臺灣博碩士論文加值系統

本論文中使用局部線性嵌入法來分析受試者血液中微量元素含量的資料藉以判斷受試者是否罹患乳癌。其資料中微量元素的種類有13 種，而檢驗結果受測者分為26 筆診斷為健康、43 筆有良性腫瘤和25 筆罹患惡性腫瘤。首先利用方法將原始資料降維，再使用支持向量機隨機選取70% 資料點作為訓練點來建立數學模型來判斷剩下的資料點以及計算該方法的靈敏度、特異度和準確度。實驗過程中我們發現在使用資料所提供的所有微量元素進行分析時，準確度的結果是不佳的，因此透過篩選元素的測試中我們得到在使用鎘、錳以及鐵這三個屬性來分析時，靈敏度、特異度以及準確度皆能呈現100%，故推測這是影響乳癌較為重要的因素。
除了使用局部線性嵌入法作為降維的方法之外，本論文也利用多維標度法以及等距特徵映射法對相同的資料進行分析，方法的比較上發現非線性的降維方法在靈敏度、特異度和準確度三個判斷向度皆優於線性降維方法。透過將資料點降維至二維平面提供可視化的圖也協助使用者更了解資料的分布情況，協助後續的分析。

In this thesis, we use Locally Linear Embedding (LLE) to analyze trace elements of the blood in participants to determine whether they suffer from breast cancer.
There were 13 types of trace elements in the data. According to the test results, 26 participants were diagnosed healthy, 43 participants were diagnosed with benign tumor and 25 participants were diagnosed with malignant tumors. First, we reduce the dimension in the data. Next, use Support Vector Machine (SVM) to randomly
select 70% of data point as the training data to establish a mathematical model for determining the remaining data point. Then, calculate sensitivity, specificity and
accuracy of the method. From the experimental tests, we have found that the performance of the analysis is not good when using all trace elements. When Cd, Mn and
Fe are selected and used for analysis, the best of screening elements indicates that the sensitivity of 100%, specificity of 100% and accuracy of 100% can be achieved.
Thus these results are leading to a speculation that they are more significant factors affecting breast cancer. In addition to using LLE for dimension reduction, we also
use Multidimensional Scaling (MDS) and Isometric Feature Mapping (ISOMAP) to analyze the same data. In these experimental tests, nonlinear dimension reduction
is superior to linear dimension reduction in the sensitivity, specificity and accuracy.
We get the visualization of data through dimension reduction. The visualization assists users to understand the distribution of data and analysis data.

第1章 緒論...1
1.1 歷史回顧...1
1.2 研究動機...2
1.3 論文大綱...3
1.4 術語和符號...4
第2章 多維標度法 (MDS)...5
2.1 導論...5
2.2 MDS...5
2.3 MDS演算法...7
2.4 實例說明...7
第3章 等距特徵映射法 (ISOMAP)...9
3.1 導論...9
3.2 ISOMAP...9
3.3 ISOMAP 演算法...10
3.4 實例說明...10
第4章 局部線性嵌入法 (LLE)...12
4.1 導論...12
4.2 LLE...12
4.3 LLE 演算法...14
4.4 實例說明...14
第5章 實驗測試...16
5.1 實驗測試一：使用所有微量元素...16
5.2 實驗測試二：使用三種微量元素組合...19
5.3 實驗測試三：LLE 與Logistic Regression 的比較...25
第6章 總結與未來展望...26
6.1 總結...26
6.2 未來展望...26
參考文獻...28

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