Handbook of Chemometrics and Qualimetrics Part B

729 Pages·1998·27.459 MB·English

by  Massart

DATA HANDLING IN SCIENCE AND TECHNOLOGY — VOLUME 20B
Handbook of Chemometrics and Qualimetrics:
PartB
DATA HANDLING IN SCIENCE AND TECHNOLOGY
Advisory Editors: B.G.M. Vandeginste and S.C. Rutan
Other volumes in this series:
Volume 1 Microprocessor Programming and Applications for Scientists and Engineers, by
R.R. Smardzewski
Volume 2 Chemometrics: A Textbook, by D.L. Massart, B.G.M. Vandeginste, S.M.
Deming, Y. Micotte and L. Kaufman
Volume 3 Experimental Design: A Chemometric Approach, by S.N. Deming and S.L.
Morgan
Volume 4 Advanced Scientific Coputing in BASIC with Applications in Chemistry, Biology
and Pharmacology, by P. Vaiko and S. Vajda
Volume 5 PCs for Chemists, edited by J. Zupan
Volume 6 Scientific Computing and Automation (Europe) 1990, Proceedings of the
Scientific Computing and Automation (Europe) Conference, 12-15 June 1990,
Maastrichit, Tine Nettierlands, edited by E.J. Karjalainen
Volume 7 Receptor Modeling for Air Quality Management, edited by P.K. Hopke
Volume 8 Design and Optimization in Organic Synthesis, by R. Carlson
Volume 9 Multivariate Pattern Recognition in Chemometrics, illustrated by case studies,
edited by R.G. Brereton
Volume 10 Sampling of Heterogeneous and Dynamic Material Systems: Theories of
Heterogeneity, Sampling and Homogenizing, by P.M. Gy
Volume 11 Experimental Design: A Chemometric Approach (Second, Revised and
Expanded Edition), by S.N. Deming and S.L. Morgan
Volume 12 Methods for Experimental Design: Principles and Applications for Physicists
and Chemists, by J.L. Goupy
Volume 13 Intelligent Software for Chemical Analysis, edited by L.M.C. Buydens and P.J.
Schoenmakers
Volume 14 The Data Analysis Handbook, by I.E. Frank and R. Todeschini
Volume 15 Adaption of Simulated Annealing to Chemical Optimization Problems, edited by
J. Kalivas
Volume 16 Multivariate Analysis of Data in Sensory Science, edited by T. Naes and E.
Risvik
Volume 17 Data Analysis for Hyphenated Techniques, by E.J. Karjalainen and U.P.
Karjalainen
Volume 18 Signal Treatment and Signal Analysis in NMR, edited by D.N. Rutledge
Volume 19 Robustness of Analytical Chemical Methods and Pharmaceutical Technological
Products, edited by M.W.B. Hendriks, J.H. de Boer and A.K. Smilde
Volume 20A Handbook of Chemometrics and Qualimetrics: Part A, by D.L. Massart, B.G.M.
Vandeginste, LM.C. Buydens, S. De Jong, P.J. Lewi and J. Smeyers-Verbeke
Volume 20B Handbook of Chemometrics and Qualimetrics: Part B, by B.G.M. Vandeginste,
D.L. Massart, L.M.C. Buydens, S. De Jong, P.J. Lewi and J. Smeyers-Verbeke
DATA HANDLING IN SCIENCE AND TECHNOLOGY — VOLUME 20B
Advisory Editors: B.G.M. Vandeginste and S.C. Rutan
Handbook of Chemometrics
and Qualimetrics: Part B
B.G.M. VANDEGINSTE
Unilever Research Laboratorium, Vlaardingen, The Netherlands
D.L. MASSART
Farmaceutisch Instituut, Dienst Farmaceutische en Biomedische Analyse, Vrije
Universiteit Brussel, Brussels, Belgium
L.M.C. BUYDENS
Vakgroep Analytische Chemie, Katholieke Universiteit Nijmegen, Faculteit
Natuun/vetenschappen, Nijmegen, The Netherlands
S. DE JONG
Unilever Research Laboratorium, Vlaardingen, The Netherlands
P.J. LEWI
Janssen Research Foundation, Center for Molecular Design, Vosselaar, Belgium
J. SMEYERS-VERBEKE
Farmaceutisch Instituut, Dienst Farmaceutische en Biomedische Analyse, Vrije
Universiteit Brussel, Brussels, Belgium
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First edition 1998
Second impression 2003
Library of Congress Cataloging-in-Publication Data
Handbook of chemometrics and qualimetrics / B.G.M. Vandeginste ... [et
al.].
p. cm. — (Data handling in science and technology ; v. 20B)
Includes index.
