Chemometrics

RICHARD G. BRERETON is Director of Brereton Consultancy and Emeritus Professor at the University of Bristol, UK. He is Fellow of the Royal Society of Chemistry, Royal Statistical Society and Royal Society of Medicine. He has applied chemometrics in a wide variety of areas including pharmaceuticals, materials, metabolomics, heritage studies and forensics, and has published over 400 articles, including writing/editing eight books.

• Preface to Second Edition xiPreface to First Edition xiiiAcknowledgements xvAbout the Companion Website xvii1 Introduction 11.1 Historical Parentage 11.1.1 Applied Statistics 11.1.2 Statistics in Analytical and Physical Chemistry 21.1.3 Scientific Computing 31.2 Developments since the 1970s 31.3 Software and Calculations 41.4 Further Reading 61.4.1 General 61.4.2 Specific Areas 7References 82 Experimental Design 112.1 Introduction 112.2 Basic Principles 142.2.1 Degrees of Freedom 142.2.2 Analysis of Variance 172.2.3 Design Matrices and Modelling 232.2.4 Assessment of Significance 292.2.5 Leverage and Confidence in Models 382.3 Factorial Designs 432.3.1 Full Factorial Designs 442.3.2 Fractional Factorial Designs 492.3.3 Plackett–Burman and Taguchi Designs 552.3.4 Partial Factorials at Several Levels: Calibration Designs 572.4 Central Composite or Response Surface Designs 622.4.1 Setting up the Design 622.4.2 Degrees of Freedom 652.4.3 Axial Points 662.4.4 Modelling 672.4.5 Statistical Factors 692.5 Mixture Designs 702.5.1 Mixture Space 702.5.2 Simplex Centroid 712.5.3 Simplex Lattice 742.5.4 Constraints 762.5.5 Process Variables 812.6 Simplex Optimisation 822.6.1 Fixed Sized Simplex 822.6.2 Elaborations 842.6.3 Modified Simplex 842.6.4 Limitations 86Problems 863 Signal Processing 1013.1 Introduction 1013.1.1 Environmental and Geological Processes 1013.1.2 Industrial Process Control 1013.1.3 Chromatograms and Spectra 1023.1.4 Fourier Transforms 1023.1.5 Advanced Methods 1023.2 Basics 1033.2.1 Peak shapes 1033.2.2 Digitisation 1073.2.3 Noise 1093.2.4 Cyclicity 1123.3 Linear Filters 1123.3.1 Smoothing Functions 1123.3.2 Derivatives 1163.3.3 Convolution 1183.4 Correlograms and Time Series Analysis 1223.4.1 Auto-correlograms 1223.4.2 Cross-correlograms 1243.4.3 Multivariate Correlograms 1273.5 Fourier Transform Techniques 1283.5.1 Fourier Transforms 1283.5.2 Fourier Filters 1353.5.3 Convolution Theorem 1403.6 Additional Methods 1423.6.1 Kalman Filters 1423.6.2 Wavelet Transforms 1453.6.3 Bayes’ Theorem 1483.6.4 Maximum Entropy 150Problems 1534 Principal Component Analysis and Unsupervised Pattern Recognition 1634.1 Introduction 1634.1.1 Exploratory Data Analysis 1634.1.2 Cluster Analysis 1644.2 The Concept and Need for Principal Components Analysis 1644.2.1 History 1644.2.2 Multivariate Data Matrices 1654.2.3 Case Studies 1664.2.4 Aims of PCA 1714.3 Principal Components Analysis: The Method 1714.3.1 Scores and Loadings 1714.3.2 Rank and Eigenvalues 1754.4 Factor Analysis 1834.5 Graphical Representation of Scores and Loadings 1844.5.1 Scores Plots 1854.5.2 Loadings Plots 1884.6 Pre-processing 1914.6.1 Transforming Individual Elements of a Matrix 1914.6.2 Row Scaling 1934.6.3 Mean Centring 1944.6.4 Standardisation 1974.6.5 Further Methods 1994.7 Comparing Multivariate Patterns 1994.7.1 Biplots 2004.7.2 Procrustes Analysis 2014.8 Unsupervised Pattern Recognition: Cluster Analysis 2014.8.1 Similarity 2024.8.2 Linkage 2044.8.3 Next Steps 