本书以化学计量学的基础知识为其主线，在讲述数学基础时就试图与其化学应用直接相连，始终注意到讲解这些知识可为化学家们提供了什么样的新思路，可以解决什么样的化学问题。本书虽用英文编写，但文中出现的一些非常用英文单词皆给出中文提示，以节省学生查阅字典的时间；凡是在书中出现重要知识点的地方，本书尽量佐以问题进行提示，以引起学生的足够注意；另外，本书在必要时还尽量给出中文注释和评述，对所授知识进一步进行解释和阐述，以提高学生的认识和降低阅读的难度。

Chapter 1 Introduction and Necessary Fundamental Knowledge of Mathematics

 1.1 Chemometrics: Definition and Its Brief History / 3

 1.2 The Relationship between Analytical Chemistry and Chemometrics / 4

 1.3 The Relationship between Chemometrics, Chemoinformatics and Bioinformatics / 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

 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 Electropherotic 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

 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

 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 Vectoral 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 Data

 5.1 Introduction / 169

5.1.1 Chemical 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 Projections / 183

5.4.1 Projection 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