由於人類基因體計畫，生物資料如微陣列資料等被大量地產生出來。既然這些資料的數量非常龐大，資料探勘的技術便可以用來幫助生物學家有效率地分析這些資料。對微陣列資料來說，同時對列（如基因）及行（如實驗條件）進行分群的雙向分群技術，已被證明在尋找令人感興趣的現象上有很大的價值。目前已有數種不同的雙向分群種類被提出。其中針對要找出一致性數值的雙向分群問題，大部份前人的方法都需要對微陣列資料中每兩個基因計算其最大維度集。但在微陣列資料中，基因的個數是遠遠大於實驗條件的個數。對每兩個基因進行計算的這個步驟是沒有效率的。在另一方面，針對要找出一致性進展的雙向分群問題，之前的學者提出了Co-gclustering這個方法。它可以同時地找出包含規則模式及相反規則模式的雙向分群。然而，此方法的時間複雜度會隨著實驗條件的個數而呈指數成長，降低了此方法的效率。因此，在此博士論文中，為了要有效率地解決微陣列資料庫中雙向分群的問題，首先，我們提出了一個條件列舉樹的方法（Condition-Enumeration Tree，CE-Tree），來探勘一致性數值的雙向分群。接著，我們提出了一個上下位元樣式的方法（Up-Down Bit Pattern，UDB），來探勘一致性進展的雙向分群。在我們提出的第一個方法CE-Tree中，為了探勘雙向分群，我們並不對每兩個基因計算其最大維度集，而是只對每兩個條件計算其最大維度集。為了有效率地找出雙向分群，我們使用了一種特殊的全域深度優先區域廣度優先方法，來生成我們提出的CE-Tree。從在真實資料上的實驗結果來看，我們顯示出CE-Tree方法可以比前人提出的方法更有效率地找出雙向分群。在我們提出的第二個方法UDB中，我們利用上下位元樣式來記錄每個基因在哪些實驗條件組合下，會呈現上升或下降的規則現象。接著，我們在這些上下位元樣式上，使用了位元運算及一個啟發式的概念，來有效率地找出分群結果。和之前學者提出的Co-gclustering方法比較起來，我們的UDB方法將時間複雜度從指數成長降到了多項式成長。從在真實資料上的實驗結果來看，我們顯示出UDB方法在效率上會比Co-gclustering方法更好。

Because of the Human Genome Project, enormous quantities of biological data, e.g., microarray data, are generated. Since the amount of biological data is very large, data mining techniques can be used to help biologists efficiently analyze the biological data. For microarray data, biclustering, which performs simulataneous clustering of rows (e.g., genes) and columns (e.g., conditions), has proved of great value for finding interesting patterns. There were several types of biclusters proposed. To mine biclusters with coherent values, most of the previous methods need to compute Maximum Dimension Sets (MDSs) for every two genes in the microarray data. Since the number of genes is far larger than the number of conditions, this step is inefficient. On the other hand, to mine biclusters with coherent evolutions, the Co-gclustering method was proposed which could simultaneously find biclusters with both coregulated and negative-coregulated patterns. However, its time complexity is exponential to the number of conditions, which is not efficient. Therefore, in this dissertation, to efficiently solve the problem of biclustering for microarray databases, first, we propose a Condition Enumeration Tree (CE-Tree) method which mines biclusters with coherent values. Second, we propose an Up-Down Bit Pattern (UDB) method which mines biclusters with coherent evolutions. In the first proposed method, CE-Tree, to mine biclusters, instead of generating MDSs for every two genes, we generate only MDSs for every two conditions. Then, we expand the CE-Tree in a special local breadth-first within global depth-first manner to efficiently find the clustering result. From the experimental results on real data, we have shown that the CE-Tree method could mine biclusters more efficiently than several previous methods. In the second proposed method, UDB, we utilize up-down bit patterns to record the condition pairs where one gene is upregulated or downregulated. Then, we utilize bit operations and apply a heuristic idea on these up-down bit patterns to efficiently find the clustering result. As compared to the Co-gclustering method, the UDB method reduces the time complexity from exponential time to polynomial time. From the experimental results on real data, we have shown that the UDB method is more efficient than the Co-gclustering method.

