Synopsis
I. Pattern Classification.- 1. Introduction.- 1.1 Development of a Classification System.- 1.2 Optimum Features.- 1.3 Classifiers.- 1.3.1 Neural Network Classifiers.- 1.3.2 Conventional Fuzzy Classifiers.- 1.3.3 Fuzzy Classifiers with Learning Capability.- 1.4 Evaluation.- 1.5 Data Sets Used in the Book.- 2. Multilayer Neural Network Classifiers.- 2.1 Three-layer Neural Networks.- 2.2 Synthesis Principles.- 2.3 Training Methods.- 2.4 Training by the Back-propagation Algorithm.- 2.5 Training by Solving Inequalities.- 2.5.1 Setting of Target Values.- 2.5.2 Formulation of Training by Solving Inequalities.- 2.5.3 Determination of Weights by Solving Inequalities.- 2.6 Performance Evaluation.- 2.6.1 Iris Data.- 2.6.2 Numeral Data.- 2.6.3 Thyroid Data.- 2.6.4 Blood Cell Data.- 2.6.5 Hiragana Data.- 2.6.6 Discussions.- 3. Support Vector Machines.- 3.1 Support Vector Machines for Pattern Classification.- 3.1.1 Conversion to Two-class Problems.- 3.1.2 The Optimal Hyperplane.- 3.1.3 Mapping to a High-dimensional Space.- 3.2 Performance Evaluation.- 3.2.1 Iris Data.- 3.2.2 Numeral Data.- 3.2.3 Thyroid Data.- 3.2.4 Blood Cell Data.- 3.2.5 Hiragana Data.- 3.2.6 Discussions.- 4. Membership Functions.- 4.1 One-dimensional Membership Functions.- 4.1.1 Triangular Membership Functions.- 4.1.2 Trapezoidal Membership Functions.- 4.1.3 Bell-shaped Membership Functions.- 4.2 Multi-dimensional Membership Functions.- 4.2.1 Extension to Multi-dimensional Membership Functions.- 4.2.2 Rectangular Pyramidal Membership Functions.- 4.2.3 Truncated Rectangular Pyramidal Membership Functions.- 4.2.4 Polyhedral Pyramidal Membership Functions.- 4.2.5 Truncated Polyhedral Pyramidal Membership Functions.- 4.2.6 Bell-shaped Membership Functions.- 4.2.7 Relations between Membership Functions.- 5. Static Fuzzy Rule Generation.- 5.1 Classifier Architecture.- 5.2 Fuzzy Rules.- 5.2.1 Fuzzy Rules with Pyramidal Membership Functions.- 5.2.2 Polyhedral Fuzzy Rules.- 5.2.3 Ellipsoidal Fuzzy Rules.- 5.3 Class Boundaries.- 5.3.1 Fuzzy Rules with Pyramidal Membership Functions.- 5.3.2 Ellipsoidal Fuzzy Rules.- 5.3.3 Class Boundaries for the Iris Data.- 5.4 Training Architecture.- 5.4.1 Fuzzy Rule Generation by Preclustering.- 5.4.2 Fuzzy Rule Generation by Postclustering.- 6. Clustering.- 6.1 Fuzzy c-means Clustering Algorithm.- 6.2 The Kohonen Network.- 6.3 Minimum Volume Clustering Algorithm.- 6.4 Fuzzy Min-max Clustering Algorithm.- 6.5 Overlap Resolving Clustering Algorithm.- 6.5.1 Approximation of Overlapping Regions.- 6.5.2 Extraction of Data from the Overlapping Regions.- 6.5.3 Clustering Algorithm.- 7. Tuning of Membership Functions.- 7.1 Problem Formulation.- 7.2 Direct Methods.- 7.2.1 Tuning of Slopes.- 7.2.2 Tuning of Locations.- 7.2.3 Order of Tuning.- 7.3 Indirect Methods.- 7.3.1 Tuning of Slopes Using the Least-squares Method.- 7.3.2 Tuning by the Steepest Descent Method.- 7.4 Performance Evaluation.- 7.4.1 Performance Evaluation of the Fuzzy Classifier with Pyramidal Membership Functions.- 7.4.2 Performance Evaluation of the Fuzzy Classifier with Polyhedral Regions.- 7.4.3 Performance Evaluation of the Fuzzy Classifier with Ellipsoidal Regions.- 8. Robust Pattern Classification.- 8.1 Why Robust Classification Is Necessary?.- 8.2 Robust Classification.- 8.2.1 The First Stage.- 8.2.2 The Second Stage.- 8.2.3 Tuning Slopes near Class Boundaries.- 8.2.4 Upper and Lower Bounds Determined by Correctly Classified Data.- 8.2.5 Range of the Interclass Tuning Parameter that Resolves Misclassification.- 8.3 Performance Evaluation.- 8.3.1 Classification Performance without Outliers.- 8.3.2 Classification Performance with Outliers.- 9. Dynamic Fuzzy Rule Generation.- 9.1 Fuzzy Min-max Classifiers.- 9.1.1 Concept.- 9.1.2 Approximation of Input Regions.- 9.1.3 Fuzzy Rule Extraction.- 9.1.4 Performance Evaluation.- 9.2 Fuzzy Min-max Classifiers with Inhibition.- 9.2.1 Concept.- 9.2.2 Fuzzy Rule Extraction.- 9.2.3 Fuzzy Rule Inference.- 9.2.4 Performance Evaluation.- 10. Compar
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