ISBN 0-444-82853-2 (pt. 20B : acid-free paper)
1. Chemistry, Analytic-Statistical methods. 2. Chemistry,
Analytic—Mathematics. 3. Chemistry, Analytic—Data processing.
I. Vandeginste, B.G.M. II. Series.
QD75.4.S8H36 1998
543\00r5195-dc21 98-42544
CIP
British Library Cataloguing in Publication Data
A catalogue record from the British Library has been applied for.
ISBN: 0-444-82853-2 (Vol. 20B)
ISBN: 0-444-82854-0 (set)
© The paper used in this publication meets the requirements of ANSI/NISO Z39.48-1992 (Permanence of Paper).
Printed in The Netherlands.
Preface
In 1991 two of us, Luc Massart and Bernard Vandeginste, discussed, during one of
our many meetings, the possibility and necessity of updating the book
Chemometrics: a textbook. Some of the newer techniques, such as partial least
squares and expert systems, were not included in that book which was written
some 15 years ago. Initially, we thought that we could bring it up to date with
relatively minor revision. We could not have been more wrong. Even during the
planning of the book we witnessed a rapid development in the application of
natural computing methods, multivariate calibration, method validation, etc.
When approaching colleagues to join the team of authors, it was clear from the
outset that the book would not be an overhaul of the previous one, but an almost
completely new book. When forming the team, we were particularly happy to be
joined by two industrial chemometricians. Dr. Paul Lewi from Janssen
Pharmaceutica and Dr. Sijmen de Jong from Unilever Research Laboratorium
Vlaardingen, each having a wealth of practical experience. We are grateful to
Janssen Pharmaceutica and Unilever Research Vlaardingen that they allowed
Paul, Sijmen and Bernard to spend some of their time on this project. The three
other authors belong to the Vrije Universiteit Brussel (Prof. An Smeyers-Verbeke
and Prof. D. Luc Massart) and the Katholieke Universiteit Nijmegen (Professor
Lutgarde Buydens), thus creating a team in which university and industry are
equally well represented. We hope that this has led to an equally good mix of
theory and application in the new book.
Much of the material presented in this book is based on the direct experience of
the authors. This would not have been possible without the hard work and input of
our colleagues, students and post-doctoral fellows. We sincerely want to acknowl-
edge each of them for their good research and contributions without which we
would not have been able to treat such a broad range of subjects. Some of them
read chapters or helped in other ways. We also owe thanks to the chemometrics
community and at the same time we have to offer apologies. We have had the
opportunity of collaborating with many colleagues and we have profited from the
research and publications of many others. Their ideas and work have made this
book possible and necessary. The size of the book shows that they have been very
productive. Even so, we have cited only a fraction of the literature and we have not
included the more sophisticated work. Our wish was to consolidate and therefore
to explain those methods that have become more or less accepted, also to
newcomers to chemometrics. Our apologies, therefore, to those we did not cite or
not extensively: it is not a reflection on the quality of their work.
Each chapter saw many versions which needed to be entered and re-entered in
the computer. Without the help of our secretaries, we would not have been able to
complete this work successfully. All versions were read and commented on by all
authors in a long series of team meetings. We will certainly retain special
memories of many of our two-day meetings, for instance the one organized by Paul
in the famous abbey of the regular canons of Premontre at Tongerlo, where we
could work in peace and quiet as so many before us have done.
Much of this work also had to be done at home, which took away precious time
from our families. Their love, understanding, patience and support was indispens-
able for us to carry on with the seemingly endless series of chapters to be drafted,
read or revised.
