在本篇論文中，我們第一次使用幾何餘裕作為實現線性可分類布林函數之非耦合細胞類神經網路模板之強韌性指標。首先我們利用支撐向量機設計強韌非耦合細胞類神經網路模板來實現線性可分類的布林函數。我們提出快速循序最小最佳化演算法來求得最大幾何餘裕分類器，進而得到強韌模板。接著我們討論一些強韌模板的特性，並提出改良式的CFC演算法來實現任一給定的布林函數。最後，我們以兩個例子來驗證所提出方法的正確性。

In this thesis, the geometric margin is used for the first time as the robustness indicator of an uncoupled cellular neural network implementing a given Boolean function. First, robust template design for uncoupled cellular neural networks implementing linearly separable Boolean functions by support vector machines is proposed. A fast sequential minimal optimization algorithm is presented to find maximal margin classifiers, which in turn determine the robust templates. Some general properties of robust templates are investigated. An improved CFC algorithm implementing an arbitrarily given Boolean function is proposed. Two illustrative examples are provided to demonstrate the validity of the proposed method.

誌謝 ii
摘要 iii
ABSTRACT iv

LIST OF FIGURES AND TABLE v

CHAPTER ONE INTRODUCTION 1

1.1 Motivation 1
1.2 Brief Sketch of the Contents 4

CHAPTER TWO CELLULAR NEURAL NETWORKS 5

2.1 Preliminary Concepts 5
2.2 Uncoupled Cellular Neural Networks 6
2.3 Output Formula for Binary Inputs 8

CHAPTER THREE SUPPORT VECTOR MACHINES 10

3.1 Linear Classifiers 10
3.2 Maximal Margin Classifiers 13
3.3 SMO Algorithm 18

CHAPTER FOUR ROBUST IMPLEMENTATION OF AN ARBITRARY BOOLEAN FUNCTION 25

4.1 Linearly Separable Boolean Functions 25
4.2 Robust Templates 27
4.3 Restricted-weight Templates 32
4.4 Decomposition Algorithm 35
4.5 Illustrative Examples 41

CHAPTER FIVE CONCLUSION 44

REFERENCES 45
APPENDIX A 48
APPENDIX B 63

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