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研究生:林孝忠
研究生(外文):Hsiao-Chung Lin
論文名稱:群集中心具有體積之模糊分群績效比較
指導教授:吳植森
指導教授(外文):Chih-Sen Wu
學位類別:碩士
校院名稱:國立成功大學
系所名稱:資訊管理研究所
學門:電算機學門
學類:電算機一般學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:中文
論文頁數:52
中文關鍵詞:相似性測度模糊分群群集中心具有體積之模糊分群演算法群集聚合
外文關鍵詞:Fuzzy Clustering AlgorithmSimilarity MeasureFuzzy ClusteringVolume Prototype BasedCluster Merging
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  經營企業需要使用各式各樣的資料來協助決策,分析資料從中找出資料的結構與意涵對管理者而言相當重要。當對資料分佈結構不清楚的時候,使用資料探勘領域中之分群演算法以協助發覺資料隱藏的樣式,以及資料在真實世界的概念。一般而言,模糊集合適合用來處理不完整,含有雜訊之資料等問題。目標函數基礎的模糊分群演算法需事先固定群集的數目,無法自動產生群集數。因此本研究使用群集中心具有體積之模糊分群演算法,在演算法中使用相似性測度自動地決定最佳的群集數。並且使用群集有效性指標來比較、驗證群集中心具有體積之模糊分群演算法的分群結果。
  本研究使用之修正型的模糊分群演算法:ME-FCM與ME-GK演算法,加入修改之模糊共變異數矩陣與群集聚合的機制,以達成研究之三個目的:(1)找出使得目標函數最小的模糊分割與群集中心。(2)在不需要事先指定群集數目的情況下,在分群過程中自動決定最適當的群集數。(3)修改模糊共變異數矩陣,減少計算上的誤差,產生較佳之分群結果。經由實證研究顯示,修正型的模糊分群演算法有較佳之分群結果與分類正確率。
  Decision making is an essential to business operation. Decision making relies on good models built from various kinds of data. Analyzing data and finding meanings of data are important tasks for knowledge workers. In real world data are hidden in a very complicated database. We need to use techniques, such as decision and clustering methods, to discover hidden patterns and real meanings of data. In general, fuzzy sets can be used to process incomplete and noisy data. However, some objective function based fuzzy clustering algorithms have to assign the number of clusters at the beginning of the process. This research uses volume
prototype based fuzzy clustering algorithm and similarity measure to figure out the number of clusters automatically. Besides, we use cluster validity index to compare the performance of volume prototype based fuzzy clustering algorithm with other fuzzy clustering algorithms.
  Two algorithms were developed in this study: ME-FCM and ME-GK algorithms. The algorithms find the fuzzy partitions and centers, and in the meanwhile, minimize the objective function minimum as well. One unique feature of the algorithm is the number of clusters can be determined automatically. Another feature is a modified fuzzy covariance matrix was used to reduce computing errors. The results show that modified fuzzy clustering algorithm can reach better consequences of clustering and accuracy of classification.
摘 要.......................................................... I
ABSTRACT ....................................................... II
誌謝.......................................................... III
目錄........................................................... IV
表目錄......................................................... VI
圖目錄........................................................ VII
第一章 緒論..................................................... 1
第一節 研究背景............................................... 1
第二節 研究動機............................................... 1
第三節 研究目的............................................... 2
第四節 研究範圍與限制......................................... 3
第五節 研究流程............................................... 4
第二章 文獻探討................................................. 5
第一節 分群(Clustering) ....................................... 5
一、分群的定義......................................... 5
二、分群演算法的分類................................... 6
三、小結............................................... 9
第二節 模糊分群(Fuzzy Clustering) ........................... 9
一、目標函數基礎的模糊c 平均值演算法................... 9
二、Gustafson-Kessel 演算法............................ 12
三、小結.............................................. 14
第三節 群集聚合(Cluster Merging) ........................... 14
第四節 體積基礎的模糊分群演算法.............................. 16
(Volume-Based Fuzzy Clustering Algorithm) .................. 16
第五節 群集有效性(Cluster Validity) ........................ 20
第三章 研究方法................................................ 23
第一節 使用傳統兩種模糊分群演算法測試分群效果................ 23
第二節 使用修正型的模糊分群演算法測試分群效果................ 24
第三節 探討分群績效.......................................... 27
V
第四章 模糊分群法演算法之實證研究............................... 28
第一節 FCM 與GK 模糊分群演算法之分群結果..................... 28
一、FCM 模糊分群演算法之分群結果....................... 28
二、GK 模糊分群演算法之分群結果........................ 31
第二節 使用E-FCM 與E-GK 模糊分群演算法之分群結果............. 33
一、E-FCM 模糊分群演算法之分群結果..................... 33
二、E-GK 模糊分群演算法之分群結果...................... 34
三、小結.............................................. 36
第三節 使ME-FCM 與ME-GK 模糊分群演算法之分群結果............. 36
一、ME-FCM 模糊分群演算法之分群結果.................... 36
二、ME-GK 模糊分群演算法之分群結果..................... 38
三、小結.............................................. 40
第四節 FCM、GK 與ME-FCM、ME-GK 演算法之比較.................. 40
一、FCM 與ME-FCM 模糊分群演算法之比較.................. 40
二、GK 與ME-GK 模糊分群演算法之比較.................... 41
三、小結.............................................. 41
第五節 E-FCM、E-GK 與ME-FCM、ME-GK 演算法之比較.............. 41
一、E-FCM 與ME-FCM 模糊分群演算法之比較................ 41
二、E-GK 與ME-GK 模糊分群演算法之比較.................. 44
三、小結.............................................. 46
第五章 結論與建議.............................................. 47
第一節 結論.................................................. 47
第二節 建議.................................................. 47
第三節 未來研究方向.......................................... 48
參考文獻....................................................... 49
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