臺灣博碩士論文加值系統

自從Zadeh 在1965年提出模糊集合理論之後，模糊聚類分析就廣泛地應用於各式各樣的領域之中，如特徵分析(Feature analysis)、影像處理(Image Processing)、醫學(Medicine)、類神經網路(Neural Networks)、地質學(Geology)、工程系統科學(Engineering Systems)、商業(Business)等。模糊C-均值分類法(Fuzzy C-means Clustering)簡稱 FCM 是一種根據 C -均值演算法衍生而來的，在模糊聚類中，模糊 C -均值演算法扮演著很重要的角色。
FCM演算法首先由Dunn所提的，而Bezdek是將模糊分類演算法有效推廣的其中一人，然而FCM演算法並不能完全解決所有的分類情形，這方法在某些應用上並非良好的，如在高維度的資料中，常常會有許多維數是不相關的，且在有干擾的資料點中會掩蓋掉存在的群，有時部份的特性質在解決這些群結構的貢獻是多於其他的，那該如何區別這些重要的特性質呢？變數的選擇及權重在聚類分析中即是重要的指標。
而我們這篇論文是提出一個新的演算法，這演算法較FCM、AWFCM、AFCM較為穩定，此外，我們也利用幾個例子來證明新的演算法比其他演算法較為穩定，算是一個較優的演算法。

Since Zadeh proposed fuzzy set theory, fuzzy clustering has been widely studied and applied in a variety of substantive areas. The clustering applications in various areas such as taxonomy, feature analysis, image processing, medicine, neural networks, geology, engineering systems and business, etc. Fuzzy c-means (FCM) are extensions of hard c-means (HCM). FCM has been become the most well-known and powerful method in cluster analysis.
In the fuzzy clustering literature, the fuzzy c-means algorithm first proposed by Dunn and then generalized by Bezdek is one of the most efficient ones among fuzzy clustering algorithm. However, fuzzy c-means algorithm take the same assumption that some applications. Often in high dimensional data, many dimensional are irrelevant and can mask existing clusters in noisy data. Sometimes part attributes contribute more than others in deciding the cluster structure. How to distinguish the importance of these attribute? Variable selection and weighting are important approaches in cluster analysis.
In this paper we propose a new metric. This proposed metric is more robustic than FCM、AWFCM and AFCM. Thus, we claim that the proposed new metric is more robust than others, which is better one.

目 錄
中文摘要 …………………………………………………………………………I
英文摘要 ………………………………………………………………………………………II
致謝辭……………………………………………………………………………………………III
目 錄 ……………………………………………………………………………………………IV
圖目錄 ….………………………………………………………………………………………V
表目錄 ….………………………………………………………………………………………VI
第一章 序論 …………………………………………………………………………………1
第二章 模糊C-均值分類法(Fuzzy C-Means clustering) …………………………….. 3
第三章 特性質權重模糊C-均值分類法(AWFCM) …………………………………. 6
第四章 相對式模糊C-均值演算法(Alternative c-means clustering algorithms) …10
第五章 特性質加權模糊聚類法(EAWFCM) ………………………………………… 13
第六章 數值比較 …………………………………………………………………………17
第七章 結 論 ………………………………………………………………………………27
參考文獻 ………………………………………………………………………………………28
圖目錄
圖一 FCM橢圓資料分類結果 ………………………………………………………….20
圖二 AFCM橢圓資料分類結果 ………………………………………………………..20
圖三 EAWFCM橢圓資料分類結果 ……………………………………………………21
圖四 FCM大小群資料分類結果 ………………………………………………………22
圖五 AFCM大小群資料分類結果(當m=2時) ……………………………………… 22
圖六 AFCM大小群資料分類結果(當m=3時) ……………………………………… 23
圖七 EAWFCM大小群資料分類結果 ………………………………………………23
圖八 FCM大小群資料加入離群點的分類結果 ……………………………………24
圖九 AFCM大小群資料加入離群點的分類結果 …………………………………25
圖十 EAWFCM大小群資料加入離群點的分類結果 ……………………………25
表目錄
表一 AWFCM Iris的分類結果錯誤數 ………………………………………………18
表二 EAWFCM Iris的分類結果錯誤數 ………………………………………………18
表三 FCM、AFCM、AWFCM、EAWFCM的Iris分類結果錯誤數 ……………18

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