近年來，基因微陣列(microarray)技術已經成為生物學家一項重要的研究工具。微陣列技術可以在一次實驗中獲得大量的基因表現資料，藉由分析微陣列的資料，我們可以選出對於疾病診斷具有重要性的基因。然而基因微陣列的資料特性卻與一般傳統的統計資料大相逕庭，典型的基因微陣列資料擁有數千甚至上萬個基因，卻因為樣本收集不易而僅有數十筆樣本數量，這種高特徵維度、低樣本數量的資料特性容易造成分類與預測時產生極大的誤差。因此近幾年來學者將研究重點擺在「基因的挑選方法」與「小樣本高特徵維度的分類方法」上，但是這些方法大都計算複雜不易使用或者需要花較多時間訓練出分類模型，因此本論文提出一套簡單的基因挑選流程，結合常用的統計分析方法，來達到較高的分類正確率。

本論文以機率抽樣為基礎應用在微陣列資料的基因挑選方法，提出一套三個階段的基因挑選流程。第一階段依據不同基因資料集的特性使用統計學上的t檢定將基因分成三個組別，然後將不重要的組別刪去，作為初步降低特徵維度的工具。第二階段考量到有許多基因是必須共同表現才具有分類重要性的特性，因此使用機率抽樣的概念來產生大量基因子集合，並透過設定門檻值來保留具有分類重要性的基因子集合。第三階段則是使用統計學上的卡方同質性檢定來挑選出最後具有分類重要性的基因，組成基因集合。實驗結果證明，在白血病(Leukemia)、結腸癌(Colon)、淋巴癌(Lymphoma)三個公開的基因資料集上面，我們提出的基因挑選流程是一套簡單、可靠且只要挑出少數幾個重要的基因就具備高分類正確率的基因挑選法。

Microarray technology has become an important tool for biologists in recent years. It can simultaneously measure expression levels of many genes in one experiment. One of the research issues of microarray is to select a set of relevant genes from large number of genes to assist clinical diagnosis. Microarray data features in high dimensional data with relatively small number of samples. That is, it usually contains thousands of genes (sometimes more than ten thousand genes) and less than 100 samples. The characteristic of microarray data renders low accuracy in clinical diagnosis. To counter this problem, many researchers have focused on “gene selection” and “dimension reduction of microarray” in recent years. However, the existing methods are usually very complex and time-consuming.

In this thesis, we propose a novel method for gene selection on microarray data. In the proposed method, we first classify genes into different groups according to their expression levels in the microarray data. Then, we use the probability sampling method to generate a large number of candidate gene subsets. Finally, we use χ2-test for homogeneity to select the relevant genes from candidate gene subsets. The experiment results show that the proposed method is better than the existing methods in terms of classification accuracy and the number of genes selected.

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