微陣列矩陣晶片是一門現今被廣泛使用在許多領域的生物醫學研究，在本文，我們主要是對寡核甘酸微陣列矩陣晶片資料的正規化感興趣。為了比較不同的正規化方法，我們致力於模擬更接近真實寡核甘酸微陣列矩陣晶片的資料。在資料的模擬上，我們主要是根據Li和Wong的模型來進行模擬，並利用階層法來設定模型的參數。最後為了判別正規化方法的好壞，我們模擬了100組資料，並且利用四個判斷準則來做比較。模擬的結果表示，我們所提出的新方法 (LOESS to Average)，一般來說都比其他的正規化方法來的好。 / Microarray technology is now widely used in many areas of biomedical research. In this thesis, we are interested in the normalization for oligonucleotide Microarray data. We aimed to simulate more realistic oligonucleotide microarry data in order to compare different normalization methods. The data simulation was based on Li and Wong's model with a hierarchical setup for parameters. In order to compare normalization methods, 100 data sets were simulated data. The performance of ten normalization methods was assessed based on four comparison criteria. Simulation results suggest that our new proposed normalization method, LOESS to Average, is generally a better method than other normalization methods.

高密度寡核甘酸基因陣列實驗是新的生物技術，可在一個晶片上蒐集到數千至上萬個基因資料，資料處理的過程相當繁複，包括背景訊號的修正、正規化、探針背景的修正及探針組資料的整合，本研究首先將介紹各資料處理步驟。其中正規化的目的是要修正資料中由實驗產生的系統化變異，去除實驗誤差，使資料更為純淨，則後續所做的統計分析才會更為精確。之後再詳細介紹三種正規化方法，包括：尺度調整法、循環平滑調整法及百分位調整法。並將以一組實際資料來說明正規化後的結果。最終採取電腦模擬的方式，以平均四分位距、平均標準差、Diff統計量及離群值的個數這四個量化準則，來研究各正規化方法的效果，以及比較這三種正規化方法的優劣，同時也將探討此四種準則的適當性。 / High-density oligonucleotide array gene experiment is a new biological technology. More than thousands of gene data can be obtained in an array. The data processing includes background correction, normalization, probe specific background correction and summarizing the probe set value into one expression measure. The goal of normalization is to remove the systematic variation induced in the experiment while keeping the biological variation of interest. Using the purified data, one will obtain more accurate conclusions in subsequent statistical analysis. Firstly, we introduce the data processing procedures. Three normalization methods, which include Scaling, Cyclic Loess and Quantile, are explained in detail and illustrated by a real data set. Moreover, a simulation study is conducted to compare the three methods. Four quantities, Mean of IQR, Mean of Standard Deviation, Diff Statistics and Outlier, are proposed for assessment. Not only the performances of the three normalization methods but also the properties of the four proposed criteria are given and studied in this research.

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基因晶片實驗包含了複雜的實驗步驟，在每個步驟都可能因為技術不佳或是人為疏失而產生系統誤差。而「正規化」（Normalization）是一個專業術語，指的就是將系統誤差自資料處理中移除的過程。由於正規化過程在基因晶片的資料處理上佔有非常重要的地位，所以新的正規化方法也不停的被提出。Kerr, Martin, 和Churchill（2000）提出了利用變異數分析模型（ANOVA model）來估計系統誤差的方法；Yang, Dudoit, Luu, and Speed（2001）提出了利用MA圖和Loess非線性函數來消除染劑差異的方法；Kerr, Afshari, Bennett, Bushel, Martinez, Walker, Churchill（2001）提出了結合先前的變異數分析模型和MA圖的新方法；Tsai, Hsueh, Chen（2002）提出了利用Loess非線性函數來估計變異數模型中晶片和基因間的交互作用以及染劑和基因間的交互作用的方法。有鑒於正規化方法眾多，但是每種方法的操作方式和使用上的優、缺點並沒有整合性的介紹和比較，本論文將詳細介紹上述正規化方法，並實際處理TCDD研究實驗的資料。接著利用模擬的資料來計算出三種正規化方法處理前、後的錯誤發現率（False Discovery Rate；FDR）和型二錯誤率（False Negative Rate；FNR）的變化情形，藉此比較三種正規化方法在使用上的優劣。 關鍵字：正規化（Normalization），變異數分析模型（ANOVA model），MA圖，Loess非線性函數，錯誤發現率（False Discovery Rate；FDR），型二錯誤率（False Negative Rate；FNR）

本研究探討高通量染色體捕捉技術 (high-throughput chromosome conformation capture, Hi-C) 實驗所產生的關聯矩陣資料之正規化方法。已知該類實驗主要用來測量染色體之間的空間距離，正規化的目的是移除資料中的系統性偏差，本文主要針對基因特徵所造成之偏差。有別於Hu等人 (2012) 所提出的「局部基因特徵正規化法」(local genome feature normalization, LGF法)，我們所提出的「二次函數正規化法」(quadratic function normalization, QF法) 建立在更為一般化的二次對數模型與負二項分配假設上。本研究透過模擬實驗以及人類淋巴細胞資料 (GSE18199) 來評估QF法的表現，並且與其他方法比較。在模擬實驗中，我們發現當模型正確時，QF法能有效消除偏差。在實例中，當基因特徵偏差被消除後，則染色體之間的相對距離在重複實驗資料之間有更為一致的結果。另一方面，我們發現實驗所採用的限制酶影響關聯矩陣的結果，而且運用這些正規化方法並不能有效消除限制酶造成的偏差。 / Recently, the high-throughput chromosome conformation capture (Hi-C) experiment is developed to explore the three-dimensional structure of genomics. To assess the chromosomal interaction, a contact matrix is produced from a Hi-C experiment. Very often, systematic technical biases appear in the contact matrix and lead to inadequate conclusions. Consequently, data normalization to remove these biases is essential and necessary prior advanced inference. In this research, we propose the so-called quadratic function normalization method, which is a modification of the local genome feature normalization (Hu et al., 2012) by considering a more general model. Simulation studies are conducted to evaluate the proposed method. When the model assumption holds, the proposed method has adequate performance. Further, a Hi-C data set of a human lymphoblastoid cell GSE18199 is employed for a comparison of our method and two existing methods. It’s observed that normalization improves the reproducibility between experimental replicates. However, the effect of normalization is lean in eliminating the bias of restriction enzymes.