臺灣博碩士論文加值系統

本論文提出以非中心參數 (Noncentrality) 作為縱式資料集群分析的一種相異度指標，對於相同時間點的縱式資料，我們利用在單因子變異數分析 (one-way ANOVA) 中相同的想法去計算非中心參數，並且在某一分群結果之下計算其非中心參數，即可得到此分群結果之下群跟群的共同差異指標，進一步使用階層式分群法進行資料分群。我們將這個指標與其他文獻之縱式資料分群法進行比較，分別為:K-means 分群法、主成份分析法 (PCA)、Chiou and Li(2007) 提出的 kCFC 分群法，及由 Wang et al.(2008) 提出的無母數分群法，在本論文內容中會詳述這些方法之演算法及進行模擬比較。最後，我們利用本論文提出的非中心參數分群法，對於陳皮的核磁共振光譜 (NMR) 資料進行分群研究及討論。

This study proposes noncentrality as an index for measuring dissimilar- ity for longitudinal data clustering. For the data sampled at the same time points, we assume that the values of different clusters fulfill the framework of one-way ANOVA and then can be calculated the noncentralities. The over- all discrepancy among clusters is reasonably measured by accumulating the noncentralities across different time points. We use this accumulated measure for hierarchical divisive clustering. Methods proposed in the literature are compared with the present one; including K-means method, principal compo- nent analysis (PCA), the method of Chiou and Li(2007), and a non-parametric method of Wang et al.(2008). Computational algorithm is proposed and sim- ulations are reported. Finally, a set of nuclear magnetic resonance (NMR) data of dried tangerine peel (DTP or ”Chen-Pi”) are analyzed to illustrate our approach.

摘要…………………..i
Abstract…………………..ii
1 緒論…………………..1
2 分群方法回顧…………………..3
2.1 FPCA 分群法…………………..3
2.2 kCFC 分群法…………………..7
2.3 PCLUST 分群法…………………..9
2.3.1檢定兩隨機向量為相同機率分配…………………..9
2.3.2檢定兩組隨機向量為相同機率分配…………………..10
2.3.3 PCLUST 分群演算法…………………..11
3 研究方法…………………..13
3.1 非中心參數介紹…………………..13
3.2 非中心參數分群演算法…………………..14
4 模擬研究…………………..19
4.1 分群相似度指標…………………..19
4.1.1正確率 (Correct Rate) …………………..20
4.1.2 調整後之 Rand 指標 (Adjusted Rand Index) …………………..20
4.2 模擬設計介紹…………………..21
4.2.1 模擬設計一…………………..21
4.2.2 模擬設計二…………………..23
4.3 非中心參數分群法之模擬…………………..26
4.4 模擬結果與討論…………………..31
5 實例研究…………………..34
5.1 資料介紹…………………..34
5.2 分群過程…………………..35
5.3 分群結果…………………..43
6 結論與後續討論…………………..47
參考文獻…………………..49

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