User Friendly Guide to Multivariate Calibration and Classification

Book Cover......Page 1 A User-Friendly Guide to Multivariate Calibration and Classification......Page 3 Contents......Page 5 1 Preface......Page 9 1.2 Acknowledgements......Page 11 2 Introduction......Page 13 2.1 Basic problems and their solutions......Page 14 3.1 Classical vs inverse calibration......Page 19 3.2 Why are multivariate methods needed?......Page 22 4.1 Multicollinearity......Page 27 4.2 Data compression......Page 30 4.3 Overfitting versus underfitting......Page 32 5.1 General model structure for PCR and PLS......Page 35 5.2 Standardisation of x-variables......Page 37 5.3 Principal component regression (PCR)......Page 38 5.4 Partial least squares (PLS) regression......Page 41 5.5 Comparison of PCR and PLS regression......Page 43 5.6 Continuum regression......Page 45 6.1 Loadings and scores in principal component analysis (PCA)......Page 47 6.2 Loadings and loading weights in PLS......Page 50 6.3 What kind of effects do the components correspond to?......Page 51 6.4 lnterpreting the results from a NIR calibration......Page 54 7.1 Variable selection for multiple regression......Page 63 7.2 Which criterion should be used for comparing models?......Page 64 7.3 Search strategies......Page 68 7.4 Using the jack-knife to select variables in PLS regression......Page 75 7.5 Some general comments......Page 77 8.1 Compressing multivariate data using basis functions......Page 79 8.2 The Fourier transformation......Page 82 8.3 The wavelet transform......Page 92 9.1 Different types of non-linearities exist......Page 101 9.2 Detecting multivariate non-linear relations......Page 103 9.3 An overview of different strategies for handling non-linearity problems......Page 105 10.1 What is light scatter?......Page 113 10.2 Derivatives......Page 115 10.3 Multiplicative scatter correction (MSC)......Page 122 10.4 Piecewise multiplicative scatter correction (PMSC)......Page 127 10.5 Path length correction method (PLC-MC)......Page 128 10.6 Orthogonal signal correction (OSC)......Page 130 10.7 Optimised scaling (0s)......Page 131 10.8 Standard normal variate method (SNV)......Page 132 11.1 The LWR method......Page 135 11.2 Determining the number of components andthe number of local samples......Page 138 11.3 Distance measures......Page 139 11.4 Weight functions......Page 141 11.5 Practical experience with LWR......Page 143 12.1 Adjusting for non-linearities using polynomialfunctions of principal components......Page 145 12.2 Splitting of calibration data into linearsubgroups......Page 148 12.3 Neural nets......Page 154 13.1 Root mean square error......Page 163 13.2 Validation based on the calibration set......Page 164 13.3 Prediction testing......Page 165 13.4 Cross-validation......Page 168 13.5 Bootstrapping used for validation......Page 170 13.6 SEP. RMSEP. BIAS and RAP......Page 171 13.7 Comparing estimates of prediction error......Page 174 13.8 The relation between SEP and confidence intervals......Page 178 13.9 How accurate can you get?......Page 180 14.1 Why outliers?......Page 185 14.2 How can outliers be detected?......Page 186 14.3 What should be done with outliers?......Page 197 15 Selection of samples for calibration......Page 199 15.1 Some different practical situations......Page 200 15.2 General principles......Page 201 15.3 Selection of samples for calibration usingx-data for a larger set of samples......Page 203 16 Monitoring calibration equations......Page 209 17.1 General aspects......Page 215 17.2 Different methods for spectral transfer......Page 217 17.3 Making the calibration robust......Page 224 17.4 Calibration transfer by correcting for bias and slope......Page 225 18.1 Supervised and unsupervised dasdfication......Page 229 18.2 Introduction to discriminant analysis......Page 230 18.3 Classification based on Bayes' rule......Page 233 18.4 Fisher's linear discriminant analysis......Page 238 18.5 The multicollinearity problem in classification......Page 242 18.6 Alternative methods......Page 251 18.7 Validation of classification rules......Page 255 18.8 Outliers......Page 256 18.9 Cluster analysis......Page 257 18.10 The collinearity problem in clustering......Page 267 19.1 Abbreviations......Page 269 19.2 Important symbols......Page 270 20 References......Page 273 A.1 An introduction to vectors and matrices......Page 293 A.2 Covariance matrices......Page 304 A.3 Simple linear regression......Page 306 A.4 Multiple linear regression (MLR)......Page 319 A.5 An intuitive description of principalcomponent analysis (PCA)......Page 323 B.1 General aspects......Page 331 B.2 More specific aspects......Page 332 C.1 Multivariate calibration......Page 337 C.2 Multivariate discriminant analysis......Page 340 C.3 Cluster analysis......Page 341 Subject index......Page 343 The field of chemometrics in general and multivariate calibration and classification in particular is now an essential tool for many analytical techniques. This book provides a readable text, for non-mathematicians, as a introduction to these areas for people with little or moderate knowledge of chemometrics. The book has been designed in an atractive and easily read format, with many diagrams and the use of margin notes to highlight important features