Chemometrics for Pattern Recognition

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ISBN: 9780470987254 | 0470987251
Cover: Hardcover
Copyright: 9/28/2009

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This is the only major text in the area of chemometrics published over the last decade focusing exclusively on pattern recognition. The coverage uses real world pattern recognition case studies, often involving quite large and complex datasets. It approaches pattern recognition as a hypothesis driven subject, and emphasizes tools such as contingency tables and ROC curves rarely used in chemometrics. The text also includes discussions on the many methods in biology and applicable to biological analytical chemistry data but are rarely known in the chemometrics or analytical chemistry community.

Acknowledgements	p. xi
Preface	p. x
Introduction	p. 1
Past, Present and Future	p. 1
About this Book	p. 9
Bibliography	p. 12
Case Studies	p. 15
Introduction	p. 15
Datasets, Matrices and Vectors	p. 17
Case Study 1: Forensic Analysis of Banknotes	p. 20
Case Study 2: Near Infrared Spectroscopic Analysis of Food	p. 23
Case Study 3: Thermal Analysis of Polymers	p. 25
Case Study 4: Environmental Pollution using Headspace Mass Spectrometry	p. 27
Case Study 5: Human Sweat Analysed by Gas Chromatography MassSpectrometry	p. 30
Case Study 6: Liquid Chromatography Mass Spectrometry of Pharmaceutical Tablets	p. 32
Case Study 7: Atomic Spectroscopy for the Study of Hypertension	p. 34
Case Study 8: Metabolic Profiling of Mouse Urine by Gas Chromatography of Urine Extracts	p. 36
Case Study 9: Nuclear Magnetic Resonance Spectroscopy for Salival Analysis of the Effect of Mouthwash	p. 37
Case Study 10: Simulations	p. 38
Case Study 11: Null Dataset	p. 40
Case Study 12: GCMS and Microbiology of Mouse Scent Marks	p. 42
Bibliography	p. 45
Exploratory Data Analysis	p. 47
Introduction	p. 47
Principal Components Analysis	p. 49
Background	p. 49
Scores and Loadings	p. 50
Eigenvalues	p. 53
PCA Algorithm	p. 57
Graphical Representation	p. 57
Dissimilarity Indices, Principal Co-ordinates Analysis and Ranking	p. 75
Dissimilarity	p. 75
Principal Co-ordinates Analysis	p. 80
Ranking	p. 84
Self Organizing Maps	p. 87
Background	p. 87
SOM Algorithm	p. 88
Initialization	p. 89
Training	p. 90
Map Quality	p. 93
Visualization	p. 95
Bibliography	p. 105
Preprocessing	p. 107
Introduction	p. 107
Data Scaling	p. 108
Transforming Individual Elements	p. 108
Row Scaling	p. 117
Column Scaling	p. 124
Multivariate Methods of Data Reduction	p. 129
Largest Principal Components	p. 129
Discriminatory Principal Components	p. 137
Partial Least Squares Discriminatory Analysis Scores	p. 145
Strategies for Data Preprocessing	p. 150
Flow Charts	p. 150
Level 1	p. 153
Level 2	p. 161
Level 3	p. 162
Level 4	p. 175
Bibliography	p. 176
Two Class Clssifiers	p. 177
Introduction	p. 177
Two Class Classifiers	p. 178
Preprocessing	p. 180
Notation	p. 180
Autoprediction and Class Boundaries	p. 181
Euclidean Distance to Centroids	p. 184
Linear Discriminant Analysis	p. 185
Quadratic Discriminant Analysis	p. 192
Partial Least Squares Discriminant Analysis	p. 196
PLS Method	p. 196
PLS Algorithm	p. 198
PLS-DA	p. 199
Learning Vector Quantization	p. 201
Voronoi Tesselation and Codebooks	p. 206
LVQ1	p. 207
LVQ3	p. 209
LVQ Illustration and Summary of Parameters	p. 211
