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Chemometrics in Excel
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Providing an easy explanation of the fundamentals, methods, and applications of chemometrics Acts as a practical guide to multivariate data analysis techniques Explains the methods used in Chemometrics and teaches the reader to perform all relevant calculations Presents the basic chemometric methods as worksheet functions in Excel Includes Chemometrics Add In for download which uses Microsoft Excel (R) for chemometrics training Online downloads includes workbooks with examples
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Table of Contents

Preface xvii PART I INTRODUCTION 1 1 What is Chemometrics? 3 1.1 Subject of Chemometrics, 3 1.2 Historical Digression, 5 2 What the Book Is About? 8 2.1 Useful Hints, 8 2.2 Book Syllabus, 9 2.3 Notations, 10 3 Installation of Chemometrics Add-In 11 3.1 Installation, 11 3.2 General Information, 14 4 Further Reading on Chemometrics 15 4.1 Books, 15 4.1.1 The Basics, 15 4.1.2 Chemometrics, 16 4.1.3 Supplements, 16 4.2 The Internet, 17 4.2.1 Tutorials, 17 4.3 Journals, 17 4.3.1 Chemometrics, 17 4.3.2 Analytical, 18 4.3.3 Mathematical, 18 4.4 Software, 18 4.4.1 Specialized Packages, 18 4.4.2 General Statistic Packages, 19 4.4.3 Free Ware, 19 PART II THE BASICS 21 5 Matrices and Vectors 23 5.1 The Basics, 23 5.1.1 Matrix, 23 5.1.2 Simple Matrix Operations, 24 5.1.3 Matrices Multiplication, 25 5.1.4 Square Matrix, 26 5.1.5 Trace and Determinant, 27 5.1.6 Vectors, 28 5.1.7 Simple Vector Operations, 29 5.1.8 Vector Products, 29 5.1.9 Vector Norm, 30 5.1.10 Angle Between Vectors, 30 5.1.11 Vector Representation of a Matrix, 30 5.1.12 Linearly Dependent Vectors, 31 5.1.13 Matrix Rank, 31 5.1.14 Inverse Matrix, 31 5.1.15 Pseudoinverse, 32 5.1.16 Matrix Vector Product, 33 5.2 Advanced Information, 33 5.2.1 Systems of Linear Equations, 33 5.2.2 Bilinear and Quadratic Forms, 34 5.2.3 Positive Definite Matrix, 34 5.2.4 Cholesky Decomposition, 34 5.2.5 Polar Decomposition, 34 5.2.6 Eigenvalues and Eigenvectors, 35 5.2.7 Eigenvalues, 35 5.2.8 Eigenvectors, 35 5.2.9 Equivalence and Similarity, 36 5.2.10 Diagonalization, 37 5.2.11 Singular Value Decomposition (SVD), 37 5.2.12 Vector Space, 38 5.2.13 Space Basis, 39 5.2.14 Geometric Interpretation, 39 5.2.15 Nonuniqueness of Basis, 39 5.2.16 Subspace, 40 5.2.17 Projection, 40 6 Statistics 42 6.1 The Basics, 42 6.1.1 Probability, 42 6.1.2 Random Value, 43 6.1.3 Distribution Function, 43 6.1.4 Mathematical Expectation, 44 6.1.5 Variance and Standard Deviation, 44 6.1.6 Moments, 44 6.1.7 Quantiles, 45 6.1.8 Multivariate Distributions, 45 6.1.9 Covariance and Correlation, 45 6.1.10 Function, 46 6.1.11 Standardization, 46 6.2 Main Distributions, 46 6.2.1 Binomial Distribution, 46 6.2.2 Uniform Distribution, 47 6.2.3 Normal Distribution, 48 6.2.4 Chi-Squared