Pattern Recognition in Chemistry

231 Pages·1980·7.31 MB·English

by  Kurt Varmuza (auth.)

Editors
Prof. Dr. Gaston Berthier Prof. Dr. Hans H. Jaffe
Universite de Paris Department of Chemistry
Institut de Biologie University of Cincinnati
Physico-Chimique Cincinnati, Ohio 45221/USA
Fondation Edmond de Rothschild
13, rue Pierre et Marie Curie Prof. Joshua Jortner
F-75005 Paris Institute of Chemistry
Tel-Aviv University
Prof. Dr. Michael J. S. Dewar
61390 Ramat-Aviv
Department of Chemistry
Tel-Aviv/Israel
The University of Texas
Austin, Texas 78712/USA
Prof. Dr. Werner Kutzelnigg
Lehrstuhl fUr Theoretische Chemi,
Prof. Dr. Hanns Fischer
der Universitat Bochum
Physikalisch-Chemisches Institut
Postfach 102148
der Universitat ZUrich
0-4630 Bochum 1
Ramistr.76
CH-8001 ZUrich
Prof. Dr. Klaus Ruedenberg
Prof. Kenichi Fukui Department of Chemistry
Kyoto University Iowa State University
Dept. of Hydrocarbon Chemistry Ames, Iowa 50010/USA
Kyoto/Japan
Prof. Dr. Eolo Scrocco
Prof. Dr. Hermann Hartmann
Via Garibaldi 88
Akademie der Wissenschaften
1-00153 Roma
und der Literatur zu Mainz
Geschwister-Scholl-StraBe 2
0-6500 Mainz Prof. Dr. Werner Zeil
Direktor des Instituts
Prof. Dr. George G. Hall fUr Physikalische und
Department of Mathematics Theoretische Chemie
The University of Nottingham der Universitat TUbingen
University Park Klinglerstr.16
Nottingham NG7 2RD/Great Britain 0-7406 Mossingen bei TUbingen
Lecture Notes in
Chemistry
Edited by G. Berthier, M. J. S. Dewar, H. Fischer
K. Fukui, G. G. Hall, H. Hartmann, H. H. Jaffe, J. Jortner
W. Kutzelnigg, K. Ruedenberg, E. Scrocco, W. Zeil
21
Kurt Varmuza
Pattern Recognition
in Chemistry
Springer-Verlag
Berlin Heidelberg New York 1980
Author
Kurt Varmuza
Institut fOr Allgemeine Chemie
der Technischen Universitat Wien
Lehargasse 4
A-1060 Wien
ISBN-13:978-3-540-10273-1 e-ISBN-13:978-3-642-93155-0
001: 10.1007/978-3-642-93155-0
This work is subject to copyright All rights are reserved, whether the whole
or part of the material is concerned, specifically those of translation, re
printing, re-use of illustrations, broadcasting, reproduction by photocopying
machine or similar means, and storage in data banks. Under § 54 of the
German Copyright Law where copies are made for other than private use,
a fee is payable to the publisher, the amount of the fee to be determined by
agreement with the publisher.
© by Springer-Verlag Berlin Heidelberg 1980
2152/3140-543210
Preface
Analytical chemistry of the recent years is strongly influenced
by automation. Data acquisition from analytica~ instruments - and some
times also controlling of instruments - by a computer are principally
solved since many years. Availability of microcomputers made these
tasks also feasible from the economic point of view. Besides these basic
applications of computers in chemical measurements scientists developed
computer programs for solving more sophisticated problems for which
some kind of "intelligence" is usually supposed to be necessary. Harm
less numerical experiments on this topic led to passionate discussions
about the theme "which jobs cannot be done by a computer but only by
human brain ?~. If this question is useful at all it should not be ans
wered a priori. Application of computers in chemistry is a matter of
utility, sometimes it is a social problem, but it is never a question
of piety for the human brain.
Automated instruments and the necessity to work on complex pro
blems enhanced the development of automatic methods for the reduction and
interpretation of large data sets. Numerous methods from mathematics,
statistics, information theory, and computer science have been exten
sively investigated for the elucidation of chemical information; a new
discipline "chemometrics" has been established.
Three different approaches have been used for computer-assisted
interpretations of chemical data. 1. Heuristic methods try to formu
late computer programs working in a similar way as a chemist would
solve the problem. 2. Retrieval methods have been successfully used
for library search (an unknown spectrum is compared with a spectral
library). 3. Pattern recognition methods are especially useful for the
classification of objects (substances, materials) into discrete classes
on the basis of measured features. A set of characteristic features
(e.g. a spectrum) of an object is considered as an abstract pattern
that contains information about a not directly measurable property
(e.g. molecular structure or biological activity) of the object. Pure
pattern recognition methods try to find relationships between the
pattern and the "obscure property" without using chemical knowledge
or chemical prejudices.
