分群問題在資料庫領域中已經被廣泛地應用，例如生物資訊學。傳統的分群演算法會考慮輸入資料集的所有維度。然而，在高維資料中，有許多維度通常是不相關的。因此，投影分群就被提出來。一個投影叢集包含了資料點的子集C以及使得C中的點之間的距離夠近的維度子集D。目前已經有很多找投影叢集的演算法被提出來了。這之中，大部分可以分為三類：分割法、以密度為基礎法以及階層法。DOC演算法是一個眾所皆知的以密度為基礎法的投影叢集演算法。它使用蒙地卡羅演算法來重複計算找出投影叢集，且定義一個用來計算投影叢集品質的公式。FPC演算法是DOC演算法的延伸版本，它使用挖掘大型項目集的方法來找出投影叢集的維度。找出大型項目集是挖掘關聯式法則的主要目標，而大型項目集指的是一群項目的集合，且這個項目集的發生次數超過給定的門檻值。雖然FPC演算法利用了挖掘大項目集的方法去加快找出投影叢集的速度，但它仍然需要許多的使用者指定參數。此外，在第一步去挑選中心點的時候，FPC演算法使用數次隨機的方式去取得中心點，這個方式需要花費許多時間，而且仍然有可能挑到壞的中心點。再者，如果將每個維度的權重考慮進去的話，計算叢集品質的方式可以更進一步改進。因此，在這篇論文中，我們提出了一個以參數關係為基礎的演算法來改進這些缺點。首先，我們觀察到參數之間的關係，並提出了一個只需要兩個參數的演算法，而非如其他大部份的演算法需要三個參數。接著，我們的演算法利用中位數去挑選中心點，我們只挑選一次中心點，而且接下來找出來的叢集的品質比FPC演算法來的好。最後，我們的品質測量公式考慮了叢集中每一個維度的權重，我們根據每個維度的出現次數給予不同的權重值。這個公式使我們找出來的投影叢集品質比FPC演算法好。它可以避免找出來的投影叢集包含太多不相關的維度。從我們的模擬結果，我們顯示了我們的演算法在執行時間以及分群品質方面比FPC演算法來的好。

The clustering problem has been discussed extensively in the database literature as a tool for many applications, for example, bioinformatics. Traditional clustering algorithms consider all of the dimensions of an input dataset in an attempt to learn as much as possible about each object described. In the high dimensional data, however, many of the dimensions are often irrelevant. Therefore, projected clustering is proposed. A projected cluster is a subset C of data points together with a subset D of dimensions such that the points in C are closely clustered in the subspace of dimensions D. There have been many algorithms proposed to find the projected cluster. Most of them can be divided into three kinds of classification: partitioning, density-based, and hierarchical. The DOC algorithm is one of well-known density-based algorithms for projected clustering. It uses a Monte Carlo algorithm for iteratively computing projected clusters, and proposes a formula to calculate the quality of cluster. The FPC algorithm is an extended version of the DOC algorithm, it uses the mining large itemsets approach to find the dimensions of projected cluster. Finding the large itemsets is the main goal of mining association rules,
where a large itemset is a combination of items whose appearing times in the dataset is greater than a given threshold. Although the FPC algorithm has used the technique of mining large itemsets to speed up finding projected clusters, it still needs many user-specified parameters to work. Moreover, in the first step, to choose the medoid, the FPC algorithm applies a random approach for several times to get the medoid, which takes long time and may still find a bad medoid. Furthermore, the way to calculate the quality of a cluster can be considered in more details, if we take the weight of dimensions into consideration. Therefore, in this thesis, we propose an algorithm which improves those disadvantages. First, we observe that the relationship between parameters, and propose a parameter-relationship-based algorithm that needs only two parameters, instead of three parameters in most of projected clustering algorithms. Next, our algorithm chooses the medoid with the median, we choose the medoid only one time and the quality of our cluster is better than that in the FPC algorithm. Finally, our quality measure formula considers the weight of each dimension of the cluster, and gives different values according to the times of occurrences of dimensions. This formula makes the quality of projected clustering based on our algorithm better than that of the FPC algorithm. It avoids the cluster containing too many irrelevant dimensions. From our simulation results, we show that our algorithm is better than the FPC algorithm,
in term of the execution time and the quality of clustering.

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Analyzing Microarray Data Using Clustering Analysis . . . . . . . . . 8
1.3 Projected Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.5 Organization of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2. A Survey of Algorithms for Projected Clustering . . . . . . . . . . 22
2.1 CLIQUE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2 PROCLUS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3 ORCLUS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4 DOC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.5 FPC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3. A Parameter-Relationship-based Approach . . . . . . . . . . . . . . 35
3.1 The Relationship Between Parameters . . . . . . . . . . . . . . . . . 35
3.2 The Proposed Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3 A Comparison with the FPC Algorithm . . . . . . . . . . . . . . . . 50
4. Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.1 The Performace Model . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2 Experiment Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.2 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

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