在本論文中，我們結合基於相似度模糊分群法（similarity-based fuzzy clustering, SFC）與主成分分析（principal component analysis, PCA）的優點提出一系列新的分群演算法，這些新的分群演算法可以找出超球體（hyper-spherical）、超橢圓體（hyper-ellipsoidal）與斜角超橢圓體（oblique hyper-ellipsoidal）形狀的群聚。這些形狀的群聚是屬於凸（convex）形狀的群聚，透過多個多個局部凸（local convex）的群聚可以組合出一個非凸（non-convex）的群聚，意即，我們所提之分群演算法所找出的群聚更能符合資料型態。
由於我們所使用的模糊分群演算法是屬於一種漸進式分群演算法，資料輸入順序與參數設定可能導致群聚數量過多與分群結果不穩定等問題，為了解決這兩個問題，我們又提出“重新分配”（re-assign）和 “改進的群聚合併”（modified cluster merge）演算法。前者是為了讓群聚更加穩定，而後者則是用來減少群聚數量，應用此兩種演算法達到群聚資料穩定以及群聚數量減少的效果。
在實驗中設計出多種不同形狀的合成資料，實驗結果顯示，斜角超橢圓體形狀的群聚更能符合各種資料分佈，我們的方法能以更少的群聚達到不錯的結果。

We propose a clustering algorithm which incorporates a similarity-based fuzzy clustering and principal component analysis. The proposed algorithm is capable of discovering clusters with hyper-spherical, hyperellipsoidal, or oblique hyper-ellipsoidal shapes. Besides, the number of the clusters need not be specified in advance by the user. For a given dataset, the orientation, locations, and the number of clusters obtained can truthfully reflect the characteristics of the dataset. Experimental results, obtained by running on datasets generated synthetically, show that our method performs better than other methods.

摘要 i
Abstract ii
圖目錄 iv
表目錄 vi
第一章 簡介 1
1.1 目的 4
1.2 符號說明 5
第二章 文獻探討 6
2.1 基於相似度模糊分群法 6
2.1.1 群聚產生與更新 6
2.1.2 群聚合併 14
2.2 主成分分析 20
2.3 K-means 22
2.4 Neural Gas 22
2.5 Kernel K-means 23
第三章 研究方法 24
3.1 基本想法 24
3.2 基於主成分相似度模糊分群法 25
3.2.1 群聚合併 35
3.2.2 即時群聚合併 42
3.3 基於相似度模糊分群法後執行局部主成分分析 49
3.4 重新分配 50
3.5 實驗架構 51
第四章 實驗與結果 52
4.1 資料集介紹 52
4.2 實驗一 55
4.2.1 參數說明 55
4.2.2 實驗結果 56
4.3 實驗二 60
4.3.1 參數說明 60
4.3.2 實驗結果 60
4.4 實驗三 70
4.4.1 參數說明 70
4.4.2 實驗結果 70
4.4.3 實驗結果總結 81
4.5 實驗四 83
4.5.1 比較其他不同演算法 84
第五章 結論與未來研究方向 92
5.1 結論 92
5.2 未來研究方向 92
參考文獻 94
附錄A 3.11公式推導 96
附錄B 3.21公式推導 97

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