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研究生： 郭靜宜
Ching-Yi Kuo
論文名稱： 以類神經網路進行型樣識別之研究
Pattern Recognition by Artificial Neural Networks
指導教授： 王小璠
Hsiao-Fan Wang
口試委員:
學位類別： 博士
Doctor
系所名稱： 工學院 - 工業工程與工程管理學系
Department of Industrial Engineering and Engineering Management
論文出版年： 2008
畢業學年度： 96
語文別： 英文
論文頁數： 143
中文關鍵詞： 型樣識別 、明確與模糊資料 、模糊集合理論 、類神經網路 、學習方法 、模糊四則運算近似法
外文關鍵詞： Pattern Recognition, Crisp and Fuzzy Data, Fuzzy Set Theory, Neural Networks, Learning Algorithm, Fuzzy Arithmetic Approximation
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    • Pattern Recognition, consists of factor/feature analysis, clustering, and classification, is a process that deals with searching structures in data. It intends to group data into categories or classes. Artificial neural network has learning capability, and the extended hybrid systems of fuzzy neural network can also deal with fuzzy data to capture the imprecise and uncertain information. The hybrid fuzzy neural system has been widely applied to the applications of pattern recognition. For each task of pattern recognition, we have specific issues to focus on. First in factor analysis, the sufficient and necessary conditions of the selected factors should be considered. Second, the core issue of clustering is the determination of the best numbers of clusters. Third, when the data are vague, the patterns are described as fuzzy data. Hence, how to recognize the fuzzy patterns shall be also coped in our study. Since each of these issues can be regarded as learning processes, we shall develop effective learning algorithms based on crisp and fuzzy neural network for the purpose of pattern recognition.

    For each issue above, analytical tool was developed with respective to two types of crisp and fuzzy data. Therefore, two categories of neural networks were proposed respectively. For crisp data, crisp neural networks were designed for first, factor analysis of which a supervised learning neural network was developed based on the hierarchical structure of factors. Second, for clustering of determining the number of clusters and grouping, a pseudo-competitive learning algorithm considering with overlapped data was developed. As regard fuzzy data, for recognizing and classifying fuzzy patterns, a new learning algorithm of the fuzzy neural network was developed in which the generalized fuzzy numbers were considered. For each case, the numerical examples and case studies were presented which have shown the accurate and effective results for the proposed algorithms.

    型樣識別為一尋找資料結構的過程，並且試圖將資料分類成數各資料群體，以利於辨別資料的特性，其主要工作包含了因素/特徵分析、資料聚類與資料分群。類神經網路則是具有學習的特性，可透過學習的方法來擷資料型態；然而事實上，也有許多的資料在本質上具有不精確性與模糊性，用模糊類神經網路來進行模糊資料的型樣識別，便可獲得並掌握這些具有不精確性的資訊。
    本論文的目的在探索明確與模糊資料的特性，尤其針對目前在型樣識別中存在的幾項主要議題提出討論、並提出解決的方法。本論文基於資料的特性分為兩大部分：第一部份針對明確資料的因素分析，首先提出一套流程，以滿足因素分析要求因子必需獨立且重要的之充分必要條件，其中以督導式的類神經網路學習法決定擷取因子的重要性；接著，提出一似競爭學習(Pseudo-competitive learning)的模糊聚類分析法，對資料依其特徵進行聚類，並且同時藉由這學習方法來決定資料的類別數(群數)。第二部份乃針對模糊資料的分群在模糊類神經網路的學習架構下，根據所發展的一般性模糊數運算近似法有效辨認與分類模糊資料。
    對於各一提所提出之解決方法，我們均以示例說明、並以實際案例來測試與比較之。由所應用的案例如電信業顧客分析、台灣茶葉品質評估、台灣地區的地震預測、IRIS聚類分析、模糊邏輯規則資料顯示所提出的分析方法在效率與準確度上均能達到相當良好的型樣識別的目的。

