DNA 微陣列是在實驗性分子生物學上最新的發展之一，並且開啟了產生分子資訊以表現許多生物系統或臨床興趣之資料集的可能性，而分群技術已被證明能幫助理解基因功能、基因調節、細胞進程以及細胞亞型。研究人員證明出大部分的情況下，多筆基因會構成一種疾病，也就刺激研究者去找出某些基因在某些條件下有相似的表現。大部分的子空間分群模組都依據物件在所有條件或部分條件下的距離來定義其相似性，然而，物件間即使距離很遠也可能有很強烈的相關性。許多已提出的方法，例如：pCluster 和zCluster，即為找出某些基因在某些條件下有一致性表現的子空間分群，然而，這兩個方法都包含很費時的步驟，也就是建構基因對的最大維度集合以及分佈其字首樹每個節點上的基因資訊。因此，在這篇論文中，我們提出一個以大項目集為基礎的分群演算法來改進pCluster 和
zCluster 的缺點。首先，我們避免產生基因對的最大維度集合，我們只建構條件對的最大維度集合以降低處理時間。再來，我們轉換從條件對的最大維度集合中挖掘出最大可能基因集合的任務為挖掘出其大項目集的問題，我們利用了挖掘關聯式法則中大項目集的概念，其中大項目集表示在交易資料中出現次數夠多的項目所組成的集合。由於我們只對擁有夠多基因的子空間分群感興趣，因此我們值得去注意在條件對的最大維度集合中出現夠多次的基因集合；換句話說，我們想從條件對的最大維度集合中找出大項目集，因此我們便可獲得和夠多條件對有關的基因集合。在這一步驟中，我們善用一個有效找出大項目集的資料結構之一的高頻模式樹之修正版本，從條件對的最大維度集合中找出基因的大項目集。因此，我們便可以避免複雜的分佈過程，並且利用高頻模式樹大量地降低搜尋空
間。最後，我們發展一個演算法從搜尋完高頻模式樹之後的基因集合和條件對中建構出最後的分群。由於我們只對夠大並且不屬於任何分群的分群感興趣，因此我們交替地合併或擴大基因集合及條件集合來建構盡可能大的子空間分群以滿足需求。根據模擬的結果，我們可以證明由於前人方法需要建構基因對的最大維度集合，所以我們提出的方法比前人的方法需要較短的處理時間。

DNA Microarrays are one of the latest breakthroughs in experimental molecular biology and have opened the possibility of creating datasets of molecular information to represent many systems of biological or clinical interest. Clustering techniques have been proven to be helpful to understand gene function, gene regulation, cellular processes, and subtypes of cells. Investigations show that more often than not, several genes contribute to a disease, which motivates researchers to identify a subset of genes whose expression levels are similar under a subset of conditions. Most of the subspace clustering models define similarity among different objects by distances over either all or only a subset of the dimensions. However, strong correlations may still exist among a set of objects, even if they are far apart from each other as measured by the distance functions. Many techniques, such as pCluster and zCluster, have been proposed to find subspace clusters with the coherence expression of a subset of genes on a subset of conditions. However, both of them contain the time-consuming steps, which are constructing gene-pair MDSs and distributing the gene information in each node of a prefix tree. Therefore, in this thesis, we propose a Large Itemset-Based Clustering (LISC) algorithm to improve the disadvantages of the pCluster and zCluster algorithms. First, we avoid to construct the gene-pair MDSs. We only construct the condition-pair MDSs to reduce the processing time. Second, we transform the task of mining the possible maximal gene sets into the mining problem of the large itemsets from the condition-pair MDSs. We make use of the concept of the large itemset which is used in mining association rules, where a large itemset is represented as a set of items appearing in a sufficient number of transactions. Since we are only interested in the subspace cluster with gene sets as large as possible, it is desirable to pay attention to those gene sets which have reasonably large support from the condition-pair MDSs. In other words, we want to find the large itemsets from the condition-pair MDSs; therefore, we obtain the gene set with respect to enough condition-pairs. In this step, we efficiently use the revised version of FP-tree structure, which has been shown to be one of the most efficient data structures for mining large itemsets, to find the large itemsets of gene sets from the condition-pair MDSs. Thus, we can avoid the complex distributing operation and reduce the search space dramatically by using the FP-tree structure. Finally, we develop an algorithm to construct the final clusters from the gene set and the condition--pair after searching the FP-tree. Since we are interested in the clusters which are large enough and not belong to any other clusters, we alternately combine or extend the gene sets and the condition sets to construct the interesting subspace clusters as large as possible. From our simulation results, we show that our proposed algorithm needs shorter processing time than those previous proposed algorithms, since they need to construct gene-pair MDSs.

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 DNAMicroarrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Clustering in a DNAMicroarray . . . . . . . . . . . . . . . . . . . . . 2
1.2.1 Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.2 Subspace Clustering . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.3 RelatedWork . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Organization of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2. A Survey of Subspace Cluster Algorithms . . . . . . . . . . . . . . 12
2.1 Biclustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 δ-Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 pCluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 zCluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3. The LISC Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1 Definitions and ProblemStatement . . . . . . . . . . . . . . . . . . . 22
3.2 The Proposed Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2.1 Step 1: Finding Condition–PairMDSs . . . . . . . . . . . . . 24
3.2.2 Step 2: Mining Conditional Pattern Bases . . . . . . . . . . . 26
3.2.3 Step 3: Constructing Subspace Clusters . . . . . . . . . . . . . 37
ii
Page
4. Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.1 Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.2 Experiment Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2.1 Synthetic Data . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2.2 RealMicroarray Datasets . . . . . . . . . . . . . . . . . . . . 52
5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.2 FutureWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

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