Chemometrics with R - Multivariate Data Analysis in the Natural Sciences and Life Sciences

Chemometrics with R

Preface

Contents

1 Introduction

Part I Preliminaries

2 Data

3 Preprocessing

3.1 Dealing with Noise

3.2 Baseline Removal

3.3 Aligning Peaks – Warping

3.3.1 Parametric Time Warping

3.3.2 Dynamic Time Warping

3.3.3 Practicalities

3.4 Peak Picking

3.5 Scaling

3.6 Missing Data

3.7 Conclusion

Part II Exploratory Analysis

4 Principal Component Analysis

4.1 The Machinery

4.2 Doing It Yourself

4.3 Choosing the Number of PCs

4.3.1 Statistical Tests

4.4 Projections

4.5 R Functions for PCA

4.6 Related Methods

4.6.1 Multidimensional Scaling

4.6.2 Independent Component Analysis and Projection Pursuit

4.6.3 Factor Analysis

4.6.4 Discussion

5 Self-Organizing Maps

5.1 Training SOMs

5.2 Visualization

5.3 Application

5.4 R Packages for SOMs

5.5 Discussion

6 Clustering

6.1 Hierarchical Clustering

6.2 Partitional Clustering

6.2.1 K-Means

6.2.2 K-Medoids

6.3 Probabilistic Clustering

6.4 Comparing Clusterings

6.5 Discussion

Part III Modelling

7 Classification

7.1 Discriminant Analysis

7.1.1 Linear Discriminant Analysis

7.1.2 Crossvalidation

7.1.3 Fisher LDA

7.1.4 Quadratic Discriminant Analysis

7.1.5 Model-Based Discriminant Analysis

7.1.6 Regularized Forms of Discriminant Analysis

Diagonal Discriminant Analysis

Shrunken Centroid Discriminant Analysis

7.2 Nearest-Neighbour Approaches

7.3 Tree-Based Approaches

7.3.1 Recursive Partitioning and Regression Trees

Constructing the Tree

7.3.2 Discussion

7.4 More Complicated Techniques

7.4.1 Support Vector Machines

Extensions to More than Two Classes

Finding the Right Parameters

7.4.2 Artificial Neural Networks

8 Multivariate Regression

8.1 Multiple Regression

8.1.1 Limits of Multiple Regression

8.2 PCR

8.2.1 The Algorithm

8.2.2 Selecting the Optimal Number of Components

8.3 Partial Least Squares (PLS) Regression

8.3.1 The Algorithm(s)

8.3.2 Interpretation

PLS Packages for R

8.4 Ridge Regression

8.5 Continuum Methods

8.6 Some Non-Linear Regression Techniques

8.6.1 SVMs for Regression

8.6.2 ANNs for Regression

8.7 Classification as a Regression Problem

8.7.1 Regression for LDA

8.7.2 Discussion

Part IV Model Inspection

9 Validation

9.1 Representativity and Independence

9.2 Error Measures

9.3 Model Selection

9.4 Crossvalidation Revisited

9.4.1 LOO Crossvalidation

9.4.2 Leave-Multiple-Out Crossvalidation

9.4.3 Double Crossvalidation

9.5 The Jackknife

9.6 The Bootstrap

9.6.1 Error Estimation with the Bootstrap

9.6.2 Confidence Intervals for Regression Coefficients

9.6.3 Other R Packages for Bootstrapping

9.7 Integrated Modelling and Validation

9.7.1 Bagging

9.7.2 Random Forests

9.7.3 Boosting

10 Variable Selection

10.1 Tests for Coefficient Significance

10.1.1 Confidence Intervals for Individual Coefficients

10.1.2 Tests Based on Overall Error Contributions

10.2 Explicit Coefficient Penalization

10.3 Global Optimization Methods

10.3.1 Simulated Annealing

10.3.2 Genetic Algorithms

10.3.3 Discussion

Part V Applications

11 Chemometric Applications

11.1 Outlier Detection with Robust PCA

11.1.1 Robust PCA

11.1.2 Discussion

11.2 Orthogonal Signal Correction and OPLS

11.3 Discrimination with Fat Data Matrices

11.3.1 PCDA

11.3.2 PLSDA

A Word of Warning

11.4 Calibration Transfer

11.5 Multivariate Curve Resolution

11.5.1 Theory

11.5.2 Finding Suitable Initial Estimates

Evolving Factor Analysis

OPA { the Orthogonal Projection Approach

11.5.3 Applying MCR

11.5.4 Constraints

11.5.5 Combining Data Sets

Part VI Appendices

A R Packages Used in this Book

References

Index