群聚分析是一種很有效的工具，可以被用來分析資料間的結構特性，並且將分析結果廣泛的應用於工程與科學上的訓練。群聚分析的主要目的是根據資料彼此之間的相似度而將一群資料分成數個群聚。在本篇論文中，我們提出了四種新的群聚分析方法，分別是藉由改良舊的群聚分析方法或類神經網路而獲得的。這四種新的方法我們將它整理如下：
(1)監督式模糊Kohonen分類網路
模糊Kohonen分類網路(FKCN)引入了模糊c-means (FCM)演算法的模型來整合Kohonen分類網路(KCN)的學習速率與迭代更新策略。因為FKCN是非監督式的，因此我們在FKCN中加入了監督式的學習演算法，而此種監督式演算法有一點類似於學習向量量化(LVQ2)演算法。許多的資料集測試被用來說明我們所提的這個方法，由結果可知我們的方法在相同條件之下的確優於其他的監督式類神經網路。除此之外，我們所提的監督式FKCN更可以在很短的時間內達到收斂的目的。
(2)改良式模糊c-means演算法
(3)具有對稱概念的模糊Kohonen分類網路
(4)新的泛學習向量量化網路
FCM、FKCN與LVQ2演算法都是使用歐基里德距離來測量資料間的相似度，而此種測量法會讓演算法傾向於尋找圓形的群聚。但在實際上我們常遭遇到的資料集中發現，資料集常常是由線、圓或橢圓形狀所組合而成的。根據這樣的問題，我們提出了一種新的距離量測法，我們稱之為對稱距離，並將此對稱距離加入FCM、FKCN與LVQ2演算法中。藉由許多的電腦模擬結果可知，改良後的FCM、FKCN與LVQ2演算法在分割線、圓與橢圓群聚上的確有很好的效果。另外，本篇論文所提的改良式LVQ2演算法更可解決群聚交叉的問題。

Cluster analysis is an efficient tool for exploring the true underlying structure of a given data set and is being applied in a wide variety of engineering and scientific disciplines. The primary objective of cluster analysis is to partition a given data set into so-called homogenous clusters such that patterns within a cluster are more similar to each other. In this thesis, we propose four cluster analysis methods using improved cluster analysis algorithm or neural networks. The new methods are summarized below.
(1) Supervised fuzzy Kohonen clustering networks
A fuzzy Kohonen clustering networks (FKCN) was proposed which integrates the fuzzy c-means (FCM) algorithm model into the learning rate and updating strategies of the Kohonen clustering networks (KCN). Because FKCN is unsupervised, we propose a supervised version of FKCN with the supervised learning algorithm that is similar to the learning vector quantization (LVQ2) algorithm. Several data sets are used to illustrate this method. The results show that proposed method is more effective than another supervised neural networks. Moreover, it can terminate quickly with the same condition.
(2) Improved fuzzy c-means algorithm
(3) Fuzzy Kohonen clustering networks using the concept of
symmetry
(4) A new generalized learning vector quantization algorithm
FCM, FKCN and LVQ2 algorithms use Euclidean distance to compute the distance between a pattern and the assigned cluster center, so the algorithms are suitable for detecting the spherical cluster. However, since most clusters (or classes) in the real data sets may be the linear, spherical or ellipsoidal shape. Based on the question, we propose a distance measure based on the concept of symmetry. FCM, FKCN and LVQ2 algorithms incorporated with the symmetrical distance can detect linear, spherical and ellipsoidal clusters very well. Through several computer simulations, the results show that the proposed methods with the random initialization are effectiveness in detecting linear, spherical and ellipsoidal clusters. Besides, the improved LVQ2 algorithm can solve the crossed question.

第一章緒論 …………………………………………1
1.1研究動機 ……………………………………1
1.2論文架構 ……………………………………3
第二章群聚分析 ……………………………………4
2.1分群 …………………………………………4
2.2群聚分析的工具 ……………………………6
2.2.l k-means演算法 ………………………6
2.2.2模糊c-means演算法 …………………9
第三章類神經網路 …………………………………13
3.1類神經網路的發展簡史 ……………………13
3.2類神經網路運作的基本原理 ………………16
3.2.1何謂類神經網路 ………………………16
3.2.2生物神經網路與類神經網路的結構 …16
3.2.3類神經網路的工作及學習 ……………18
3.2.4類神經網路測試 ………………………19
3.3學習向量量化網路 …………………………19
3.4 Kohonen分類網路 …………………………21
3.5模糊Kohonen分類網路 ……………………24
第四章監督式模糊Kohonen分類網路 ……………27
4.1監督式模糊Kohonen分類網路 ……………27
4.2實驗結果 ……………………………………29
第五章改良式模糊c-means演算法 ………………44
5.1對稱距離 ……………………………………44
5.2改良式模糊c-means演算法 ………………45
5.3實驗結果 ……………………………………46
第六章具有對稱概念的模糊Kohonen分類網路 …56
6.1具有對稱概念的模糊Kohonen分類網路 …56
6.2實驗結果 ……………………………………57
第七章新的泛學習向量量化網路 …………………67
7.1新的泛學習向量量化網路 …………………67
7.2實驗結果 ……………………………………68
第八章結論與展望 …………………………………81
8.1結論 …………………………………………81
8.2展望 …………………………………………81
參考文獻 ……………………………………………83

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