臺灣博碩士論文加值系統

在模糊聚類分析中，模糊c均值(fuzzy c-means, FCM)聚類演算法為最著名也是最廣泛被使用的方法。在很多的文獻中，都針對於FCM演算法做進一步的推廣，因此很多的模糊聚類演算法，比如：CFCM,AFCM,PFCM,PIM,ICS,MEC及FGcM演算法等等，都是FCM的推廣，且這些演算法都可被視為廣義FCM(generalized FCM, GFCM)的一種。
在此論文中，我們將探討GFCM中一些特殊演算法的特性，並從GFCM中產生一個新的聚類演算法，即是在ICS上增加刑罰項(penalty term)的新演算法，我們稱它為刑罰形ICS(PICS)演算法。在論文中，我們將就五種演算法探討其對常態混合型的參數估計的結果與比較，第一種為模糊c均值(FCM)演算法，第二種為刑罰形模糊c均值(PFCM) 演算法，第三種為分割指標最大(PIM)演算法，第四種為群間分離(ICS)演算法，而第五種為新提出的刑罰形群間分離(PICS)演算法。我們將此五種演算法針對混合常態分配作參數估計，並以精確性和計算效率性作為衡量標準來比較這五種演算法的優劣性。

In cluster analysis, the fuzzy c-means (FCM) clustering algorithm is the best known and most used method. There are many generalized types of FCM. Some of them such as the conditional fuzzy c-means (CFCM), alternative fuzzy c-means (AFCM), penalized fuzzy c-means (PFCM), partition index maximization (PIM), inter-cluster separation (ICS), maximum entropy-based clustering (MEC) and fuzzy generalized c-means (FGcM) will be studied in this thesis. In fact, these algorithms can be thought of a generalized FCM (GFCM).
We proposed a new algorithm based on GFCM. We add a penalty term to the ICS and then extend the ICS to the so-called penalized ICS (PICS). Described here are five approaches for estimating the parameters of a mixture of normal distributions.
These are FCM, PFCM, PIM, ICS, and PICS clustering algorithms. The accuracy and
computational efficiency of these five types of algorithms for estimating the parameters of the normal mixtures are compared using samples drawn from some univariate normal mixtures of two classes.

目錄
中文摘要 --------------------------------------------------------I
英文摘要 -------------------------------------------------------Ⅱ
致謝辭 ----------------------------------------------------------Ⅲ
目錄 -------------------------------------------------------------Ⅳ
圖表目錄 -------------------------------------------------------Ⅴ
第一章 序論 ----------------------------------------------------1
第二章 GFCM演算法及其各種變化的探討 ------------3
第三章 數值比較與結果 -----------------------------------11
第四章 結論 ---------------------------------------------------18
參考文獻 -------------------------------------------------------19
作者簡介 --------------------------------------------------------21

圖表目錄
表一 不同混合常態分配之設計 ------------------------------------------------------------------12
表二 測試A中參數估計結果之MSE與遞迴次數(NI) ----------------------------------------13
表三 測試B中參數估計結果之MSE與遞迴次數(NI) ---------------------------------------14
表四 測試B中多加一離群點參數估計結果之MSE與遞迴次數(NI) ---------------------16
圖一 進行FCM,PFCM,PIM,ICS和PICS演算法之分群結果-----------------------------------15
圖二 增加一組離群點進行FCM,PFCM,PIM,ICS和PICS演算法之分群結果------------17

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