2064.8.4 Dendrograms 2064.9 Multi-way Pattern Recognition 2074.9.1 Tucker3 Models 2074.9.2 Parallel Factor Analysis (PARAFAC) 2084.9.3 Unfolding 209Problems 2105 Classification and Supervised Pattern Recognition 2155.1 Introduction 2155.1.1 Background 2155.1.2 Case Study 2165.2 Two-Class Classifiers 2165.2.1 Distance-Based Methods 2175.2.2 Partial Least-Squares Discriminant Analysis 2245.2.3 K Nearest Neighbours 2265.3 One-Class Classifiers 2295.3.1 Quadratic Discriminant Analysis 2295.3.2 Disjoint PCA and SIMCA 2325.4 Multi-Class Classifiers 2365.5 Optimisation and Validation 2375.5.1 Validation 2385.5.2 Optimisation 2455.6 Significant Variables 2465.6.1 Partial Least-Squares Discriminant Loadings and Weights 2485.6.2 Univariate Statistical Indicators 2505.6.3 Variable Selection for SIMCA 251Problems 2526 Calibration 2656.1 Introduction 2656.1.1 History, Usage and Terminology 2656.1.2 Case Study 2676.2 Univariate Calibration 2676.2.1 Classical Calibration 2696.2.2 Inverse Calibration 2726.2.3 Intercept and Centring 2746.3 Multiple Linear Regression 2766.3.1 Multi-detector Advantage 2766.3.2 Multi-wavelength Equations 2776.3.3 Multivariate Approaches 2806.4 Principal Components Regression 2846.4.1 Regression 2846.4.2 Quality of Prediction 2876.5 Partial Least Squares Regression 2896.5.1 PLS1 2896.5.2 PLS2 2946.5.3 Multi-way PLS 2976.6 Model Validation and Optimisation 3026.6.1 Auto-prediction 3026.6.2 Cross-validation 3036.6.3 Independent Test Sets 305Problems 3097 Evolutionary Multivariate Signals 3237.1 Introduction 3237.2 Exploratory Data Analysis and Pre-processing 3257.2.1 Baseline Correction 3257.2.2 Principal Component-Based Plots 3257.2.3 Scaling the Data after PCA 3297.2.4 Scaling the Data before PCA 3327.2.5 Variable Selection 3397.3 Determining Composition 3417.3.1 Composition 3417.3.2 Univariate Methods 3427.3.3 Correlation- and Similarity-Based Methods 3457.3.4 Eigenvalue-Based Methods 3487.3.5 Derivatives 3527.4 Resolution 3557.4.1 Selectivity for All Components 3567.4.2 Partial Selectivity 3607.4.3 Incorporating Constraints: ITTFA, ALS and MCR 362Problems 365A Appendix 375A.1 Vectors and Matrices 375A.1.1 Notation and Definitions 375A.1.2 Matrix and Vector Operations 375A.2 Algorithms 377A.2.1 Principal Components Analysis 377A.2.2 PLS1 378A.2.3 PLS2 379A.2.4 Tri-Linear PLS1 380A.3 Basic Statistical Concepts 381A.3.1 Descriptive Statistics 381A.3.2 Normal Distribution 383A.3.3 χ2-Distribution 383A.3.4 t-Distribution 386A.3.5 F-Distribution 386A.4 Excel for Chemometrics 390A.4.1 Names and Addresses 390A.4.2 Equations and Functions 394A.4.3 Add-Ins 398A.4.4 Charts 398A.4.5 Downloadable Macros 400A.5 Matlab for Chemometrics 408A.5.1 Getting Started 408A.5.2 File Types 409A.5.3 Matrices 411A.5.4 Importing and Exporting Data 416A.5.5 Introduction to Programming and Structure 417A.5.6 Graphics 418Answers to the Multiple Choice Questions 429Index 433

"... fills a gap in the chemometrics literature landscape. With its unique approach of learning-by-doing it is best suited for practitioners, which do not want to dig too deep into the theory and are not interested in a full coverage of methods. Nevertheless, the most important and usual applied chemometrics methods are introduced... The example data sets of the book are also worth exploring by itself, because they are well chosen and nicely structured."—Thomas Bocklitz, Analytical and Bioanalytical Chemistry (2019)