Introduction to Multivariate Statistical Analysis in Chemometrics

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ISBN: 9781420059472 | 1420059475
Cover: Hardcover
Copyright: 2/17/2009

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While multivariate statistical methods play a prominent role in chemometrics, they are often misunderstood or unknown among research and laboratory professionals. Using only a short segment of matrix algebra for the description of methods, Introduction to Multivariate Statistical Analysis in Chemometricspresents simple but thorough explanations of the most important multivariate statistical methods used for analyzing chemical data. This practical guide demonstrates methods using the R software package, considering also robust methods, providing software tools, fully worked out examples, and demo data from chemistry fields.Â Various graphical schemes and illustrations supplement the text.

Preface	p. ix
Acknowledgments	p. xi
Authors	p. xiii
Introduction	p. 1
Chemoinformatics-Chemometrics-Statistics	p. 1
This Book	p. 3
Historical Remarks about Chemometrics	p. 4
Bibliography	p. 6
Starting Examples	p. 8
Univariate versus Bivariate Classification	p. 8
Nitrogen Content of Cereals Computed from NIR Data	p. 9
Elemental Composition of Archaeological Glasses	p. 10
Univariate Statistics-A Reminder	p. 12
Empirical Distributions	p. 12
Theoretical Distributions	p. 16
Central Value	p. 19
Spread	p. 20
Statistical Tests	p. 22
References	p. 25
Multivariate Data	p. 31
Definitions	p. 31
Basic Preprocessing	p. 33
Data Transformation	p. 34
Centering and Scaling	p. 35
Normalization	p. 36
Transformations for Compositional Data	p. 37
Covariance and Correlation	p. 38
Overview	p. 38
Estimating Covariance and Correlation	p. 40
Distances and Similarities	p. 44
Multivariate Outlier Identification	p. 47
Linear Latent Variables	p. 50
Overview	p. 50
Projection and Mapping	p. 51
Example	p. 53
Summary	p. 56
References	p. 58
Principal Component Analysis	p. 59
Concepts	p. 59
Number of PCA Components	p. 63
Centering and Scaling	p. 64
Outliers and Data Distribution	p. 66
Robust PCA	p. 67
Algorithms for PCA	p. 69
Mathematics of PCA	p. 69
Jacobi Rotation	p. 71
Singular Value Decomposition	p. 72
NIPALS	p. 73
Evaluation and Diagnostics	p. 75
Cross Validation for Determination of the Number of Principal Components	p. 75
Explained Variance for Each Variable	p. 77
Diagnostic Plots	p. 78
Complementary Methods for Exploratory Data Analysis	p. 81
Factor Analysis	p. 82
Cluster Analysis and Dendrogram	p. 82
Kohonen Mapping	p. 84
Sammon's Nonlinear Mapping	p. 87
Multiway PCA	p. 89
Examples	p. 91
Tissue Samples from Human Mummies and Fatty Acid Concentrations	p. 91
Polycyclic Aromatic Hydrocarbons in Aerosol	p. 96
Summary	p. 99
References	p. 101
Calibration	p. 103
Concepts	p. 103
Performance of Regression Models	p. 108
Overview	p. 108
Overfitting and Underfitting	p. 110
Performance Criteria	p. 112
Criteria for Models with Different Numbers of Variables	p. 114
Cross Validation	p. 115
Bootstrap	p. 118
Ordinary Least-Squares Regression	p. 119
Simple OLS	p. 119
Multiple OLS	p. 124
Confidence Intervals and Statistical Tests in OLS	p. 126
Hat Matrix and Full Cross Validation in OLS	p. 129
Multivariate OLS	p. 129
Robust Regression	p. 131
Overview	p. 131
Regression Diagnostics	p. 133
Practical Hints	p. 137
Variable Selection	p. 137
Overview	p. 137
Univariate and Bivariate Selection Methods	p. 139
Stepwise Selection Methods	p. 140
Best-Subset Regression	p. 141
Variable Selection Based on PCA or PLS Models	p. 143
Genetic Algorithms	p. 143
Cluster Analysis of Variables	p. 146
Example	p. 146
Principal Component Regression	p. 148
Overview	p. 148
Number of PCA Components	p. 150
Partial Least-Squares Regression	p. 150
Overview	p. 150
Mathematical Aspects	p. 154
Kernel Algorithm for PLS	p. 157
NIPALS Algorithm for PLS	p. 158