Contents
Preface v
Chapter 28 Introduction to Part B 1
References 5
Chapter 29 Vectors, Matrices and Operations on Matrices 7
29.1 Vector space 8
29.2 Geometrical properties of vectors 10
29.3 Matrices 15
29.4 Matrix product 19
29.5 Dimension and rank 27
29.6 Eigenvectors and eigenvalues 30
29.7 Statistical interpretation of matrices 42
29.8 Geometrical interpretation of matrix products 51
References 56
Chapter 30 Cluster Analysis 57
30.1 Clusters 57
30.2 Measures of (dis)similarity 60
30.2.1 Similarity and distance 60
30.2.2 Measures of (dis)similarity for continuous variables 60
30.2.2.1 Distances 60
30.2.2.2 Correlation coefficient 62
30.2.2.3 Scaling 64
30.2.3 Measures of (dis)similarity for other variables 65
30.2.3.1 Binary variables 65
30.2.3.2 Ordinal variables 66
30.2.3.3 Mixed variables 67
30.2.4 Similarity matrix 68
30.3 Clustering algorithms 69
30.3.1 Hierarchical methods 69
30.3.2 Non-hierarchical methods 76
30.3.3 Other methods 79
30.3.4 Selecting clusters 82
30.3.4.1 Measures for clustering tendency 82
30.3.4.2 How many clusters? 83
30.3.5 Conclusion 84
References 85
Chapter 31 Analysis of Measurement Tables 87
Introduction 87
31.1 Principal components analysis 88
31.1.1 Singular vectors and singular values 89
31.1.2 Eigenvectors and eigenvalues 91
Vlll
31.1.3 Latent vectors and latent values 95
31.1.4 Scores and loadings 95
31.1.5 Principal components 96
31.1.6 Transition formulae 100
31.1.7 Reconstructions 100
31.2 Geometrical interpretation 104
31.2.1 Line of closest fit . 104
31.2.2 Distances 108
31.2.3 Unipolar axes 112
31.2.4 Bipolar axes 113
31.3 Preprocessing 115
31.3.1 No transformation 118
31.3.2 Column-centering 119
31.3.3 Column-standardization 122
31.3.4 Log column-centering 123
31.3.5 Log double-centering 125
31.3.6 Double-closure 130
31.4 Algorithms 134
31.4.1 Singular value decomposition 134
31.4.2 Eigenvalue decomposition 138
31.5 Validation 140
31.5.1 Scree-plot 142
31.5.2Malinowski'sF-test 143
31.5.3 Cross-validation 144
31.6 Principal coordinates analysis 146
31.6.1 Distances defined from data 146
31.6.2 Distances derived from comparisons of pairs 148
31.6.3 Eigenvalue decomposition 148
31.7 Non-linear principal components analysis 149
31.7.1 Extensions of the data by higher order terms 149
31.7.2 Non-linear transformations of the data 149
31.7.3 Non-linear PCAbiplot 150
31.8 Three-way principal components analysis 153
31.8.1 Unfolding 153
31.8.2 The Tucker3 model 154
31.8.3 The PARAFAC model 156
31.9 PCA and cluster analysis 156
References 158
Chapter 32 Analysis of Contingency Tables 161
32.1 Contingency table 161
32.2 Chi-square statistic 166
32.3 Closure 167
32.3.1 Row-closure 168
32.3.2 Column-closure 168
32.3.3 Double-closure .169
32.4 Weighted metric 170
32.5 Distance of chi-square 175
32.5.1 Row-closure 175
32.5.2 Column-closure 176
32.5.3 Double-closure 177
32.6 Correspondence factor analysis 182
32.6.1 Historical background 182
32.6.2 Generalized singular value decomposition 183
32.6.3 Biplots. 187
32.6.4 Application 193
32.7 Log-linear model 201
32.7.1 Historical introduction 201
32.7.2 Algorithm 201
32.7.3 Application 204
References 205
Chapter 33 Supervised Pattern Recognition 207
33.1 Supervised and unsupervised pattern recognition 207
33.2 Derivation of classification rules 208
33.2.1 Types of classification rules 208
33.2.2 Canonical variates and linear discriminant analysis 213
33.2.3 Quadratic discriminant analysis and related methods 220
33.2.4 The k-nearest neighbour method 223
33.2.5 Density methods. 225
33.2.6 Classification trees 227
33.2.7 UNEQ,SIMCA and related methods 228
33.2.8 Partial least squares 232
33.2.9 Neural networks 233
33.3 Feature selection and reduction 236
33.4 Validation of classification rules 238
References 239
Chapter 34 Curve and Mixture Resolution by Factor Analysis and Related Techniques . . 243
34.1 Abstract and true factors 243
34.2 Full-rank methods 251
34.2.1 A qualitative approach 251
34.2.2 Factor rotations 252
34.2.3 The Varimax rotation . 254
34.2.4. Factor rotation by target transformation factor analysis (TTFA) . 256
34.2.5 Curve resolution based methods 260
34.2.5.1 Curve Resolution of two-factor systems 260
34.2.5.2 Curve resolution of three-factor systems 267
34.2.6 Factor rotation by iterative target transformation factor
analysis (ITTFA) 268
34.3 Evolutionary and local rank methods 274
34.3.1 Evolving factor analysis (EFA) 274
34.3.2 Fixed-size window evolving factor analysis (FSWEFA) 278
34.3.3 Heuristic evolving latent projections (HELP) 280
34.4 Pure column (or row) techniques 286
34.4.1 The variance diagram (VARDIA) technique 286
34.4.2 SimpHsma 292
34.4.3 Orthogonal projection approach (OPA) 295
34.5 Quantitative methods for factor analysis 298
34.5.1 Generalized rank annihilation factor analysis (GRAFA) 298
34.5.2 Residual bilinearization(RBL) 300