Support Vector Machines	p. 213
Linear Learning Machines	p. 214
Kernels	p. 218
Controlling Complexity and Soft Margin SVMs	p. 223
SVM Parameters	p. 228
Bibliography	p. 231
One Class Classifiers	p. 233
Introduction	p. 233
Distance Based Classifiers	p. 235
PC Based Models and SIMCA	p. 236
Indicators of Significance	p. 239
Gaussian Density Estimators and Chi-Squared	p. 239
Hotelling's T²	p. 241
D-Statistic	p. 243
Q-Statistic or Squared Prediction Error	p. 248
Visualization of D- and Q-Statistics for Disjoint PC Models	p. 249
Multivariate Normality and What to do if it Fails	p. 263
Support Vector Data Description	p. 266
Summarizing One Class Classifiers	p. 275
Class Membership Plots	p. 275
ROC Curves	p. 279
Bibliography	p. 286
Multiclass Classifiers	p. 289
Introduction	p. 289
EDC, LDA and QDA	p. 291
LVQ	p. 295
PLS	p. 298
PLS2	p. 298
PLS1	p. 300
SVM	p. 304
One against One Decisions	p. 304
Bibliography	p. 309
Validation and Optimization	p. 311
Introduction	p. 311
Validation	p. 311
Optimization	p. 315
Classification Abilities, Contingency Tables and Related Concepts	p. 315
Two Class Classifiers	p. 315
Multiclass Classifiers	p. 318
One Class Classifiers	p. 318
Validation	p. 320
Testing Models	p. 320
Test and Training Sets	p. 321
Predictions	p. 324
Increasing the Number of Variables for the Classifier	p. 331
Iterative Approaches for Validation	p. 335
Predictive Ability, Model Stability, Classification by Majority Vote and Cross Classification Rate	p. 335
Number of Iterations	p. 348
Test and Training Set Boundaries	p. 352
Optimizing PLS Models	p. 361
Number of Components: Cross-Validation and Bootstrap	p. 361
Thresholds and ROC Curves	p. 374
Optimizing Learning Vector Quantization Models	p. 377
Optimizing Support Vector Machine Models	p. 380
Bibliography	p. 390
Determining Potential Discriminatory Variables	p. 393
Introduction	p. 393
Two Class Distributions	p. 394
Multiclass Distributions	p. 395
Multilevel and Multiway Distributions	p. 396
Sample Sizes	p. 399
Modelling after Variable Reduction	p. 401
Preliminary Variable Reduction	p. 405
Which Variables are most Significant?	p. 405
Basic Concepts: Statistical Indicators and Rank	p. 405
T-Statistic and Fisher Weights	p. 407
Multiple Linear Regression, ANOVA and the F-Ratio	p. 417
Partial Least Squares	p. 431
Relationship between the Indicator Functions	p. 434
How Many Variables are Significant?	p. 440
Probabilistic Approaches	p. 440
Empirical Methods: Monte Carlo	p. 442
Cost/Benefit of Increasing the Number of Variables	p. 447
Bibliography	p. 450
Bayesian Methods and Unequal Class Sizes	p. 453
Introduction	p. 453
Contingency Tables and Bayes' Theorem	p. 453
Bayesian Extensions to Classifiers	p. 458
Bibliography	p. 467
Class Separation Indices	p. 469
Introduction	p. 469
Davies Bouldin Index	p. 470
Silhouette Width and Modified Silhouette Width	p. 475
Silhouette Width	p. 475
Modified Silhouette Width	p. 475
Overlap Coefficient	p. 477
Bibliography	p. 478
Comparing Different Patterns	p. 479
Introduction	p. 479
Correlation Based Methods	p. 481
Mantel Test	p. 481
R_v Coefficient	p. 483
Consensus PCA	p. 484
Procrustes Analysis	p. 487
Bibliography	p. 492
Index	p. 493
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Chemometrics for Pattern Recognition

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