對於現實生活中，在資料串流(data stream)中對權重頻繁樣式探勘(Weighted frequent pattern mining)是一個非常重要領域，比如說，超市。其中探勘最大權重頻繁樣式(Weighted maximal frequent pattern)也是一個重要議題。一個最大權重頻繁樣式是指其不是其他權重頻繁樣式的子集且同時它的權重值是大於或等於門檻值。但很多之前方法是沒辦法使用在權重頻繁樣式探勘上，因為它們大部份採用了anti-monotone property。這個特性是說，即使有一個樣式Y的子集X,此子集X不是weighted frequent pattern，但是但樣式Y卻仍可能是weighted frequent pattern。此外，由於資料串流具有速度快、連續性、沒有限制性與即時性等特性，因此我們只可掃描資料庫一次。所以，之前在傳統資料庫探勘之演算法是不適用於資料串流。再則，很多應用都著重於距離現在時間較近的資料串流，而移動式視窗(sliding window model) 正是處理最近資料串流的模式。為了在移動式視窗中找出最大權重頻繁樣式，Ryu學者等人提出了WMFP-SW演算法。WMFP-SW演算法使用FP-tree去探勘最大權重頻繁樣式。它還使用了最大權重來減少候補樣式。但是它在視窗移動的時候花了太多時間。因為當新的交易資料到達的時候，WMFP-SW演算法必須重建整個FP-tree。除此之外，WMFP-SW演算法可能會有missing case。為了解決這些問題，在這個論文中，基於移動式視窗為模型的演算法，我們提出Weighted-Order-Based Lattice演算法。我們使用晶格(lattice)來儲存交易的資料。晶格資料結構會儲存父節點與子節點之間的關係。在每一個晶格節點，我們會儲存項目集與數量。當新的交易資料到達的時候，我們根據交易特性分成五種集合關係 : (1) equivalent、(2) subset、(3) intersection、(4) empty set與 (5) superset。根據這五種集合關係，我們要新增或更新資料的時候會更有效率。此外，我們使用global maximal weight pruning方式 與local maximal weight pruning 方式去避免不必要的運算。從效能成果研讀，我們顯示了在真實資料與在模擬資料之測試，我們的Weighted-Order-Based Lattice演算法都比WMFP-SW演算法更有效率。

Weighted frequent pattern mining in data streams is an important field for the real world, such as the supermarket. Moreover, mining the weighted maximal frequent patterns is also an important issue. The weighted maximal frequent pattern is the pattern which is not the subset of any other pattern and the weighted support is larger than the threshold. However, many previous Apriori-like algorithms cannot be used in weighted frequent pattern mining. The reason is that even through a subset X of a pattern Y is not a weighted frequent pattern, the pattern Y may be a weighted frequent pattern. Besides, because data streams are continuous, high speed, unbounded, and real time, we can only scan once for the data streams. Therefore, the previous algorithms in the traditional databases are not suitable for the data streams. Furthermore, many applications are interested in the recent data streams, and the sliding window is the model which deals with the most recent data streams. In order to solve mining weighted maximal frequent patterns based on the sliding window model, Ryu et al. propose the WMFP-SW algorithm. The WMFP-SW algorithm uses the FP-tree to mine the weighted maximal frequent patterns. It also uses maximal weight to prune the patterns. But it takes long time in mining the weighted maximal frequent patterns. Because when the new transaction comes, the WMFP-SW algorithm always has to reconstruct the FP-tree. Moreover, the WMFP-SW algorithm may have a missing case. To solve those problems, in this thesis, we propose the Weighted-Order-Based Lattice algorithm based on the sliding window model. We use the lattice structure to store the information of the transactions. The structure of the lattice stores the relationship between the child node and the father node. In each node, we record the itemset and the count. When the new transaction comes, we consider five relations: (1) equivalent, (2) subset, (3) intersection, (4) empty set, (5) superset. With those five relations, we can add the new transactions and update the support efficiently. Moreover, we use global maximal weight pruning strategy and local maximal weight pruning strategy to avoid generating invalid candidate patterns. From the the performance study, including the real data and synthetic data, we show that theWeighted-Order-Based Lattice algorithm provides better performance than the WMFP-SW algorithm both in the case of real data and the case of simulation in both cases.

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Data Stream Mining . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.1 Window Models in Data Streams . . . . . . . . . . . . . . . . 2
1.2 Mining Weighted Maximal Frequent Itemsets . . . . . . . . . . . . . . 4
1.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.5 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.6 Organization of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . 12
2. A Survey of Algorithms for Mining Weighed Frequent Patterns . 13
2.1 The MWFIM Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 The WMFP-SW Algorithm . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.1 Data Structures for WMFP-SW . . . . . . . . . . . . . . . . . 15
2.2.2 Pruning Patterns by MaxW . . . . . . . . . . . . . . . . . . . 19
2.2.3 Pruning Patterns in Single-Path . . . . . . . . . . . . . . . . . 20
2.3 The MWS Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4 The Set-Checking Algorithm . . . . . . . . . . . . . . . . . . . . . . . 22
2.4.1 Data structure . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4.2 The Set-Checking Algorithm . . . . . . . . . . . . . . . . . . . 22
3. A Weight-Order-Based Lattice Algorithm . . . . . . . . . . . . . . . 26
3.1 Data Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2 Our Proposed Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.1 Data Initialization . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.2 The Pruning Strategy . . . . . . . . . . . . . . . . . . . . . . 31
3.2.3 Data Deletion . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2.4 Data Insertion . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2.5 A Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4. Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.1 The Performance Model . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.2 Experiment Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2.1 Real Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2.2 Simulation Data . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

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