User Friendly Guide to Multivariate Calibration and Classification

Tormod Naes0952866625, 9780952866626

Table of contents :
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