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Machine Learning, Neural and Statistical
Classification
Editors: D. Michie, D.J. Spiegelhalter, C.C. Taylor
February 17, 1994

Contents
1 Introduction 1
1.1 INTRODUCTION
1
1.2 CLASSIFICATION
1
1.3 PERSPECTIVES ON CLASSIFICATION
2
1.3.1 Statistical approaches
2
1.3.2 Machine learning
2
1.3.3 Neural networks
3
1.3.4 Conclusions
3
1.4 THE STATLOG PROJECT
4
1.4.1 Quality control
4
1.4.2 Caution in the interpretations of comparisons
4
1.5 THE STRUCTURE OF THIS VOLUME
5
2 Classification 6
2.1 DEFINITION OF CLASSIFICATION
6
2.1.1 Rationale
6
2.1.2 Issues
7
2.1.3 Class definitions
8
2.1.4 Accuracy
8
2.2 EXAMPLES OF CLASSIFIERS
8
2.2.1 Fisher’s linear discriminants
9
2.2.2 Decision tree and Rule-based methods
9
2.2.3 k-Nearest-Neighbour
10
2.3 CHOICE OF VARIABLES
11
2.3.1 Transformations and combinations of variables
11
2.4 CLASSIFICATION OF CLASSIFICATION PROCEDURES
12
2.4.1 Extensions to linear discrimination
12
2.4.2 Decision trees and Rule-based methods
12

ii [Ch. 0
2.4.3 Density estimates
12
2.5 A GENERAL STRUCTURE FOR CLASSIFICATION PROBLEMS
12
2.5.1 Prior probabilities and the Default rule
13
2.5.2 Separating classes
13
2.5.3 Misclassification costs
13
2.6 BAYES RULE GIVEN DATA
14
2.6.1 Bayes rule in statistics
15
2.7 REFERENCE TEXTS
16
3 Classical Statistical Methods 17
3.1 INTRODUCTION
17
3.2 LINEAR DISCRIMINANTS
17
3.2.1 Linear discriminants by least squares
18
3.2.2 Special case of two classes
20
3.2.3 Linear discriminants by maximum likelihood
20
3.2.4 More than two classes
21
3.3 QUADRATIC DISCRIMINANT
22
3.3.1 Quadratic discriminant - programming details
22
3.3.2 Regularisation and smoothed estimates
23
3.3.3 Choice of regularisation parameters
23
3.4 LOGISTIC DISCRIMINANT
24
3.4.1 Logistic discriminant - programming details
25
3.5 BAYES’ RULES
27
3.6 EXAMPLE
27
3.6.1 Linear discriminant
27
3.6.2 Logistic discriminant
27
3.6.3 Quadratic discriminant
27
4 Modern Statistical Techniques 29
4.1 INTRODUCTION
29
4.2 DENSITY ESTIMATION
30
4.2.1 Example
33
4.3
-NEAREST NEIGHBOUR
35
4.3.1 Example
36
4.4 PROJECTION PURSUIT CLASSIFICATION
37
4.4.1 Example
39
4.5 NAIVE BAYES
40
4.6 CAUSAL NETWORKS
41
4.6.1 Example
45
4.7 OTHER RECENT APPROACHES
46
4.7.1 ACE
46
4.7.2 MARS
47

Sec. 0.0] iii
5 Machine Learning of Rules and Trees 50
5.1 RULES AND TREES FROM DATA: FIRST PRINCIPLES
50
5.1.1 Data fit and mental fit of classifiers
50
5.1.2 Specific-to-general: a paradigm for rule-learning
54
5.1.3 Decision trees
56
5.1.4 General-to-specific: top-down induction of trees
57
5.1.5 Stopping rules and class probability trees
61
5.1.6 Splitting criteria
61
5.1.7 Getting a “right-sized tree”
63
5.2 STATLOG’S ML ALGORITHMS
65
5.2.1 Tree-learning: further features of C4.5
65
5.2.2 NewID
65
5.2.3
67
5.2.4 Further features of CART
68
5.2.5 Cal5
70
5.2.6 Bayes tree
73
5.2.7 Rule-learning algorithms: CN2
73
5.2.8 ITrule
77
5.3 BEYOND THE COMPLEXITY BARRIER
79
5.3.1 Trees into rules
79
5.3.2 Manufacturing new attributes
80
5.3.3 Inherent limits of propositional-level learning
81
5.3.4 A human-machine compromise: structured induction
83
6 Neural Networks 84
6.1 INTRODUCTION
84
6.2 SUPERVISED NETWORKS FOR CLASSIFICATION
86
6.2.1 Perceptrons and Multi Layer Perceptrons
86
6.2.2 Multi Layer Perceptron structure and functionality
87
6.2.3 Radial Basis Function networks
93
6.2.4 Improving the generalisation of Feed-Forward networks
96
6.3 UNSUPERVISED LEARNING
101
6.3.1 The K-means clustering algorithm
101
6.3.2 Kohonen networks and Learning Vector Quantizers
102
6.3.3 RAMnets
103
6.4 DIPOL92
103
6.4.1 Introduction
104
6.4.2 Pairwise linear regression
104
6.4.3 Learning procedure
104
6.4.4 Clustering of classes
105
6.4.5 Description of the classification procedure
105

iv [Ch. 0
7 Methods for Comparison 107
7.1 ESTIMATION OF ERROR RATES IN CLASSIFICATION RULES
107
7.1.1 Train-and-Test
108
7.1.2 Cross-validation
108
7.1.3 Bootstrap
108
7.1.4 Optimisation of parameters
109
7.2 ORGANISATION OF COMPARATIVE TRIALS
110
7.2.1 Cross-validation
111
7.2.2 Bootstrap
111
7.2.3 Evaluation Assistant
111
7.3 CHARACTERISATION OF DATASETS
112
7.3.1 Simple measures
112
7.3.2 Statistical measures
112
7.3.3 Information theoretic measures
116
7.4 PRE-PROCESSING
120
7.4.1 Missing values
120
7.4.2 Feature selection and extraction
120
7.4.3 Large number of categories
121
7.4.4 Bias in class proportions
122
7.4.5 Hierarchical attributes
123
7.4.6 Collection of datasets
124
7.4.7 Preprocessing strategy in StatLog
124
8 Review of Previous Empirical Comparisons 125
8.1 INTRODUCTION
125
8.2 BASIC TOOLBOX OF ALGORITHMS
125
8.3 DIFFICULTIES IN PREVIOUS STUDIES
126
8.4 PREVIOUS EMPIRICAL COMPARISONS
127
8.5 INDIVIDUAL RESULTS
127
8.6 MACHINE LEARNING vs. NEURAL NETWORK
127
8.7 STUDIES INVOLVING ML, k-NN AND STATISTICS
129
8.8 SOME EMPIRICAL STUDIES RELATING TO CREDIT RISK
129
8.8.1 Traditional and statistical approaches
129
8.8.2 Machine Learning and Neural Networks
130
9 Dataset Descriptions and Results 131
9.1 INTRODUCTION
131
9.2 CREDIT DATASETS
132
9.2.1 Credit management (Cred.Man)
132
9.2.2 Australian credit (Cr.Aust)
134
9.3 IMAGE DATASETS
135
9.3.1 Handwritten digits (Dig44)
135
9.3.2 Karhunen-Loeve digits (KL)
137
9.3.3 Vehicle silhouettes (Vehicle)
138
9.3.4 Letter recognition (Letter)
140
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