Data Analysis with Neuro-Fuzzy Methods
Contents
1 Introduction 1
2 Intelligent Data Analysis 7
2.1 What is Intelligent Data Analysis? . . . . . . . . . . . . . . . . . . . 8
2.2 Knowledge Discovery in Databases and Data Mining . . . . . . . . . 11
3Neuro-F uzzy Systems 15
3.1 Fuzzy Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Neural Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3 Neuro-Fuzzy Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.4 Interpretable Fuzzy Systems for Data Analysis . . . . . . . . . . . . . 36
4 Learning Fuzzy Rules from Data 41
4.1 Structure Learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2 LearningMamdani-type Fuzzy Rules . . . . . . . . . . . . . . . . . . 50
4.3 Handling Symbolic Data . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.4 Treatment ofMissing Values . . . . . . . . . . . . . . . . . . . . . . . 67
4.5 Analysis of the Learning Algorithms . . . . . . . . . . . . . . . . . . 71
5 Optimization of Fuzzy Rule Bases 77
5.1 Adaptive RuleWeights . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.2 TrainingMembership Functions . . . . . . . . . . . . . . . . . . . . . 94
5.3 Mamdani-type Fuzzy Systems . . . . . . . . . . . . . . . . . . . . . . 98
5.4 Fuzzy Classifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.5 Pruning Fuzzy Rule Bases . . . . . . . . . . . . . . . . . . . . . . . . 115
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5.6 Analysis of the Learning Algorithms . . . . . . . . . . . . . . . . . . 117
6 Data Analysis with NEFCLASS 121
6.1 Network Representation of NEFCLASS . . . . . . . . . . . . . . . . . 122
6.2 Implementational Aspects . . . . . . . . . . . . . . . . . . . . . . . . 124
6.3 Effects of RuleWeights . . . . . . . . . . . . . . . . . . . . . . . . . . 127
6.4 Creating Small Classifiers . . . . . . . . . . . . . . . . . . . . . . . . 130
6.5 U sing Symbolic Variables . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.6 Classification as Preprocessing . . . . . . . . . . . . . . . . . . . . . . 135
7 Conclusions 139
Bibliography 143
Index 155
List of Symbols 157