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研究生：	王俊凱 Wang, Jiun-Kai
論文名稱：	最小群聚結構鑑別之自我調節群聚演算法及其應用 A Self-Regulating Clustering Algorithm for Identification of Minimal Cluster Configuration and Its Applications
指導教授：	王振興 Wang, Jeen-Shing
學位類別：	碩士 Master
系所名稱：	電機資訊學院 - 電機工程學系 Department of Electrical Engineering
論文出版年：	2004
畢業學年度：	92
語文別：	英文
論文頁數：	54
中文關鍵詞：	函數近似、徑向基類神經網路、群聚演算法
外文關鍵詞：	function approximation, radial basis function networks, clustering algorithm
相關次數：	點閱：110 下載：6
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　　群聚分析被認為是找出大量未分類資料內部的架構。在執行群聚分析時，最大的問題在於如何決定資料內部群組的數目。為了解決此類問題，已有大量的研究投入於研發群聚演算法使其具有系統化的機制自動地找出資料內部的群聚架構。從群聚演算法的文獻探討中，這些有效的機制可被分為成長、合併及分裂等三類。在群聚分析的過程中，每個機制擁有其各別的重要性並且扮演著不同的角色在找出群聚架構的資訊。本論文提出了一個自我調節群聚演算法，此演算法能夠在沒有任何先驗知識的條件下確認出資料的群聚結構。將成長、合併和分裂三個機制伴隨著即時操作功能的特性整合成自我調節群聚演算法。這些機制可以幫助自我調節群聚演算法確認出一個合適的資料群聚結構。除此之外，本論文也提出一個新的想法，稱之為群聚邊界估測，此方法能夠有效地利用精簡的高維度橢圓形狀邊界結構來表示最後群聚結果。邊界估測的方法是利用虛擬的群聚寬度和調節向量使得自我調節群聚演算法能夠找出接近實際情況的簡潔群聚結構。在最後利用兩個不同的應用，包括常被引用的測試範例以及利用徑向基類神經網路來實現函數近似的例子，來驗證自我調節群聚演算法的效能。

　　Clustering analysis can be considered as finding a structure in a collection of unlabeled data. One substantial problem in performing a cluster analysis is to determine the number of clusters in the data set. To solve such a problem, a great amount of research effort has been directed to equip clustering algorithms with systematic frameworks to automatically reveal the cluster configuration of the data set. From a review of the clustering literature, these effective frameworks can be classified into growing, merging or splitting mechanisms. Each of these mechanisms possesses its own significance and plays an important role in revealing the information of cluster configuration during clustering analysis. In this study, a self-regulating clustering algorithm (SRCA) has been developed to provide an alternative solution for identifying the cluster configuration without a priori knowledge regarding the given data set. Growing, merging and splitting mechanisms with online operation capability are integrated into the proposed SRCA. These mechanisms enable the SRCA to identify a suitable cluster configuration. In addition, a novel idea for cluster boundary estimation has been proposed to effectively maintain the resultant clusters with compact hyper-elliptic-shaped boundaries. A virtual cluster spread coupled with a regulating vector enables the proposed SRCA to reveal the compact cluster configuration which may close to the real one if it exists. Finally, the effectiveness of the proposed SRCA was validated by two applications—benchmark examples and function approximation problems using radial basis function networks.

CHINESE ABSTRACT	            i
ABSTRACT	                   ii
LIST OF TABLES	                    v
LIST OF FIGURES	                   vi

Introduction	          1-1
1	Motivation	          1-1
2	Literature Survey	1-2
3	Purpose of the Study	1-3
4	Organization of the Thesis	1-4

Clustering Algorithms	2-1
1	Hierarchical Clustering Algorithms	2-1
2	Partitioning Clustering Algorithms	2-4
2.1	Static Adaptation Methods	2-5
2.2	Dynamic Adaptation Methods	2-6
2.2.1	 Growing Partitioning Algorithms	2-7 
2.2.2	 Shrinking Partitioning Algorithms	2-8 
3	Self-Regulating Clustering Algorithm (SRCA)	2-12
3.1	Cluster Boundary Estimation	2-12
3.2	Three Major Mechanisms—Growing, Merging and Splitting Mechanisms	2-16     
3.2.1	Growing Mechanism	2-16
3.2.2	Merging Mechanism	2-17
3.2.3	Splitting Mechanism	2-27
 
Radial Basis Function Networks and Parameter Learning Algorithms	3-1
1	Radial Basis Function Networks	3-1
1.1	Conventional Radial Basis Function Network	3-2
1.2	Normalized Radial Basis Function Network	3-4
2	Parameter Learning Algorithms	3-5

Simulations	4-1
1	Benchmark Examples	4-1
1.1	Artificial Data	4-1
1.2	Iris Data	4-2
2	Function Approximation Using RBFNs	4-5
2.1	Example 1	4-5
2.2	Example 2	4-6
Conclusions and Future Works	5-1
References

LIST OF TABLES
Table	Page
1	The information of the generated artificial data.	4-4
2	The estimated cluster distribution by the SRCA and the estimation errors.	4-4
3	The estimated Iris cluster distribution by the SRCA.	4-4
4	The errors between the actual and estimated cluster distribution.	4-5
5	The NRMSE of function approximation of three different cluster algorithms for Example 1.	4-7
6	The NRMSE of function approximation for three different cluster algorithms for Example 2.	4-7

LIST OF FIGURES
Figure	Page
1	Hierarchical clustering algorithms. (a) Single linkage. (b) Complete linkage.	2-2
2	Flowchart of growing partitioning algorithm.	2-7
3	The flowchart of SRCA.	2-11
4	The dynamic trajectory of the regulating vector R.	2-14
5	Mapping consistency of the MCA.	2-20
6	Three clusters merge into two clusters with different measures.	2-20
7	Three different situations for the index �. (a) Fix variations of � and C; only consider the relation between � and �. (b) Fix variations of � and�; only consider the relation between � and C. (c) Fix variations of � and C; only consider the relation between � and �.	2-23
8	The surface of the index �i,j with different C and � of cluster j.	2-24
9	Cluster split-up: one cluster splits into two clusters.	2-28
1	One dimensional radial basis function. (a) The representation of the one dimensional RBF and its equation. (b) One dimensional Gaussian function.	3-2
2	Two dimensional radial basis function. (a) The representation of two dimensional RBF and its equation. (b) Two dimensional Gaussian function.	3-3
3	The architecture of the conventional radial basis function network.	3-4
4	The architecture of the normalized radial basis function network.	3-5
1	The results of artificial clusters. (a) The distribution of the input space. (b) The distribution of the output space	4-3
2	The estimated Iris clusters by the proposed SRCA.	4-3
3	Example 1 of function approximation. (a) The training samples and the training result. (b) The approximation result by the SRCA.	4-6
4	Example 2 of function approximation. (a) The original function surface. (b)The approximated result.	4-7
                                    

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