SIMPLS Algorithm for PLS	p. 160
Other Algorithms for PLS	p. 161
Robust PLS	p. 162
Related Methods	p. 163
Canonical Correlation Analysis	p. 163
Ridge and Lasso Regression	p. 166
Nonlinear Regression	p. 168
Basis Expansions	p. 168
Kernel Methods	p. 169
Regression Trees	p. 170
Artificial Neural Networks	p. 171
Examples	p. 172
GC Retention Indices of Polycyclic Aromatic Compounds	p. 172
Principal Component Regression	p. 173
Partial Least-Squares Regression	p. 177
Robust PLS	p. 178
Ridge Regression	p. 179
Lasso Regression	p. 181
Stepwise Regression	p. 182
Summary	p. 184
Cereal Data	p. 185
Summary	p. 188
References	p. 190
Classification	p. 195
Concepts	p. 195
Linear Classification Methods	p. 197
Linear Discriminant Analysis	p. 197
Bayes Discriminant Analysis	p. 197
Fisher Discriminant Analysis	p. 200
Example	p. 204
Linear Regression for Discriminant Analysis	p. 205
Binary Classification	p. 205
Multicategory Classification with OLS	p. 206
Multicategory Classification with PLS	p. 207
Logistic Regression	p. 207
Kernel and Prototype Methods	p. 209
SIMCA	p. 209
Gaussian Mixture Models	p. 212
k-NN Classification	p. 214
Classification Trees	p. 217
Artificial Neural Networks	p. 221
Support Vector Machine	p. 223
Evaluation	p. 228
Principles and Misclassification Error	p. 228
Predictive Ability	p. 229
Confidence in Classification Answers	p. 230
Examples	p. 231
Origin of Glass Samples	p. 231
Linear Discriminant Analysis	p. 231
Logistic Regression	p. 233
Gaussian Mixture Models	p. 234
k-NN Methods	p. 235
Classification Trees	p. 236
Artificial Neural Networks	p. 237
Support Vector Machines	p. 238
Overall Comparison	p. 238
Recognition of Chemical Substructures from Mass Spectra	p. 240
Summary	p. 246
References	p. 247
Cluster Analysis	p. 251
Concepts	p. 251
Distance and Similarity Measures	p. 254
Partitioning Methods	p. 260
Hierarchical Clustering Methods	p. 263
Fuzzy Clustering	p. 266
Model-Based Clustering	p. 267
Cluster Validity and Clustering Tendency Measures	p. 270
Examples	p. 272
Chemotaxonomy of Plants	p. 272
Glass Samples	p. 278
Summary	p. 279
References	p. 281
Preprocessing	p. 283
Concepts	p. 283
Smoothing and Differentiation	p. 283
Multiplicative Signal Correction	p. 284
Mass Spectral Features	p. 287
Logarithmic Intensity Ratios	p. 288
Averaged Intensities of Mass Intervals	p. 288
Intensities Normalized to Local Intensity Sum	p. 288
Modulo-14 Summation	p. 289
Autocorrelation	p. 289
Spectra Type	p. 289
Example	p. 289
References	p. 291
Symbols and Abbreviations	p. 293
Matrix Algebra	p. 297
Definitions	p. 297
Addition and Subtraction of Matrices	p. 298
Multiplication of Vectors	p. 298
Multiplication of Matrices	p. 299
Matrix Inversion	p. 300
Eigenvectors	p. 301
Singular Value Decomposition	p. 302
References	p. 303
Introduction to R	p. 305
General Information on R	p. 305
Installing R	p. 305
Starting R	p. 305
Working Directory	p. 306
Loading and Saving Data	p. 306
Important R Functions	p. 306
Operators and Basic Functions	p. 307
Mathematical and Logical Operators, Comparison	p. 307
Special Elements	p. 308
Mathematical Functions	p. 308
Matrix Manipulation	p. 308
Statistical Functions	p. 308
Data Types	p. 309
Missing Values	p. 309
Data Structures	p. 309
Selection and Extraction from Data Objects	p. 310
Examples for Creating Vectors	p. 310
Examples for Selecting Elements from a Vector or Factor	p. 310
Examples for Selecting Elements from a Matrix, Array, or Data Frame	p. 310
Examples for Selecting Elements from a List	p. 310
Generating and Saving Graphics	p. 311
Functions Relevant for Graphics	p. 311
Relevant Plot Parameters	p. 311
Statistical Graphics	p. 311
Saving Graphic Output	p. 311
References	p. 312
Index	p. 313
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Introduction to Multivariate Statistical Analysis in Chemometrics

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