| Summary: | 碩士 === 國立中興大學 === 應用數學系所 === 105 === In this thesis, we mainly focus on a nonlinear dimension reduction technique of Laplacian Eigenmaps (LE), and also use two techniques for dimension reduction which are Principal Component Analysis (PCA) and Locally Linear Embedding(LLE) respectively. We analyze data of trace elements in blood offered by Wu et al. to determine whether the breast tumor is malignant or non-malignant (normal and benign). The data indicate that there were 13 types of trace elements and the testing results show that 25 participants were diagnosed with malignant tumors, 43
participants were diagnosed with benign tumors and 26 participants were diagnosed healthy. The data of randomly-selected 50% of trace elements were available as a train set, and data of the remaining trace elements are a test set. Moreover, we use the above mentioned methods to analyze data, and apply Support Vector Machine
(SVM) method to determine different types of data for further calculation. In addition to the test results of above three techniques, the results of Logistic Regression analysis by Wu et al. are compared. We have found out that the trace elements of cadmium, manganese and iron play important roles in breast cancer, and 100% of sensitivity, specificity and accuracy can be achieved for these techniques used in this thesis. In the meantime, we analyze the most appropriate parameters to establish the mathematical model.
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