Introduction to Multivariate Statistical Analysis in Chemometrics

Using formal descriptions, graphical illustrations, practical examples, and R software tools, Introduction to Multivariate Statistical Analysis in Chemometrics presents simple yet thorough explanations of the most important multivariate statistical methods for analyzing chemical data. It includes discussions of various statistical methods, such as principal component analysis, regression analysis, classification methods, and clustering.

Written by a chemometrician and a statistician, the book reflects the practical approach of chemometrics and the more formally oriented one of statistics. To enable a better understanding of the statistical methods, the authors apply them to real data examples from chemistry. They also examine results of the different methods, comparing traditional approaches with their robust counterparts. In addition, the authors use the freely available R package to implement methods, encouraging readers to go through the examples and adapt the procedures to their own problems.

Focusing on the practicality of the methods and the validity of the results, this book offers concise mathematical descriptions of many multivariate methods and employs graphical schemes to visualize key concepts. It effectively imparts a basic understanding of how to apply statistical methods to multivariate scientific data.

Introduction
Chemoinformatics–Chemometrics–Statistics
This Book
Historical Remarks about Chemometrics
Bibliography
Starting Examples
Univariate Statistics—A Reminder
Multivariate Data
Definitions
Basic Preprocessing
Covariance and Correlation
Distances and Similarities
Multivariate Outlier Identification
Linear Latent Variables
Summary
Principal Component Analysis (PCA)
Concepts
Number of PCA Components
Centering and Scaling
Outliers and Data Distribution
Robust PCA
Algorithms for PCA
Evaluation and Diagnostics
Complementary Methods for Exploratory Data Analysis
Examples
Summary
Calibration
Concepts
Performance of Regression Models
Ordinary Least Squares Regression
Robust Regression
Variable Selection
Principal Component Regression
Partial Least Squares Regression
Related Methods
Examples
Summary
Classification
Concepts
Linear Classification Methods
Kernel and Prototype Methods
Classification Trees
Artificial Neural Networks
Support Vector Machine
Evaluation
Examples
Summary
Cluster Analysis
Concepts
Distance and Similarity Measures
Partitioning Methods
Hierarchical Clustering Methods
Fuzzy Clustering
Model-Based Clustering
Cluster Validity and Clustering Tendency Measures
Examples
Summary
Preprocessing
Concepts
Smoothing and Differentiation
Multiplicative Signal Correction
Mass Spectral Features
Appendix 1: Symbols and Abbreviations
Appendix 2: Matrix Algebra
Appendix 3: Introduction to R
Index
References appear at the end of each chapter.