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Computational Biology . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Clustering forMicroarray Databases . . . . . . . . . . . . . . . . . . 3
1.3 RelatedWork of Biclustering . . . . . . . . . . . . . . . . . . . . . . . 11
1.4 Motivations and Contributions . . . . . . . . . . . . . . . . . . . . . . 14
1.4.1 A Condition-Enumeration Tree Method of Biclustering with
Coherent Values . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.4.2 An Up-Down Bit Pattern Method of Biclustering with Coherent
Evolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.5 Organization of the Dissertation . . . . . . . . . . . . . . . . . . . . . 18
2. A Survey of Biclustering Methods . . . . . . . . . . . . . . . . . . . 19
2.1 Methods of Biclustering with Coherent Values . . . . . . . . . . . . . 19
2.1.1 Cheng and Church’s Method . . . . . . . . . . . . . . . . . . . 19
2.1.2 The pClustering Method . . . . . . . . . . . . . . . . . . . . . 21
2.1.3 The zCluster Method . . . . . . . . . . . . . . . . . . . . . . . 25
2.1.4 TheMicroCluster Method . . . . . . . . . . . . . . . . . . . . 28
2.2 Methods of Biclustering with Coherent Evolutions . . . . . . . . . . . 30
2.2.1 The BiModule Method . . . . . . . . . . . . . . . . . . . . . . 30
2.2.2 The OP-Cluster Method . . . . . . . . . . . . . . . . . . . . . 33
2.2.3 Cheung et al.’s Method . . . . . . . . . . . . . . . . . . . . . . 34
2.2.4 The Co-gclustering Method . . . . . . . . . . . . . . . . . . . 35
3. A Condition-Enumeration Tree Method of Biclustering with Coherent
Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.1 A Condition-Enumeration TreeMethod . . . . . . . . . . . . . . . . . 40
3.1.1 Step 1: Generating Condition-PairMDSs . . . . . . . . . . . . 40
3.1.2 Step 2: The Pruning Step . . . . . . . . . . . . . . . . . . . . 44
3.1.3 Step 3: The Joining Step . . . . . . . . . . . . . . . . . . . . . 46
3.1.3.1 The Condition Enumeration Tree . . . . . . . . . . . 46
3.1.3.2 The ⊗ Operation . . . . . . . . . . . . . . . . . . . . 50
3.1.3.3 The Bounding Techniques . . . . . . . . . . . . . . . 55
3.1.4 Improving the Joining Process . . . . . . . . . . . . . . . . . . 60
3.1.4.1 The Signature Table . . . . . . . . . . . . . . . . . . 61
3.1.4.2 The New Joining Process . . . . . . . . . . . . . . . 65
3.2 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.2.1 Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . 68
3.2.2 Accuracy of the CE-TreeMethod . . . . . . . . . . . . . . . . 70
3.2.3 Efficiency of the CE-TreeMethod . . . . . . . . . . . . . . . . 72
3.2.3.1 Generating Object-PairMDSs . . . . . . . . . . . . . 72
3.2.3.2 TheMicroCluster Method . . . . . . . . . . . . . . . 75
3.2.4 Discussion on pClusters fromReal Data . . . . . . . . . . . . 78
3.2.5 Efficiency of Pruning and Bounding Techniques . . . . . . . . 82
3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4. An Up-Down Bit Pattern Method of Biclustering with Coherent
Evolutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.1 An Up-Down Bit PatternMethod . . . . . . . . . . . . . . . . . . . . 85
4.1.1 Step 1: Determining Up-Down Bit Patterns . . . . . . . . . . 86
4.1.2 Step 2: Clustering Genes Based on Up-Down Bit Patterns . . 89
4.1.3 An Improved Version of Step 2 . . . . . . . . . . . . . . . . . 93
4.1.4 Step 3: Post-processing the Clusters . . . . . . . . . . . . . . 96
4.2 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.2.1 Simulation Results on Synthetic Data Sets . . . . . . . . . . . 99
4.2.2 Experimental Results on Real Data Sets . . . . . . . . . . . . 104
4.3 A Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.2 The Future Research Direction . . . . . . . . . . . . . . . . . . . . . 112
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114

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