This book gives in the first part an introduction to some pattern
recognition methods from a chemist's point of view. This introduction
is by no means systematical or exhaustive but has been restricted to
simple mathematical methods. No previous knowledge of pattern recog
nition should be necessary for the reader.
Chapter 1 gives some basi·c ideas of pattern recognition; this
Chapter may be skipped by readers already familiar with pattern recog
nition.
Chapters 2 to 8 describe several pattern recognition methods with
emphasis'on binary classifiers and methods already applied in chemistry.
Each Chapter is preceded by an introductory part showing the principles
of the method. These Chapters shouLd be readable in arbitrary sequence.
Chapters 9 and 10 deal with preprocessing of original data and fea
ture selection. These problems must be treated at the beginning of a
pattern recognition application. These Chapters have not been positioned
at the beginning of the text because a more detailed description of these
subjects requires some basic knowledge of pattern recognition methods.
Chapter 11 deals extensively with objective methods for evaluating
pattern classifiers - a subject which has been often neglected in
chemical applications of pattern recognition methods.
After reading appropriate Chapters of the first part of this book a
reader with some knowledge in computer programming should be able to
apply simple versions of pattern recognition methods to actual problems
without further studies.
The second part of this book presents a description of reported
applications in chemistry. The aim of these Chapters was completeness;
however, the boundaries of chemistry are diffuse and the papers are
spread over many journals. It was not always possible to judge the actual
merit of pattern recognition methods in distinct fields of chemistry:
conclusions should be drawn by the reader himseLf considering specific
and varying demands and previous knowledge of actual classification
problems.
Chapter 12 gives an overview about pattern recognition applications
in chemistry. Chapters 13 to 20 extensively describe applications in
spectral analysis, chromatography, electrochemistry, material classifi
cation, structure-activity--relationship research, clinical chemistry,
environmental chemistry and classification of analytical methods.
A comprehensive list of literature references, an author and subject
index should facilitate a retrieval of detailed and original information
about pattern recognition in chemistry. All cited literature except a few
has been used in original form.
Further developments on this field are necessary. It would be an
honor for the author if this book was an aid to or stimulant of the
reader.
Vienna, April 1980 K. Varmuza
Technical Re,marks
This text has been typed by the author himself using a self-written
simple text-editor-program running on a mass spectrometric data system.
Therefore the author is responsible for all errors in the manuscript.
For technical reasons vectors are denoted by over-lined characters; e.g.
x
is a vector with components x1, x2, ••• but not a mean value!
The reference list and author list have been handled by a couple of self
written Fortran programs running at the Computer Centre of the Technical
University of Vienna. The author apologizes for some unusual notations.
Acknowledgements
Many thanks to my colleague and friend Dr. Heinz Rotter for stimulating
and critical discussions. Also thanks to Harold Urban for the drawings.
CON TEN T S
Page
Part A Introductiori to Some Pattern Recognition Methods
1. Basic Concepts 2
1.1. First Ideas of Pattern Recognition, 2
1.2. Pattern Space, 3
1.3. Binary Classifiers, 5
1.4. Training and Evaluation of Classifiers, 8
1.5. Additional Aspects, 11
1.6. Warning, 11
1.7. Applications of Pattern Recognition, 13
1.8. Literature, 14
1.8.1. General Pattern Recognition, 14
1.8.2. Pattern Recognition from the Chemist's
Point of View, 15
2. Computation of Binary Classifiers 18
2.1. Classification by Distance Measurements to Centres of
Gravity 18
2.1.1. Principle, 18
2.1.2. Centres of Gravity in a d-Dimensional Space, 19
2.1.3. Classification by Distance Measurements, 19
2.1.4. Classification by the Symmetry PLane, 21
2~1.5. Classification by Mean Vectors, 22
2.1.6. Evaluation, 23
