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Chapter 1 Introduction and Necessary Fundamental Knowledge of Mathematics 3

1.1 Chemometrics:Definition and Its Brief History 3

1.2　The Relationship between Analytical Chemistry and Chemometries 4

1.3　The Relationship between Chemometrics,Chemoinformatics and Bioinformatic 7

1.4　Necessary Knowledge of Mathematics 9

1.4.1　Vector and Its Calculation 10

1.4.2　Matrix and Its Calculation 19

Chapter 2　Chemical Experiment Design 39

2.1 Introduction 39

2.2　Factorial Design and Its Rational Analysis 41

2.2.1 Computation of Effects Using Sign Tables 44

2.2.2　Normal Plot of Effects and Residuals 45

2.3　Fractional Factorial Design 47

2.4　Orthogonal Design and Orthogonal Array 52

2.4.1　Definition of Orthogonal Design Table 53

2.4.2　Orthogonal Arrays and Their Inter-effect Tables 54

2.4.3　Linear Graphs of Orthogonal Array and Its Applications 55

2.5　Uniform Experimental Design and Uniform Design Table 55

2.5.1 Uniform Design Table and Its Construction 56

2.5.2　Uniformity Criterion and Accessory Tables for Uniform Design 59

2.5.3　Uniform Design for Pseudo-level 60

2.5.4　An Example for Optimization of Eleetropherotic Separation Using Uniform Design 61

2.6　D-Optimal Experiment Design 65

2.7　Optimization Based on Simplex and Experiment Design 68

2.7.1　Constructing an Initial Simplex to Start the Experiment Design 69

2.7.2　Simplex Searching and Optimization 70

Chapter 3　Processing of Analytic Signals 77

3.1 Smoothing Methods of Analytical Signals 77

3.1.1　Moving-Window Average Smoothing Method 77

3.1.2 Savitsky-Golay Filter 77

3.2　Derivative Methods of Analytical Signals 83

3.2.1 Simple Difference Method 83

3.2.2　Moving-Window Polynomial Least-Squares Fitting Method 84

3.3　Background Correction Method of Analytical Signals 89

3.3.1　Penalized Least Squares Algorithm 89

3.3.2　Adaptive Iteratively Reweighted Procedure 90

3.3.3　Some Examples for Correcting the Baseline from Different Instruments 92

3.4　Transformation Methods of Analytical Signals 94

3.4.1　Physical Meaning of the Convolution Algorithm 94

3.4.2 Multichannel Advantage in Spectroscopy and Hadamard Transformation 96

3.4.3　Fourier Transformation 99

Appendix 1:A Matlab Program for Smoothing the Analytical Signals 108

Appendix 2:A Matlab Program for Demonstration of FT Applied to Smoothing 112

Chapter 4　Multivariate Calibration and Multivariate Resolution 116

4.1　Multivariate Calibration Methods for White Analytical Systems 116

4.1.1　Direct Calibration Methods 116

4.1.2　Indirect Calibration Methods 121

4.2　Multivariate Calibration Methods for Grey Analytical Systems 126

4.2.1　Veetoral Calibration Methods 127

4.2.2　Matrix Calibration Methods 127

4.3　Multivariate Resolution Methods for Black Analytical Systems 129

4.3.1　Self-modeling Curve Resolution Method 131

4.3.2　Iterative Target Transformation Factor Analysis 134

4.3.3　Evolving Factor Analysis and Related Methods 137

4.3.4　Window Factor Analysis 141

4.3.5　Heuristic Evolving Latent Projections 145

4.3.6　Subwindow Factor Analysis 152

4.4　Multivariate Calibration Methods for Generalized Grey Analytical Systems 154

4.4.1　Principal Component Regression(PCR) 156

4.4.2　Partial Least Squares(PLS) 157

4.4.3　Leave-one-out Cross-validation 159

Chapter 5　Pattern Recognition and Pattern Analysis for Chemical Analytical Data5.1 Introduction 169

5.1.1 Chemieal Pattern Space 169

5.1.2　Distance in Pattern Space and Measures of Similarity 171

5.1.3 Feature Extraction Methods 173

5.1.4 Pretreatment Methods for Pattern Recognition 173

5.2 Supervised Pattern Recognition Methods:Discriminant Analysis Methods 174

5.2.1 Discrimination Method Based on Euclidean Distance 175

5.2.2 Discrimination Method Based on Mahalanobis Distance 175

5.2.3 Linear Learning Machine 176

5.2.4 k-Nearest Neighbors Discrimination Method 177

5.3 Unsupervised Pattern Recognition Methods:Clustering Analysis Methods 179

5.3.1 Minimum Spanning Tree Method 179

5.3.2 k-means Clustering Method 181

5.4 Visual Dimensional Reduction Based on Latent Proiections 183

5.4.1 Proj ection Discrimination Method Based on Principal Component Analysis 183

5.4.2 SMICA Method Based on Principal Component Analysis 186

5.4.3 Classification Method Based on Partial Least Squares 193