本論文的研究主題是模糊聚類分析，其詣旨就是使用模糊理論於資料的分類處理，以呈現資料原本就無法明確分類的本質。本論文共分為三個部分，第一個部分是對模糊聚類分析做概要介紹，第二個部分是針對現有結合演化式計算與模糊聚類分析的做法，提出兩個切割搜尋空間的分散式途徑，減小整體的搜尋空間，以克服因為搜尋空間過於巨大，而不易收斂的缺點，尤其對一些中空形狀的資料分佈特別有用。在第三個部分，我們提出一種稱為多重神經鍵網路的新架構，以解決各種最佳化的問題，傳統的Hopfield網路，只能處理二次方型態的目標方程式，因此應用上受到限制，而多重神經鍵網路則可以處理所有的高維多項式，甚至包含有logarithmic與sinusoidal 型態的目標方程。應用多重神經鍵網路的新架構，我們建立一個稱為fuzzy bidirectional associative clustering network (FBACN)的網路，來處理模糊聚類分析。這是自從有里程碑指標意義的方法fuzzy c-means被提出之後的一個全新方法。其優點也就是fuzzy c-means所欠缺的分類限制條件處理能力，因為FBACN有繼承自recurrent神經網路不需要analytical solutions的優點。運用FBACN處理分類限制條件的能力，我們再提出命名為part crisp and part fuzzy clustering之新概念。基本上FBACN是由兩層神經網路所組成，第一層可以是Hopfield網路或是多重神經鍵網路，這要視聚類重心有無超過二次方的限制條件而定，但第二層就必須是多重神經鍵網路。在論文的第三個部分，一共有三個例子，前面兩個是有名的butterfly與Anderson’s Iris data sets，最後一個例子是兩個同心圓，用來驗證FBACN在有限制條件的模糊聚類分析能力。

The area of research in this dissertation is fuzzy c-partition clustering, which is understood to be the grouping of similar objects with the concept of fuzzy set theory to incorporate the uncertainty of the final classification results. There are three parts in this dissertation. The first part is an overview of fuzzy c-partition clustering. In the second part, two distributed approaches of genetic search strategies for fuzzy clustering are proposed to surmount the problem of huge search space in the traditional combination of evolutionary algorithms and fuzzy c-partition clustering. The distributed optimization approaches proposed can divide the huge search space into many small ones, which in effect will lower the size of the total search space. The benefit of our approaches is especially shown in clusters with shell shapes, of which the basins of attraction of local minima are very small. In the third part, a new neural architecture, the multi-synapse neural network, is developed for constrained optimization problems, whose objective functions may include high order, logarithmic, sinusoidal forms, unlike the traditional Hopfield networks which can only handle quadratic form optimization. Meanwhile, based on the application of this new architecture, a fuzzy bidirectional associative clustering network (FBACN) is proposed for fuzzy c-partition clustering according to the objective-functional method. It is well known that fuzzy c-means is a milestone algorithm in the area of fuzzy c-partition clustering. All of the following objective-functional-based fuzzy c-partition algorithms incorporate the formulas of fuzzy c-means as the prime mover in their algorithms. However, when an application of fuzzy c-partition has sophisticated constraints, the necessity of analytical solutions in a single iteration step becomes a fatal issue of the existing algorithms. The largest advantage of FBACN is that it does not need analytical solutions. For the problems on which some prior information is known, we bring a concept of the combination of part crisp and part fuzzy clustering. Basically, the FBACN is composed of two layers of recurrent networks. Layer 1 can be a Hopfield network or a multi-synapse neural network based on whether its objective function is a quadratic form or a high order form. Yet layer 2 is definitely a multi-synapse neural network. Three examples are given in part III. The first two are the famous butterfly and Anderson’s Iris data sets, which are usually utilized as benchmarks. The last one is a data set with two concentric circles used to demonstrate the constrained fuzzy c-partition.

CONTENTS
中文摘要....................................................I
ABSTRACT....................................................II
誌謝........................................................III
LIST OF FIGURES.............................................VI
LIST OF TABLES..............................................VIII
CHAPTER 1 Introduction......................................1
1.1 Survey of Crisp Clustering and Fuzzy Clustering........1
1.2 Motivation.............................................5
1.3 Definition of Fuzzy C-Partition........................5
1.4 Fuzzy C-Means..........................................5
1.5 Dissertation Organization..............................8
CHAPTER 2 The Distributed Approaches of Genetic Algorithm for
Fuzzy Clustering..................................10
2.1 Multiparameter Coding and Discretization...............10
2.2 The Distributed Approach When Choosing Cluster Centers as
the Parameters.........................................13
2.3 The Distributed Approach When Choosing Membership Grades
as the Parameters......................................14
CHAPTER 3 Fuzzy Bidirectional Associative Clustering Network
..................................................19
3.1 The Implementation of Layer 1: a Hopfield or Multi-synapse
Neural Network.........................................21
3.2 The Implementation of Layer 2: a multi-synapses neural
network................................................28
CHAPTER 4 The Convergence of the Fuzzy Bidirectional
Associative Clustering Neural Network.............36
4.1 Theorems for the Convergence of FBACN..................36
4.2 The Convergence of the Neural Network of Layer 1.......40
4.3 The Convergence of the Neural Network of Layer 2.......42
CHAPTER 5 Constrained Fuzzy C-Partition by Using Multi-Synapse-
Based FBACN.......................................44
5.1 Fuzzy Clustering with the Maximum Entropy..............45
5.2 Part Crisp and Part Fuzzy Clustering...................46
5.3 Fuzzy Clustering of the Outlying Data Sets.............47
5.4 Fuzzy Clustering of Two Concentric Circles.............48
CHAPTER 6 The Implementation Algorithms.....................51
6.1 Algorithm of the Distributed Optimization Approach of
Cluster Centers........................................51
6.2 Algorithm of the Distributed Optimization Approach of
Membership grades......................................52
6.3 Algorithm of the FBACN.................................53
6.4 Algorithm of the FBACN with Simulated Annealing........55
CHAPTER 7 Experimental Results..............................58
7.1 Clustering Based on the Distributed Approaches of genetic
Algorithm..............................................58
7.2 Clustering Based on the FBACN and FBACN with Simulated
Annealing..............................................65
CHAPTER 8 Conclusions and Future Work.......................74
8.1 Conclusions............................................74
8.2 Future Work............................................76
REFERENCES..................................................77
作者簡介....................................................81
授權書......................................................82

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