2.1.7. PrOjection of Pattern Points on a Hypersphere, 24
2.1.8. Distance Measurements in Pattern Space (Overview), 25
2.1.9. Distance Measurements with Weighted Features
(Generalized Distances), 27
2.1.10. ChemicaL AppLications, 29
2.2. Learning Machine 30
2.2.1. PrincipLe, 30
2.2.2. InitiaL Weight Vector, 32
2.2.3. Correction of the Weight Vector, 33
2.2.4. Methods of Training, 35
2.2.5. Restrictions, 37
2.2.6. EvaLuation, 38
2.2.7. Dead Zone Training, 39
2.2.8. ChemicaL AppLications, 41
VIII
2.3. Linear Regression (Least-Squares Classification) 42
2.3.1. Principle, 42
2.3.2. Mathematical Treatment, 43
2.3.3. Characteristics and Variations of the Method, 46
2.3.4. Chemical Applications, 48
2.4. Simplex Optimization of Classifiers 48
2.4.1. Principle, 48
2.4.2. Starting the Simplex, 50
2.4.3. Response Function, 51
2.4.4. Moving the Simplex, 52
2.4.5. Halting the Simplex, 55
2.4.6 •. Chemical Applications, 55
2.5. Piecewise-Linear Classifiers 56
2.6. Implementation of Binary Classifiers 57
2.6.1. Discrete or Continuous Response, 57
2.6.2. Classification by a Committee of Classifiers, 59
2.6.3. Multicategory Classification, 59
3. K - Nearest Neighbour Classification (KNN-Method) 62
3.1. Principle, 62
3.2. Maximum Risk of KNN-Classifications, 63
3.3. Characteristics and Variations of the KNN-Method, 64
3.4. Classification with Potential Functions, 65
3.5. KNN-Classification with a Condensed Data Set, 69
3.6. Chemical Applications, 69
4. Classification by Adaptive Networks 72
4.1. Perceptron, 72
4.2. Adaptive Digital Learning Network, 74
4.3. Chemical Applications, 75
5. Parametric Classification Methods 78
5.1. Principle, 78
5.2. Bayes- and Maximum Likelihood Classifiers, 78
5.3. Estimation of Probability Densities, 80
5.4. Bayes- and Maximum Likelihood Classifiers for Binary
Encoded Patterns, 83
5.5~ A Simple Sequential Classification Method Based on
Probability Densities, 85
5.6. Chemical Applications, 87
6. Modelling of Clusters 88
6.1. Principle, 88
6.2. Modelling by a Hypersphere, 88
6.3. SIMCA-Method, 89
7. Clustering Methods 92
7.1. Principle, 92
7.2. Hierarchical Clustering, 93
7.3. Minimal Spanning Tree Clustering, 95
7.4. Chemical Applications, 96
8. Display Methods 97
8.1. Principle, 97
8.2. Linear Methods; 97
8.3. Nonlinear Methods, 100
8.4. Chemical Applications, 101
~. Preprocessing 102
9.1. Principle, 102
9.2. Scaling, 102
9.3. Weighting, 103
9.4. Transformation, 104
9.5. Combination of Features, 104
'0. Feature Selection 106
10.1. Principle, 106
10.2. Feature Selection by Using Data Statistics, 107
10.2.1. Variance Weighting, 107
10.2.2. Fisher Weighting, 108
10.2.3. Use of Probability Density Curves, 109
10.2.4. Methods for Binary Encoded Patterns, 110
10.2.5. Elimination of Correlations, 111
10.3. Feature Selection by Using Classification Results, 112
10.3.1. Evaluation of the Components of a Single
Weight Vector, 112
10.3.2. Feature Selection with the Learning Machine, 112
10.3.3. Other Methods, 113
10.4. Number of Intrinsic Dimensions and Number of Patterns
(n/d - Problem), 114
x
11. Evaluation of Classifiers 118
11.1. Principle, 118
11.2. Predictive Abilities, 119
11.3. Loss, 123
11.4. A posteriori Probabilities, 123
11.5. Terminology Problems, 127
11.6. Application of Information Theory, 129
11.6.1. Introduction to Information Theory, 129
11.6.2. Transinformation, 131
11.6.3. Figure of Merit, 136
11.7. Evaluation of Classifiers with Continuous Response, 136
11.8. Confidence of Predictive Abilities, 138
11.9. Comparison with the Capability of Chemists, 140
Part B Application of Pattern Recognition Methods in Chemistry
12. General Aspects of Pattern Recognition in Chemistry 142
13. Spectral Analysis 145
13.1. Mass Spectrometry, 145
13.1.1. Survey, 145
13.1.2. Representation of Mass Spectra as
Pattern Vectors, 146
13.1.3. Determination of Molecular Formulas and
Molecular Weights, 150
13.1.4. Recognition of Molecular Structures, 152
13.1.5. Chemical Interpretation of Mass Spectral
Classifiers, 154
13.1.6. Simulation of Mass Spectra, 155
13.1.7. Miscellaneous, 156
13.2. Infrared Spectroscopy, 157
13.3. Raman Spectroscopy, 160
13.4. Nuclear Magnetic Resonance Spectroscopy, 161
13.5. Gamma-Ray Spectroscopy, 164
13.6. Combined Spectral Data, 165
14. Chromatography 166
14.1. Gas Chromatograp~y, 166
14.2. Thin Layer Chromatography, 168