Chemometrics for Pattern Recognition

Preface.

1 Introduction.

1.1 Past, Present and Future.

1.2 About this Book.

Bibliography.

2 Case Studies.

2.1 Introduction.

2.2 Datasets, Matrices and Vectors.

2.3 Case Study 1: Forensic Analysis of Banknotes.

2.4 Case Study 2: Near Infrared Spectroscopic Analysis of Food.

2.5 Case Study 3: Thermal Analysis of Polymers.

2.6 Case Study 4: Environmental Pollution using Headspace Mass Spectrometry.

2.7 Case Study 5: Human Sweat Analysed by Gas Chromatography Mass Spectrometry.

2.8 Case Study 6: Liquid Chromatography Mass Spectrometry of Pharmaceutical Tablets.

2.9 Case Study 7: Atomic Spectroscopy for the Study of Hypertension.

2.10 Case Study 8: Metabolic Profiling of Mouse Urine by Gas Chromatography of Urine Extracts.

2.11 Case Study 9: Nuclear Magnetic Resonance Spectroscopy for Salival Analysis of the Effect of Mouthwash.

2.12 Case Study 10: Simulations.

2.13 Case Study 11: Null Dataset.

2.14 Case Study 12: GCMS and Microbiology of Mouse Scent Marks.

Bibliography.

3 Exploratory Data Analysis.

3.1 Introduction.

3.2 Principal Components Analysis.

3.2.1 Background.

3.2.2 Scores and Loadings.

3.2.3 Eigenvalues.

3.2.4 PCA Algorithm.

3.2.5 Graphical Representation.

3.3 Dissimilarity Indices, Principal Co-ordinates Analysis and Ranking.

3.3.1 Dissimilarity.

3.3.2 Principal Co-ordinates Analysis.

3.3.3 Ranking.

3.4 Self Organizing Maps.

3.4.1 Background.

3.4.2 SOM Algorithm.

3.4.3 Initialization.

3.4.4 Training.

3.4.5 Map Quality.

3.4.6 Visualization.

Bibliography.

4 Preprocessing.

4.1 Introduction.

4.2 Data Scaling.

4.2.1 Transforming Individual Elements.

4.2.2 Row Scaling.

4.2.3 Column Scaling.

4.3 Multivariate Methods of Data Reduction.

4.3.1 Largest Principal Components.

4.3.2 Discriminatory Principal Components.

4.3.3 Partial Least Squares Discriminatory Analysis Scores.

4.4 Strategies for Data Preprocessing.

4.4.1 Flow Charts.

4.4.2 Level 1.

4.4.3 Level 2.

4.4.4 Level 3.

4.4.5 Level 4.

Bibliography.

5 Two Class Classifiers.

5.1 Introduction.

5.1.1 Two Class Classifiers.

5.1.2 Preprocessing.

5.1.3 Notation.

5.1.4 Autoprediction and Class Boundaries.

5.2 Euclidean Distance to Centroids.

5.3 Linear Discriminant Analysis.

5.4 Quadratic Discriminant Analysis.

5.5 Partial Least Squares Discriminant Analysis.

5.5.1 PLS Method.

5.5.2 PLS Algorithm.

5.5.3 PLS-DA.

5.6 Learning Vector Quantization.

5.6.1 Voronoi Tesselation and Codebooks.

5.6.2 LVQ1.

5.6.3 LVQ3.

5.6.4 LVQ Illustration and Summary of Parameters.

5.7 Support Vector Machines.

5.7.1 Linear Learning Machines.

5.7.2 Kernels.

5.7.3 Controlling Complexity and Soft Margin SVMs.

5.7.4 SVM Parameters.

Bibliography.

6 One Class Classifiers.

6.1 Introduction.

6.2 Distance Based Classifiers.

6.3 PC Based Models and SIMCA.

6.4 Indicators of Significance.

6.4.1 Gaussian Density Estimators and Chi-Squared.

6.4.2 Hotelling’s T².

6.4.3 D-Statistic.

6.4.4 Q-Statistic or Squared Prediction Error.

6.4.5 Visualization of D- and Q-Statistics for Disjoint PC Models.

6.4.6 Multivariate Normality and What to do if it Fails.

6.5 Support Vector Data Description.

6.6 Summarizing One Class Classifiers.

6.6.1 Class Membership Plots.

6.6.2 ROC Curves.

Bibliography.

7 Multiclass Classifiers.

7.1 Introduction.

7.2 EDC, LDA and QDA.

7.3 LVQ.

7.4 PLS.

7.4.1 PLS2.

7.4.2 PLS1.

7.5 SVM.

7.6 One against One Decisions.

Bibliography.

8 Validation and Optimization.

8.1 Introduction.

8.1.1 Validation.

8.1.2 Optimization.

8.2 Classification Abilities, Contingency Tables and Related Concepts.

8.2.1 Two Class Classifiers.

8.2.2 Multiclass Classifiers.

8.2.3 One Class Classifiers.

8.3 Validation.

8.3.1 Testing Models.

8.3.2 Test and Training Sets.

8.3.3 Predictions.

8.3.4 Increasing the Number of Variables for the Classifier.

8.4 Iterative Approaches for Validation.

8.4.1 Predictive Ability, Model Stability, Classification by Majority Vote and Cross Classification Rate.

8.4.2 Number of Iterations.

8.4.3 Test and Training Set Boundaries.

8.5 Optimizing PLS Models.

8.5.1 Number of Components: Cross-Validation and Bootstrap.

8.5.2 Thresholds and ROC Curves.

8.6 Optimizing Learning Vector Quantization Models.

8.7 Optimizing Support Vector Machine Models.

Bibliography.

9 Determining Potential Discriminatory Variables.

9.1 Introduction.

9.1.1 Two Class Distributions.

9.1.2 Multiclass Distributions.

9.1.3 Multilevel and Multiway Distributions.

9.1.4 Sample Sizes.

9.1.5 Modelling after Variable Reduction.

9.1.6 Preliminary Variable Reduction.

9.2 Which Variables are most Significant?.

9.2.1 Basic Concepts: Statistical Indicators and Rank.

9.2.2 T-Statistic and Fisher Weights.

9.2.3 Multiple Linear Regression, ANOVA and the F-Ratio.

9.2.4 Partial Least Squares.

9.2.5 Relationship between the Indicator Functions.

9.3 How Many Variables are Significant?

9.3.1 Probabilistic Approaches.

9.3.2 Empirical Methods: Monte Carlo.

9.3.3 Cost/Benefit of Increasing the Number of Variables.

Bibliography.

10 Bayesian Methods and Unequal Class Sizes.

10.1 Introduction.

10.2 Contingency Tables and Bayes’ Theorem.

10.3 Bayesian Extensions to Classifiers.

Bibliography.

11 Class Separation Indices.

11.1 Introduction.

11.2 Davies Bouldin Index.

11.3 Silhouette Width and Modified Silhouette Width.

11.3.1 Silhouette Width.

11.3.2 Modified Silhouette Width.

11.4 Overlap Coefficient.

Bibliography.

12 Comparing Different Patterns.

12.1 Introduction.

12.2 Correlation Based Methods.

12.2.1 Mantel Test.

12.2.2 R_V Coefficient.

12.3 Consensus PCA.

12.4 Procrustes Analysis.

Bibliography.

Index.