臺灣博碩士論文加值系統

微生物晶片資料通常包含的基因數非常多(數千個)，但相對的腫瘤樣本數不到100個。從這些大量的基因中去挑選對於分類具有顯著關係的基因稱為基因選取(gene or feature selection)。我們在本文中回顧了一些基因選取的方法以及統計學家對於"大p小n "問題的處裡。我們著重的方法是Support Vector Machines (SVMs)，將從模擬實驗去探討線性以及非線性分類問題。對於線性分類問題，我們主要探討基因之間相關性的影響和資料具有部份重疊(overlap)的情況;對於非線性分類問題，我們使用兩種基因選取方法，並比較其重要基因的選取結果及分類精確度。

Microarray data contains large number of p genes (usually several thousands) and small number of n patients (usually nearly 100 or less). The problem of identifying the features best discriminate among the classes to improve the ability of a classifier is known as feature selection. Some current feature selection methods and the problem of dealing with "large p, small n" are reviewed. The Support Vector Machines (SVMs) has proofed excellent performance in practice as a classification methodology. For linear classification problem, this paper studies the following two issues: (i) the number of one gene s surrogates somehow affects the importance of the gene; (ii) the case of overlapping classes. For nonlinear classification problem, we utilize two procedures: 1. mapping the original nonlinear separable data to the high dimension space, and then use SVM RFE with linear kernel to find crucial genes; 2. using SVM RFE with nonlinear kernel. Then we compare these two methods on nonlinear toy problem.

ABSTRACT (in Chinese) i
ABSTRACT (in English) ii
ACKNOWLEDGEMENTS (in Chinese) iii
CONTENTS iv
1 Introduction 1
2 Literature Review 3
3 Support Vector Machines 5
3.1 Linear Classifier for Linearly Separable Data 6
3.2 Linear Classifier for Overlapping Classes 8
3.3 Nonlinear Classifier for Nonlinearly Separable Data 9
3.4 Popular Kernel and Standard Type of Classification 10
4 Feature Selection Methods for Kernel Machines 11
4.1 Linear Case 11
4.2 Nonlinear Case 12
5 Simulation Studies 13
5.1 Linear problem 13
5.1.1 Overlapping Classes 13
5.1.2 Correlated Data 14
5.2 Nonlinear problem 15
5.2.1 Compare several different cases using nonlinear SVMs 15
5.2.2 Toy experiment 19
6 Conclusion and Future Research 20
Reference 21

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