Chemometrics in Analytical Spectroscopy (RSC Analytical Spectroscopy Momographs)

225 Pages·1995·6.23 MB·English

by  M. J. Adams

ANALYTICAL
SPECTROSCOPY Series Editor
MONOGRAPHS Veil W. Barnett
ANALYTICAL
SPECTROSCOPY
MONOGRAPHS
This new series takes a tutorial approach to the use of spectrometric
and spectroscopic measurement techniques in analytical science,
providing immediate guidance and advice to individuals in the course
of their work. The coverage of the series is wide-ranging, including
both established and emerging techniques.
Each monograph places emphasis on the practical application of the
technique it covers, yet also includes sufficient theory and detail on
instrumentation to enable new graduates and non-specialists alike to
grasp fully the fundamentals concerned.
The series will also cover related topics such as sample preparation;
detection systems; chemical sensing; environmental monitoring; and
process analytical chemistry.
Chemometrics in Analytical Spectroscopy provides students and
practising analysts with a tutorial guide to the use and application of
the more commonly encountered techniques used in processing and
interpreting analytical spectroscopic data.
In detail the book covers the basic elements of univariate and
multivariate data analysis, the acquisition of digital data and signal
enhancement by filtering and smoothing, feature selection and
extraction, pattern recognition, exploratory data analysis by clustering,
and common algorithms in use for multivariate calibration techniques.
An appendix is included which serves as an introduction or refresher
in matrix algebra.
The extensive use of worked examples throughout gives
Chemometrics in Analytical Spectroscopy special relevance in
teaching and introducing chemometrics to undergraduates and post-
graduates taking analytical science courses. It assumes only a very
moderate level of mathematics, making the material far more
accessible than other publications on chemometrics. The book is also
ideal for analysts with little specialist background in statistics or
mathematical methods who wish to appreciate the wealth of material
published in chemometrics.
ISBN 0-85404-555-4
RSC Analytical Spectroscopy Monographs
Series Editor: Neil Barnett, Deakin University, Victoria, Australia.
Advisory Panel: F. Adams, Universitaire Instelling Antwerp, Wirijk, Belgium;
R. Browner, Georgia Institute of Technology, Georgia, USA;J . Callis,
Washington University, Washington, USA;J . Chalmers, ZCZ Materials,
Middlesbrough, UK; J. Monaghan, ZCZ Chemicals and Polymers Ltd., Runcorn,
UK; A. Sanz Medel, Universidad de Oviedo, Spain; R. Snook, UMZST,
Manchester. UK.
The series aims to provide a tutorial approach to the use of spectrometric and
spectroscopic measurement techniques in analytical science, providing guidance
and advice to individuals on a day-to-day basis during the course of their work
with the emphasis on important practical aspects of the subject.
Flame Spectrometry in Environmental Chemical Analysis: A Practical Guide
by Malcolm S. Cresser, Department of Plant and Soil Science, University of
Aberdeen, Aberdeen, UK
Chemometrics in Analytical Spectroscopy
by Mike J. Adams, School of Applied Sciences, University of Wolverhampton,
Wolverhampton, UK
How to obtain future titles on publication
A standing order plan is available for this series. A standing order will bring
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information, please write to:
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Chemometrics in Analytical
Spectroscopy
Mike J. Adams
School of Applied Sciences, University of Wolverhampton,
Wolverhampton, UK
A catalogue record for this book is available from the British Library.
ISBN 0-85404-555-4
0 The Royal Society of Chemistry 1995
All Rights Reserved
No part of this book may be reproduced or transmitted in any form
or by any means-graphic, electronic, including photocopying, recording,
taping, or information storage and retrieval systemcwithout written
permission from The Royal Society of Chemistry
Published by The Royal Society of Chemistry,
Thomas Graham House, Science Park, Cambridge CB4 4WF
Typeset by Computape (Pickering) Ltd, Pickering, North Yorkshire
Printed by Bookcraft (Bath) Ltd.
Preface
The term chemometrics was proposed more than 20 years ago to describe the
techniques and operations associated with the mathematical manipulation and
interpretation of chemical data. It is within the past 10 years, however, that
chemometrics has come to the fore, and become generally recognized as a
subject to be studied and researched by all chemists employing numerical data.
This is particularly true in analytical science. In a modern instrumentation
laboratory, the analytical chemist may be faced with a seemingly overwhelming
amount of numerical and graphical data. The identification, classification and
interpretation of these data can be a limiting factor in the efficient and effective
operation of the laboratory. Increasingly, sophisticated analytical instru-
mentation is also being employed out of the laboratory, for direct on-line or
in-line process monitoring. This trend places severe demands on data manipu-
lation, and can benefit from computerized decision making.
Chemometrics is complementary to laboratory automation. Just as auto-
mation is largely concerned with the tools with which to handle the mechanics
and chemistry of laboratory manipulations and processes, so chemometrics
seeks to apply mathematical and statistical operations to aid data handling.
This book aims to provide students and practising spectroscopists with an
introduction and guide to the application of selected chemometric techniques
used in processing and interpreting analytical data. Chapter 1 covers the basic
elements of univariate and multivariate data analysis, with particular emphasis
on the normal distribution. The acquisition of digital data and signal enhance-
