在資料探勘中找出頻繁項目集對於產生關聯規則而言，是一個非常關鍵的步驟。若最小支持度被設定在一個非常小的數值，或者被處理的交易資料庫的交易項目非常多的時候，頻繁項目集的數目常可能會相當巨大，因此在過去有一些精簡表示的方法被提出，以有效紀錄頻繁項目集。例如，最大項目集的方法用保存頻繁與非頻繁項目集間的分隔線方式，以減少保存頻繁項目集所需的資訊。此種方法可回復所有頻繁項目集，但卻無法得知這些頻繁項目集的支持度。相較於最大項目集，封閉項目集的做法則可以同時回復頻繁項目集及其支持度，但所需之保存數量較多。因此在本論文中，我們提出一種介於最大項目集和封閉項目集之間的近似表示方式，其能正確回復完整的頻繁項目集，並能計算出這些頻繁項目集的近似支持度。我們也提出並推導了這個近似表示法的一些特性。此外我們利用兩種不同的資料結構來組織頻繁項目集並分別提出了兩個不同的方法來求其近似表示。第一個方法採用前綴樹的結構，而第二個方法則使用了流量網路的方式。最後我們也針對不同的資料集及變換多個參數值來驗證這兩個方法的效能，而實驗結果也顯示我們所提的方法和封閉項目集相比，確實可以達到較佳的壓縮比率。

In data mining, finding frequent itemsets is a critical step for deriving association rules. The number of frequent itemsets may be huge if the minimum support is set at a low value or if the number of items in a transaction database is large. In the past, some approaches were proposed to record frequent itemsets with compact representation. For example, the approach of maximal itemsets keeps a borderline composed of the maximal itemsets, which separate frequent itemsets from non-frequent ones. It can recover all the frequent itemsets, but cannot get their real supports back. On the contrary, the approach of closed itemsets can correctly recover each frequent itemset and its support. In the thesis, we propose approximate representation of derived frequent itemsets, which lies between maximal itemsets and closed itemsets. It can correctly get back all the derived itemsets and can calculate their approximate supports. Some properties with the representation are also derived. Two methods are then proposed to get the approximate representation by organizing frequent itemsets with two special data structures. The first one adopts a prefix tree, and the other utilizes a flow network. Finally, some experiments on different datasets and with a variety of parameter values are conducted to show the performance of the two methods. The results reflect the proposed methods have better compact rates than the closed itemsets.

誌謝 + i
中文摘要 + iii
ABSTRACT + iv
Chapter 1 INTRODUCTION + 1
1.1. Background and Motivation + 1
1.2. Thesis Organization + 4
Chapter 2 REVIEW OF RELATED WORKS + 5
2.1. Maximal Itemsets + 5
2.2. Closed Itemsets + 6
2.3. Other Concepts + 8
Chapter 3 THE METHOD BASED ON PREFIX TREE + 11
3.1. Term Definitions + 11
3.2. Problem Statement + 18
3.3. Proposed Concepts and Methods + 22
3.4. Experiments + 38
3.4.1. Experimental Datasets and Criteria + 38
3.4.2. Experimental Results + 39
Chapter 4 THE METHOD BASED ON FLOW NETWORK + 50
4.1. Term Definitions + 50
4.1.1. Flow Network + 51
4.1.2. Lattice of Frequent Itemsets + 52
4.1.3. Simple Flow Network of Frequent Itemsets + 54
4.1.4. Complex Flow Network of Frequent Itemsets + 57
4.2. Preliminary Observations and Problem Statement + 59
4.3. Proposed Concepts and Methods + 65
4.3.1. Setting Capacities of Correcting Edge Pairs + 65
4.3.2. Dividing the itemsets at a Level as Intervals + 69
4.4. Experiments + 77
4.4.1. Experimental Datasets and Criteria + 77
4.4.2. Experimental Results + 79
Chapter 5 DISCUSSION AND CONCLUSION + 85
5.1. Comparison of the Two Proposed Methods + 85
5.2. Comparison of the Two Methods with Closed Sets and Free Sets + 86
5.3. CONCLUSION AND FUTURE WORK + 87
REFERENCES + 88

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