.2 Cross-validation . . . . . . 315

5.6.3 Independent Test Sets . . . . . . 317

Problems . . . . . . . . . 323

6 Evolutionary Signals . . . . . . . 339

6.1 Introduction . . . . . . . . 339

6.2 Exploratory Data Analysis and Preprocessing . . . . 341

6.2.1 Baseline Correction . . . . . . . 341

6.2.2 Principal Component Based Plots . . . . 342

6.2.3 Scaling the Data . . . . . . . 350

6.2.4 Variable Selection . . . . . . 360

6.3 Determining Composition . . . . . . . 365

6.3.1 Composition . . . . . . 365

6.3.2 Univariate Methods . . . . . . . 367

6.3.3 Correlation and Similarity Based Methods . . . . 372

6.3.4 Eigenvalue Based Methods . . . . . . 376

6.3.5 Derivatives . . . . . . . 380

6.4 Resolution . . . . . . . 386

6.4.1 Selectivity for All Components. . . . . . 387

6.4.2 Partial Selectivity. . . . . . . 392

6.4.3 Incorporating Constraints. . . . . . 396

Problems . . . . . . . . . 398

Appendices . . . . . . . 409

A.1 Vectors and Matrices . . . . . . 409

A.2 Algorithms . . . . . . . 412

A.3 Basic Statistical Concepts . . . . . 417

A.4 Excel for Chemometrics. . . . . . 425

A.5 Matlab for Chemometrics . . . . . 456

Index . . . . . . . . . 479