ment by filtering and smoothing are discussed in Chapter 2. These processes are
fundamental to data analysis but are often neglected in chemometrics research
texts. Having acquired data, it is often necessary to process them prior to
analysis. Feature selection and extraction are reviewed in Chapter 3; the main
emphasis is on deriving information from data by forming linear combinations
of measured variables, particularly principal components. Pattern recognition
comprises a wide variety of chemometric and multivariate statistical techniques
and the most common algorithms are described in Chapters 4 and 5. In Chapter
4, exploratory data analysis by clustering is discussed, whilst Chapter 5 is
concerned with classification and discriminant analysis. Multivariate cali-
bration techniques have become increasingly popular and Chapter 6 provides a
vi Preface
summary and examples of the more common algorithms in use. Finally, an
Appendix is included which aims to serve as an introduction or refresher in
matrix algebra.
A conscious decision has been made not to provide computer programs of
the algorithms discussed. In recent years, the range and quality of software
available commercially for desktop, personal computers has improved dramati-
cally. Statistical software packages with excellent graphic display facilities are
available from many sources. In addition, modem mathematical software tools
allow the user to develop and experiment with algorithms without the problems
associated with developing machine specific inputloutput routines or high
resolution graphic interfaces.
The text is not intended to be an exhaustive review of chemometrics in
spectroscopic analysis. It aims to provide the reader with sufficient detail of
fundamental techniques to encourage further study and exploration, and aid in
dispelling the 'black-box' attitude to much of the software currently employed
in instrumental analytical analysis.
Contents
Chapter 1 Descriptive Statistics
1 Introduction
2 Normal Distribution
Significance Tests
Analysis of Variance
Outliers
3 Lorentzian Distribution
4 Multivariate Data
Covariance and Correlation
Multivariate Normal
5 Displaying Data
Chapter 2 The Acquisition and Enhancement of Data
1 Introduction
2 Sampling Theory
3 Signal-to-Noise Ratio
4 Detection Limits
5 Reducing Noise
Signal Averaging
Signal Smoothing
Filtering in the Frequency Domain
6 Interpolation
Chapter 3 Feature Selection and Extraction
1 Introduction
2 Differentiation
3 Integration
4 Combining Variables
Linear Combinations
Principal Components Analysis
Factor Analysis
.. .
Contents
Vlll
Chapter 4 Pattern Recognition I - Unsupervised Analysis
1 Introduction
2 Choice of Variables
3 Measures between Objects
Similarity Measures
Distance Measures
4 Clustering Techniques
Hierarchical Techniques
K-Means Algorithm
Fuzzy Clustering
Chapter 5 Pattern Recognition I1 - Supervised Learning
1 Introduction
2 Discriminant Functions
Bayes' Theorem
Linear Discriminant Function
3 Nearest Neighbours
4 The Perceptron
5 Artificial Neural Networks
Chapter 6 Calibration and Regression Analysis
1 Introduction
2 Linear Regression
Errors and Goodness of Fit
Regression through the Origin
3 Polynomial Regression
Orthogonal Polynomials
4 Multivariate Regression
Selection of Variables for Regression
Principal Components Regression
Partial Least Squares Regression
Appendix Matrix Tools and Operations
A1 Introduction
A2 Simple Matrix Operations
A3 Matrix Multiplication
A4 Sums of Squares and Products
A5 Inverse of a Matrix
A6 Simultaneous Equations
A7 The Quadratic Form
Subject Index
CHAPTER 1
Descriptive Statistics
1 Introduction
The mathematical manipulation of experimental data is a basic operation
associated with all modern instrumental analytical techniques. Computeri-
zation is ubiquitous and the range of computer software available to spectro-
scopists can appear overwhelming. Whether the final result is the determination
of the composition of a sample or the qualitative identification of some species
present, it is necessary for analysts to appreciate how their data are obtained
and how they can be subsequently modified and transformed to generate the
required information. A good starting point in this understanding is the study
of the elements of statistics pertaining to measurement and errors.'-3 Whilst
there is no shortage of excellent books on statistics and their applications in
spectroscopic analysis, no apology is necessary here for the basics to be
reviewed.
Even in those cases where an analysis is qualitative, quantitative measures
are employed in the processes associated with signal acquisition, data extrac-
tion, and data processing. The comparison of, say, a sample's infrared spectrum
with a set of standard spectra contained in a pre-recorded database involves
some quantitative measure of similarity in order to find and identify the best
match. Differences in spectrometer performance, sample preparation methods,
and the variability in sample composition due to impurities will all serve to
make an exact match extremely unlikely. In quantitative analysis the variability
in results may be even more evident. Within-laboratory tests amongst staff and
inter-laboratory round-robin exercises often demonstrate the far from perfect
nature of practical quantitative analysis. These experiments serve to confirm
the need for analysts to appreciate the source of observed differences and to
understand how such errors can be treated to obtain meaningful conclusions
from the analysis.
Quantitative analytical measurements are always subject to some degree of
1 C. Chatfield, 'Statistics for Technology', Chapman and Hall, London, UK, 1976.
P.R. Bevington, 'Data Reduction and Error Analysis for the Physical Sciences', McGraw-Hill,
New York, USA, 1969.
J.C. Miller and J.N. Miller, 'Statistics for Analytical Chemistry', Ellis Horwood, Chichester, UK,
1993.