Distribution, 50 6.2.5 Student s Distribution, 52 6.2.6 F-Distribution, 53 6.2.7 Multivariate Normal Distribution, 54 6.2.8 Pseudorandom Numbers, 55 6.3 Parameter Estimation, 56 6.3.1 Sample, 56 6.3.2 Outliers and Extremes, 56 6.3.3 Statistical Population, 56 6.3.4 Statistics, 57 6.3.5 Sample Mean and Variance, 57 6.3.6 Sample Covariance and Correlation, 58 6.3.7 Order Statistics, 59 6.3.8 Empirical Distribution and Histogram, 60 6.3.9 Method of Moments, 61 6.3.10 The Maximum Likelihood Method, 62 6.4 Properties of the Estimators, 62 6.4.1 Consistency, 62 6.4.2 Bias, 63 6.4.3 Effectiveness, 63 6.4.4 Robustness, 63 6.4.5 Normal Sample, 64 6.5 Confidence Estimation, 64 6.5.1 Confidence Region, 64 6.5.2 Confidence Interval, 65 6.5.3 Example of a Confidence Interval, 65 6.5.4 Confidence Intervals for the Normal Distribution, 65 6.6 Hypothesis Testing, 66 6.6.1 Hypothesis, 66 6.6.2 Hypothesis Testing, 66 6.6.3 Type I and Type II Errors, 67 6.6.4 Example, 67 6.6.5 Pearson s Chi-Squared Test, 67 6.6.6 F-Test, 69 6.7 Regression, 70 6.7.1 Simple Regression, 70 6.7.2 The Least Squares Method, 71 6.7.3 Multiple Regression, 72 Conclusion, 73 7 Matrix Calculations in Excel 74 7.1 Basic Information, 74 7.1.1 Region and Language, 74 7.1.2 Workbook, Worksheet, and Cell, 76 7.1.3 Addressing, 77 7.1.4 Range, 78 7.1.5 Simple Calculations, 78 7.1.6 Functions, 78 7.1.7 Important Functions, 81 7.1.8 Errors in Formulas, 85 7.1.9 Formula Dragging, 86 7.1.10 Create a Chart, 87 7.2 Matrix Operations, 88 7.2.1 Array Formulas, 88 7.2.2 Creating and Editing an Array Formula, 90 7.2.3 Simplest Matrix Operations, 91 7.2.4 Access to the Part of a Matrix, 91 7.2.5 Unary Operations, 93 7.2.6 Binary Operations, 95 7.2.7 Regression, 95 7.2.8 Critical Bug in Excel 2003, 99 7.2.9 Virtual Array, 99 7.3 Extension of Excel Possibilities, 100 7.3.1 VBA Programming, 100 7.3.2 Example, 101 7.3.3 Macro Example, 103 7.3.4 User-Defined Function Example, 104 7.3.5 Add-Ins, 105 7.3.6 Add-In Installation, 106 Conclusion, 107 8 Projection Methods in Excel 108 8.1 Projection Methods, 108 8.1.1 Concept and Notation, 108 8.1.2 PCA, 109 8.1.3 PLS, 110 8.1.4 Data Preprocessing, 111 8.1.5 Didactic Example, 112 8.2 Application of Chemometrics Add-In, 113 8.2.1 Installation, 113 8.2.2 General, 113 8.3 PCA, 114 8.3.1 ScoresPCA, 114 8.3.2 LoadingsPCA, 114 8.4 PLS, 116 8.4.1 ScoresPLS, 116 8.4.2 UScoresPLS, 117 8.4.3 LoadingsPLS, 118 8.4.4 WLoadingsPLS, 119 8.4.5 QLoadingsPLS, 120 8.5 PLS2, 121 8.5.1 ScoresPLS2, 121 8.5.2 UScoresPLS2, 122 8.5.3 LoadingsPLS2, 124 8.5.4 WLoadingsPLS2, 125 8.5.5 QLoadingsPLS2, 126 8.6 Additional Functions, 127 8.6.1 MIdent, 127 8.6.2 MIdentD2, 127 8.6.3 MCutRows, 129 8.6.4 MTrace, 129 Conclusion, 130 PART IIICHEMOMETRICS 131 9 Principal Component Analysis (PCA) 133 9.1 The Basics, 133 9.1.1 Data, 133 9.1.2 Intuitive Approach, 134 9.1.3 Dimensionality Reduction, 136 9.2 Principal Component