神經科學的近期研究指出，憂鬱症患者與正常人的某些大腦區塊所含的binding potential
(BP) 有所差異。利用此特性，藉由3D BP 影像來區分憂鬱症患者與正常人。

我們使用的分類方法為正規化最佳線性判別(regularized optimal affine discriminant
(ROAD))，是近代發展出來的分類法，而且適用於高維度資料的處理。但是我們的影像資料有functional 結構，ROAD 並沒有考慮到此特性。因此我們修正了ROAD 的準則，搭配影像經過離散化小波轉換(discrete wavelet transformation)。每一片2D 影像皆透過修正的ROAD建構子分類器，將所有子分類器整合起來得到最終的分類準則。

我們有模擬影像的資料，針對ROAD 與其他分類法所得到的判錯率做比較。除此之外，
我們也將實際資料3D BP 影像套用我們的方法來分析。在本文中可以看到模擬影像與實際資料的結果。

Recent studies in neuroscience have shown that there are differences in binding potential (BP) in some regions of the brain between patients with major depressive disorder (MDD) and normal controls. The aim of this study was to distinguish these two groups(patients with MDD vs. normal controls) using their 3D BP images.

Regularized optimal affine discriminant (ROAD) method is a recently developed classificationalgorithm especially suitable for high-dimensional data. However, when applied to our high-dimensional imaging data, the original ROAD method ignores the spatial correlation structure inherited in the images. Therefore, we modified the ROAD method to adapt to our imaging data using the discrete wavelet transformation. For each slice of the image (2D image), a weak classifier is constructed using the modified ROAD method.Then our proposed classifier is obtained by assembling the weak learners from all of the slices.

We conducted some simulations to compare the relative performance
(misclassification rate) of our proposed method with other approaches. In addition, we applied our proposed algorithm to classify the real 3D BP images. In this thesis, we will present both simulation results and results of real data analysis.

目錄
論文審定書i
誌謝ii
摘要iii
Abstract iv
1 研究動機與目的1
2 資料描述2
2.1 憂鬱症來由. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 PET 影像. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.3 BP 影像. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3 研究方法5
3.1 Fisher’s linear discriminant rule . . . . . . . . . . . . . . . . . . . . . . . . 5
3.2 Regularized optimal affine discriminant (ROAD) . . . . . . . . . . . . . . . 5
3.3 ROAD for functional data . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4 小波介紹7
4.1 小波定義. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
5 影像模擬10
5.1 利用SPCA 演算法(Johnstone and Lu (2009)) 模擬影像. . . . . . . . . . . 10
5.2 方法比較. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
6 實際資料分析13
6.1 將3D 影像切割成2D 橫截面影像. . . . . . . . . . . . . . . . . . . . . . . . 13
6.1.1 資料分析流程. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
6.1.2 Ensemble 方法：random forest . . . . . . . . . . . . . . . . . . . . . 14
6.1.3 分類結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
6.2 將3D 影像每邊等分成小方塊(cube) . . . . . . . . . . . . . . . . . . . . . . 16
6.2.1 資料分析流程. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
6.2.2 分類結果(ensemble 方法為random forest) . . . . . . . . . . . . . . 17
6.3 Screening and Logistic Lasso . . . . . . . . . . . . . . . . . . . . . . . . . . 19
6.3.1 資料分析流程. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
6.3.2 分類結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
7 結語與討論22
7.1 結語. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
7.2 討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
參考文獻23
附錄24

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