資料分類(Classification)是在資料挖掘(Data Mining)中重要技術之一。此技術已廣泛地應用在生物資訊上，例如，疾病診斷。近來，資料分類的技術已被使用於微陣列(Microarray)資料集，其中一個微陣列是生物資訊研究基因表現(Gene Expression)程度的一個好用的工具。在微陣列資料集的資料分類問題部份，我們考慮兩個生物資料集，其為對給定相同的測試資料集有兩極化反應的相異類別。基本上，分類過程包含了兩階段：(1)訓練階段，以及(2)測試階段。訓練階段的目的是找出這兩個資料集中各具代表的浮現樣式(Emerging Patterns，EPs)，其中EP是滿足某些條件從一個資料集到另一個資料集的成長率的項目集。注意成長率代表兩個資料集的差異程度。在訓練階段之後，把每個資料集收集到的EP視為一個分類器。在測試階段中，測試的樣本將會依照一個近似函數的評估結果預測其將會被分配到哪個資料集，而近似函數是把成長率和support值列入考量。評估分類的準則是精確度。很明顯地，一個分類器的精確度愈高，其效能愈好。因此，一些以浮現樣式為基礎的分類器，如EJEP和NEP的方法，已被提出來達到這個目的。EJEP方法只考慮成長率為無窮大的項目集，因為它認為高成長率可以導致高精確度。然而，EJEP方法不能保留一些有用的EP，其成長率非常大但不是無窮大。在另一方面，真實世界的資料總是參雜雜質。NEP方法考慮雜質而且提供了比EJEP方法更高的精確度。然而，它仍然可能會忽略了某些成長率高的項目集，而可能造成低的精確度。因此，在這篇論文中，我們提出一個高成長率浮現樣式(High Growth-rate EP，HGEP)的方法來改進EJEP和NEP方法的缺點。除了考慮EJEP方法中具有無窮大成長率的項目集與NEP方法中的雜質樣式，我們的HGEP方法考慮當成長率是有限的項目集，其成長率大於它所有子集的成長率。如此一來，高成長率的項目集導致高的相似度，而高的相似度可預測測試資料集到正確的類別。因此，我們的HGEP可以提供高的精確度。在我們的效能分析中，我們使用數個真實資料集去評估它們的平均精確度。此外，我們也做了模擬測試。從實驗結果中，我們顯示出我們方法的平均精確度比NEP方法來得好。

Data classification is one of important techniques in data mining. This technique has
been applied widely in many applications, e.g., disease diagnosis. Recently, the data
classification technique has been be used for microarray datasets, where a microarray
is a very good tool to study the gene expression levels in Bioinformatics. In the
part of data classification problem for microarray datasets, we consider two biology
datasets which reflect two extreme different classes for the given same sets of tests.
Basically, the classification process contains two phases: (1) the training phase, and
(2) the testing phase. The propose of the training phase is to find the representative
Emerging Patterns (EPs) in each of these two datasets, where an EP is an itemset
which satisfies some conditions of the growth rate from one dataset to another dataset.
Note that the growth rate represents the differences between these two datasets. After
the training phase, we take the collections of EPs in each dataset as a classifier. A
test sample in the testing phase will be predicted to one of the two datasets based on
the result of a similarity function, which takes the growth rate and the support into
consideration. The evaluating criteria of a classifier is the accuracy. Obviously, the
higher the accuracy of a classifier is, the better the performance is. Therefore, several
EP-based classifiers, e.g., the EJEP and the NEP strategies, have been proposed to
achieve this goal. The EJEP strategy considers only those itemsets whose growth
rates are infinite, since it claims that the high growth rates may result in the high
accuracy. However, the EJEP strategy will not keep those useful EPs whose growth
rates are very high but not infinite. On the other hand, the real-world data always
contains noises. The NEP strategy considers noises and provides the higher accuracy
than the EJEP strategy. However, it still may miss some itemsets with high growth
rates, which may result in the low accuracy. Therefore, in this thesis, we propose
a High Growth-rate EP (HGEP) strategy to improve the disadvantages of the NEP
and the EJEP strategies. In addition to considering itemsets whose growth rates
are infinite in the EJEP strategy and noise patterns in the NEP strategy, our HGEP
strategy considers those itemsets which have the growth rate higher than all its proper
subsets when the growth rates are finite. In this way, the itemsets with high growth
rates could result in high similarity, and the high similarity predicts the sets of tests
into the correct class. Therefore, our HGEP can provide high accuracy. In our
performance study, we use several real datasets to evaluate the average accuracy
of them. Moreover, we also do simulation study of increasing noises. From the
experiment results, we show that the average accuracy of our HGEP strategy is
higher than that of the NEP strategy.

TABLE OF CONTENTS
Page
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Microarrays in Bioinformatics . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Disease Diagnosis and Data mining . . . . . . . . . . . . . . . . . . . 2
1.3 Emerging Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Emerging Patterns and EP-based Classifiers . . . . . . . . . . . . . . 7
1.4.1 Strategies of Two-Class Classification . . . . . . . . . . . . . . 7
1.4.2 EP-based Classifiers . . . . . . . . . . . . . . . . . . . . . . . 9
1.5 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.6 Organization of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2. A Survey of EP-based Strategies . . . . . . . . . . . . . . . . . . . . 15
2.1 Strategies for Mining Emerging Patterns . . . . . . . . . . . . . . . . 15
2.1.1 Emerging Pattern . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.2 Essential Jumping Emerging Pattern . . . . . . . . . . . . . . 17
2.1.3 Noise-tolerant Emerging Pattern . . . . . . . . . . . . . . . . . 20
2.2 Classifiers Based on Emerging Patterns . . . . . . . . . . . . . . . . . 21
2.2.1 Classification by Aggregating Emerging Patterns . . . . . . . . 22
2.2.2 Jumping Emerging Pattern-Classifier . . . . . . . . . . . . . . 22
2.2.3 Prediction by Collective Likelihood of Emerging Patterns . . . 23
3. The HGEP Classifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1 The High Growth Rate Emerging Pattern . . . . . . . . . . . . . . . 25
3.2 The Contrast Pattern Tree Structure . . . . . . . . . . . . . . . . . . 29
3.2.1 The Ordered List . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2.2 The Contrast Pattern Tree (CP-tree) . . . . . . . . . . . . . . 30
3.2.3 The Construction of the Contrast Pattern Tree . . . . . . . . 33
3.2.4 The Difference Between CP-trees and FP-trees . . . . . . . . . 36
3.3 The Mining HGEPs Process . . . . . . . . . . . . . . . . . . . . . . . 37
3.3.1 The Merging Process . . . . . . . . . . . . . . . . . . . . . . . 37
3.3.2 Algorithms for Mining HGEPs . . . . . . . . . . . . . . . . . . 39
4. Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.1 The Real Microarray Datasets . . . . . . . . . . . . . . . . . . . . . . 49
4.2 Experiment Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.2 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

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