    ABSTRACT i 中文摘要 iii 誌謝 iv TABLE OF CONTENTS v FIGURE CAPTIONS viii TABLE CAPTIONS x GLOSSARY OF MAIN SYMBOLS xii CHAPTER 1 INTRODUCTION 1 1.1 Pattern Recognition 1 1.2 Methodologies 2 1.2.1 Artificial Neural Networks 2 1.2.2 Fuzzy Sets 4 1.3 Motivation of the Study 5 CHAPTER 2 LITERATURES REVIEW 8 2.1 Factor Analysis 8 2.2 Clustering 10 2.3 Classification 12 2.4 Summary 15 PART I. PATTERN RECOGNITION BY CRISP NEURAL NETWORKS 16 CHAPTER 3 HIERARCHICAL FACTOR ANALYSIS WITH SUPERVISED NEURAL NETWORK 16 3.1 Introduction 16 3.2 Factor Analysis 17 3.3 Procedure of Factor Analysis 20 3.3.1 Measure of Independence 21 3.3.2 Measure of Importance 24 3.3.3 Measure of Completeness 27 3.3.4 Summary and Evaluation of the Method 29 3.4 Numerical Illustration - Analysis Customers’ Contribution Demand 31 3.5 Case Study - Analysis of Churn Customers 37 3.6 Discussions and Conclusions 38 CHAPTER 4 FUZZY CLUSTERING WITH PSEUDO-COMPETITIVE LEARNING 41 4.1 Introduction 41 4.2 Algorithms for Fuzzy Clustering 44 4.2.1 Fuzzy C-means (FCM) 44 4.2.2 Competitive-learning Algorithm 45 4.2.3 Summary 46 4.3 The Proposed Pseudo-competitive Learning Algorithm 48 4.3.1 The Objective Function 48 4.3.2 The Learning Rule 49 4.3.3 Determination of the Cluster Numbers 51 4.3.4 Summary of the Algorithm 53 4.4 Numerical Illustrations and Case Study 55 4.5 Discussions and Conclusions 59 PART II. PATTERN RECOGNITION BY FUZZY NEURAL NETWORKS 61 CHAPTER 5 FUZZY PATTERN CLASSIFICATION BY A LEARNING ALGORITHM WITH FUZZY ARITHMETIC APPROXIMATION 61 5.1 Introduction 61 5.2 Basic Concepts and Definition of Three-parameter Fuzzy Arithmetic Approximation 64 5.2.1 Fuzzy Numbers 65 5.2.2 Fuzzy Arithmetic Approximation of L-R Fuzzy Numbers 66 5.3 Fuzzy Neural Networks with Signals of L-R Fuzzy Numbers 74 5.3.1 Single Layer Perceptron 74 5.3.2 Multilayer Perceptron 81 5.3.3 Summary and Evaluation of the Method 85 5.3.4 Numerical Illustrations 87 5.4 Cases Studies 90 5.4.1 Taiwanese Tea Data 90 5.4.2 Taiwan Disastrous Earthquakes 94 5.5 Discussions and Conclusions 100 CHAPTER 6 COMPARISON OF LEARNING ALGORITHMS OF FUZZIFIED NEURAL NETWORKS 102 6.1 Introduction 102 6.2 Fuzzy Neural Networks 103 6.2.1 Forward Pass 105 6.2.2 Backward Pass 106 6.2.3 Summary 106 6.3 Fuzzy Arithmetic on Forward Pass 107 6.3.1 Level-set Approach 107 6.3.2 Three-parameter Approach 108 6.3.3 Summary 110 6.4 Fuzzy Arithmetic on Backward Pass 111 6.4.1 Level-set Approach 112 6.4.2 Three-parameter Approach 114 6.4.3 Summary 115 6.5 Comparisons of the Performances 115 6.5.1 Time Complexity of the Algorithms 115 6.5.2 Accuracy and Efficiency of the Algorithms 116 6.5.3 Analysis of the Comparison 121 6.6 Summary and Conclusions 127 CHAPTER 7 CONCLUSIONS 130 REFERENCES 132 APPENDIX 138 Appendix A: Learning Rules of Backward Pass in FNNs 138 A-(I). Level-set Approach 138 A-(II). Three-parameter Approach 140 Appendix B: ANOVA in Comparison of the Learning Algorithms 143 B-(I). Case 1: Nonlinear Mapping of Fuzzy Numbers 143 B-(II). Case 2: Realization of Fuzzy IF-THEN Rules 144

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