近幾十年來，資料的資料量及資料維度日益漸增。而在處理龐大資料時，有鑒於特徵選取能夠降低雜訊及找尋具有鑑別力的特徵，特徵選取的相關議題越來越備受重視。在現今，特徵選取已被廣泛應用於不同領域，舉例來講，在醫學上醫療人員可以透過特徵選取來找尋與癌症較為相關的眾多特徵並檢測出癌症徵兆，而此時特徵選取也可稱為基因選取。一般在處理基因選取問題時，我們期望能夠在選到最少基因的情況下去最大化分類的正確率。因此，在本質上來講，基因選取是一個雙目標問題。有鑑於此，為了更貼近其問題本質，本研究提出了一個多目標基因選取方法，其方法是結合了多個過濾器模型及多目標簡化群體演算法所完成之方法。在本方法中，首先我們會建立一個包含五種過濾器模型的層級架構並用層級分析法去決定哪些基因該被剔除。而在多數的非相關基因被剔除後，藉由多目標簡化群體演算法及支撐向量機搭配留一驗證法以評估迭代過程中各個基因集合的表現並找出最佳的基因集合。而在最終的實驗結果當中，本研究以十組癌症相關的資料做為測試資料，以本研究所提出之方法與過去文獻所提出之方法進行筆較；結果顯示，本研究提出之方法是能夠在選到較少基因的情況下得到較高的分類正確率。

In recent decades, feature selection has become an important issue since it is capable of reducing the noise and find discriminate features while dealing with high dimensional data. Nowadays, feature selection has been widely applied to many research field, such as medical research related to cancer. Feature selection can also called gene selection in the context of finding discriminate genes related to cancer. Via gene selection, medical personnel can detect the symptoms of cancer at medical early stage. Generally, while dealing with gene selection problem, the maximization of the classification accuracy and the minimization of number of selected genes need to be satisfied simultaneously. As a result, to be closer to reality, in this research, we develop a gene selection method with multi-objective design while dealing with 10 benchmark gene expression datasets. The proposed method is called hybrid filter models and multi-objective simplified swarm optimization (HF-MOSSO). In the HF-MOSSO, firstly, the AHP structure with five filter models is constructed to remove most irrelevant genes. After irrelevant genes have been removed, we develop a multi-objective simplified swarm optimization (MOSSO) using SVM with leave-one-out cross validation (LOOCV) as evaluator to evaluate the performance of gene subsets. In the experimental results, the proposed HF-MOSSO is compared with some previous methods in the literature and the results showed that the proposed method can obtain better accuracy while choosing less genes.

LIST OF CONTENTS
致謝 I
中文摘要 II
ABSTRACT III
LIST OF CONTENTS IV
LIST OF TABLES VI
LIST OF FIGURES VII
CHAPTER 1 INTRODUCTION 1
1.1 BACKGROUND AND MOTIVATION 1
1.2 RESEARCH FRAMEWORK 5
CHAPTER 2 LITERATURE REVIEW 6
2.1 FEATURE SELECTION MODEL 6
2.2 GENE SELECTION 7
2.3 META-HEURISTIC ALGORITHMS IN GENE SELECTION 7
2.4 MULTI-OBJECTIVE OPTIMIZATIONS 8
CHAPTER 3 METHODOLOGY 11
3.1 ANALYTIC HIERARCHY PROCESS 11
3.2 RANDOM FOREST 12
3.3 ANALYSIS OF VARIANCE (ANOVA) 13
3.4 ENTROPY BASED FILTER FEATURE SELECTION METHODS 14
3.5 FILTER FEATURE SELECTION BASED ON CRAMER’S V 15
3.6 SIMPLIFIED SWARM OPTIMIZATION (SSO) 16
3.7 SUPPORT VECTOR MACHINE 17
CHAPTER 4 THE PROPOSED ALGORITHM 20
4.1 THE AHP STRUCTURE 20
4.2 NOTATIONS 21
4.3 FEASIBLE SEARCH SPACE REDUCTION 22
4.4 FITNESS FUNCTION 24
4.5 MULTI-OBJECTIVE SIMPLIFIED SWARM OPTIMIZATION (MOSSO) 24
4.6 THE PROPOSED HF-MOSSO 27
CHAPTER 5 EXPERIMENTAL RESULTS 30
5.1 EXPERIMENT DATA 30
5.2 WEIGHTS OF FIVE FILTER MODELS 31
5.3 DESIGN OF EXPERIMENTS 31
5.4 COMPARED TO PREVIOUS METHODS 34
5.5 COMPARED TO ORIGINAL SSO 42
CHAPTER 6 CONCLUSIONS 44
6.1 DISCUSSIONS AND CONCLUSION 44
REFERENCES 46


CHAPTER 6 CONCLUSIONS 44
6.1 DISCUSSIONS AND CONCLUSION 44
REFERENCES 46

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