Analysis, 136 9.2.1 Formal Specifications, 136 9.2.2 Algorithm, 137 9.2.3 PCA and SVD, 137 9.2.4 Scores, 138 9.2.5 Loadings, 139 9.2.6 Data of Special Kind, 140 9.2.7 Errors, 140 9.2.8 Validation, 143 9.2.9 Decomposition Quality , 143 9.2.10 Number of Principal Components, 144 9.2.11 The Ambiguity of PCA, 145 9.2.12 Data Preprocessing, 146 9.2.13 Leverage and Deviation, 146 9.3 People and Countries, 146 9.3.1 Example, 146 9.3.2 Data, 147 9.3.3 Data Exploration, 147 9.3.4 Data Pretreatment, 148 9.3.5 Scores and Loadings Calculation, 149 9.3.6 Scores Plots, 151 9.3.7 Loadings Plot, 152 9.3.8 Analysis of Residuals, 153 Conclusion, 153 10 Calibration 156 10.1 The Basics, 156 10.1.1 Problem Statement, 156 10.1.2 Linear and Nonlinear Calibration, 157 10.1.3 Calibration and Validation, 158 10.1.4 Calibration Quality , 160 10.1.5 Uncertainty, Precision, and Accuracy, 162 10.1.6 Underfitting and Overfitting, 163 10.1.7 Multicollinearity, 164 10.1.8 Data Preprocessing, 166 10.2 Simulated Data, 166 10.2.1 The Principle of Linearity, 166 10.2.2 Pure Spectra, 166 10.2.3 Standard Samples, 166 10.2.4 X Data Creation, 167 10.2.5 Data Centering, 168 10.2.6 Data Overview, 168 10.3 Classic Calibration, 169 10.3.1 Univariate (Single Channel) Calibration, 169 10.3.2 The Vierordt Method, 172 10.3.3 Indirect Calibration, 174 10.4 Inverse Calibration, 176 10.4.1 Multiple Linear Calibration, 177 10.4.2 Stepwise Calibration, 178 10.5 Latent Variables Calibration, 180 10.5.1 Projection Methods, 180 10.5.2 Latent Variables Regression, 184 10.5.3 Implementation of Latent Variable Calibration, 185 10.5.4 Principal Component Regression (PCR), 186 10.5.5 Projection on the Latent Structures-1 (PLS1), 188 10.5.6 Projection on the Latent Structures-2 (PLS2), 191 10.6 Methods Comparison, 193 Conclusion, 197 11 Classification 198 11.1 The Basics, 198 11.1.1 Problem Statement, 198 11.1.2 Types of Classes, 199 11.1.3 Hypothesis Testing, 199 11.1.4 Errors in Classification, 200 11.1.5 One-Class Classification, 200 11.1.6 Training and Validation, 201 11.1.7 Supervised and Unsupervised Training, 201 11.1.8 The Curse of Dimensionality, 201 11.1.9 Data Preprocessing, 201 11.2 Data, 202 11.2.1 Example, 202 11.2.2 Data Subsets, 203 11.2.3 Workbook Iris.xls, 204 11.2.4 Principal Component Analysis, 205 11.3 Supervised Classification, 205 11.3.1 Linear Discriminant Analysis (LDA), 205 11.3.2 Quadratic Discriminant Analysis (QDA), 210 11.3.3 PLS Discriminant Analysis (PLSDA), 214 11.3.4 SIMCA, 217 11.3.5 k-Nearest Neighbors (kNN), 223 11.4 Unsupervised Classification, 225 11.4.1 PCA Again (Revisited), 225 11.4.2 Clustering by K-Means, 225 Conclusion, 229 12 Multivariate Curve Resolution 230 12.1 The Basics, 230 12.1.1 Problem Statement, 230 12.1.2 Solution Ambiguity, 232 12.1.3 Solvability Conditions, 234 12.1.4 Two Types of Data, 235 12.1.5 Known Spectrum or Profile, 236 12.1.6 Principal Component Analysis (PCA), 236 12.1.7 PCA and MCR, 237 12.2 Simulated Data, 237 12.2.1 Example, 237 12.2.2 Data, 238 12.2.3 PCA, 238 12.2.4 The HELP Plot, 240 12.3 Factor Analysis, 241 12.3.1 Procrustes Analysis, 241 12.3.2 Evolving Factor Analysis (EFA), 244 12.3.3 Windows Factor Analysis (WFA), 246 12.4 Iterative Methods, 249 12.4.1 Iterative Target Transform Factor Analysis (ITTFA), 249 12.4.2 Alternating Least Squares (ALS), 250 Conclusion, 252 PART IV SUPPLEMENTS 255 13 Extension Of Chemometrics Add-In 257 13.1 Using Virtual Arrays, 257 13.1.1 Simulated Data, 257 13.1.2 Virtual Array, 259 13.1.3 Data Preprocessing, 259 13.1.4 Decomposition, 260 13.1.5 Residuals Calculation, 260 13.1.6 Eigenvalues Calculation, 262 13.1.7 Orthogonal Distances Calculation, 263 13.1.8 Leverages Calculation, 264 13.2 Using VBA Programming, 265 13.2.1 VBA Advantages, 265 13.2.2 Virtualization of Real Arrays, 265 13.2.3 Data Preprocessing, 266 13.2.4 Residuals Calculation, 267 13.2.5 Eigenvalues Calculation, 268 13.2.6 Orthogonal Distances Calculation, 269 13.2.7 Leverages Calculation, 270 Conclusion, 271 14 Kinetic Modeling of Spectral Data 272 14.1 The Grey Modeling Method, 272 14.1.1 Problem Statement, 272 14.1.2 Example, 274 14.1.3 Data, 274 14.1.4 Soft Method of Alternating Least Squares (Soft-ALS), 275 14.1.5 Hard Method of Alternating Least Squares (Hard-ALS), 277 14.1.6 Using Solver Add-In, 279 Conclusions, 282 15 MATLAB (R): Beginner s Guide 283 15.1 The Basics, 283 15.1.1 Workspace, 283 15.1.2 Basic Calculations, 285 15.1.3 Echo, 285 15.1.4 Workspace Saving: MAT-Files, 286 15.1.5 Diary, 286 15.1.6 Help, 287 15.2 Matrices, 287 15.2.1 Scalars, Vectors, and Matrices, 287 15.2.2 Accessing Matrix Elements, 289 15.2.3 Basic Matrix Operations, 289 15.2.4 Special Matrices, 290 15.2.5 Matrix Calculations, 292 15.3 Integrating Excel and MATLAB (R), 294 15.3.1 Configuring Excel, 294 15.3.2 Data Exchange, 294 15.4 Programming, 295 15.4.1 M-Files, 295 15.4.2 Script File, 296 15.4.3 Function File, 297 15.4.4 Plotting, 298 15.4.5 Plot Printing, 300 15.5 Sample Programs, 301 15.5.1 Centering and Scaling, 301 15.5.2 SVD/PCA, 301 15.5.3 PCA/NIPALS, 302 15.5.4 PLS1, 303 15.5.5 PLS2, 304 Conclusion, 306 Afterword. The Fourth Paradigm 307 Index 311

About the Author

Alexey L Pomerantsev is a Leading Researcher at The RussianAcademy of Science. He is a founding member and Chair of theRussian Chemometrics Society, being instrumental in organizing theannual Winter Symposium on Chemometrics. He is a peer reviewer andmember of Editorial Board of the Journal Chemometrics andIntelligent Laboratory Systems. Dr. Pomerantsev has over 100publications, many of them dealing with Chemometric Investigations.

Reviews

The book is for sure very interesting and very well written, and it covers all the major topics of chemometrics. (Journal of Chemometrics, 14 July 2015)

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