1st Edition

Introduction to Multivariate Statistical Analysis in Chemometrics

By Kurt Varmuza, Peter Filzmoser Copyright 2009
    336 Pages 130 B/W Illustrations
    by CRC Press

    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.

    Biography

    Kurt Varmuza, Peter Filzmoser