近年來，與時間相關的資料探勘(temporal data mining)已經成為重要的議題並且吸引許多相關研究，而時間資料探勘主要是分析時間資料及找出與時間有關的樣式(temporal patterns)。儘管已經有許多被提出來的演算法能夠用來找出與時間相關的樣式，但仍然只能找出對於整個資料庫而言是頻繁出現的樣式(frequent patterns)。因此，T.P. Hong學者等人提出一個新的概念：最新且頻繁出現的樣式(frequent up-to-date patterns)，用來找出從某個最早的時間點到目前的時間點，這段期間內會成為頻繁出現的項目或項目集。T.P. Hong學者等人也提出利用建立UDP-tree演算法及探勘UDP-growth演算法來找出所有最新且頻繁出現的樣式。建立UDP-tree演算法首先先找出長度為1的最新且頻繁出現的樣式，並且得到出現次數及合理的生命週期；之後，建立UDP-tree；再來，利用UDP-growth演算法探勘出長度為2以上之最新且頻繁出現的樣式，並且得到出現次數及合理的生命週期。然而，建立UDP-tree演算法及挖掘UDP-growth演算法在找出所有最新且頻繁出現的樣式時會有一些問題：首先，當想找出長度為k(k≥1)之最新且頻繁出現的樣式時，他們需要花很多時間在檢查候選人是否在相對應的生命週期裡會成為最新且頻繁出現的樣式。因此，UDP演算法浪費很多執行時間。再者，當檢查長度為k(k≥3)之候選人是否會成為最新且頻繁出現的樣式時，UDP演算法需要將所有的候選人都帶入公式檢查是否滿足條件。因此，也會浪費許多執行時間。第三點，利用UDP演算法得到的結果有些是不合理的。為了避免這些問題以及改善效能，我們提出一個以最早出現時間點包含兩個刪除的策略(pruning strategy)適用於建立樹的演算法與探勘演算法中的方法。第一個刪除的策略適用於當在找出所有長度為k(k≥1)的候選人是否會成為最新且頻繁出現的樣式時，利用這個策略能夠減少許多執行時間；而第二個刪除的策略則是適用於當在找出所有長度為k(k≥3)的候選人是否會成為最新且頻繁出現的樣式時，這個策略能夠刪減掉許多不可能會成為最新且頻繁出現的候選人以降低執行時間；最後，我們也提出能夠避免得到不合理之結果的方法。因此，我們的方法會比UDP演算法來的更快速且不會得到不合理的結果。根據我們的模擬結果，顯示出我們的方法比UDP演算法來的更有效率。

　　Recently, temporal data mining has been considered as an important topic attracting many researchers. Analyzing temporal data and discovering temporal patterns are the main concerns in temporal data mining. Although we can discover temporal patterns by these proposed algorithms, we only derive frequent patterns in the whole database. Therefore, a new concept of up-to-date patterns is proposed by Hong et al., which only cares about the items or itemsets that are frequent for a flexible period of time from the current time to the oldest past time. Hong et al. also propose the UDP-tree construction algorithm and the UDP-growth mining algorithm to find out all frequent up-to-date patterns. The UDP-tree construction algorithm first derives frequent up-to-date 1-patterns with their frequency and valid lifetime. Second, it constructs an UDP-tree. Then, the UDP-growth mining algorithm is proposed to find out up-to-date k-patterns (k ≥ 2) from the UDP-tree. However, the UDP-tree construction algorithm and the UDP-growth mining algorithm have some problems for finding all frequent up-to-date patterns. First, when they derive frequent up-to-date k-patterns (k ≥ 1), they need many times to check whether the item or itemset is frequent with corresponding lifetime or not. That is, the UDP algorithm needs long execution time for checking whether the item or itemset is frequent up-to-date pattern or not. Second, when checking whether the candidate k-pattern (k ≥ 3) is frequent up-to-date k-pattern or not, the UDP algorithm may check all candidate up-to-date k-patterns by the formula. It also wastes execution time. Third, some of the results which derived from the UDP algorithm are unreasonable. Therefore, to avoid these problems and improve the performance, we propose an Earliest-Time-Point approach to use two pruning strategies in the process of the tree construction algorithm and the mining algorithm. The first pruning strategy is applied to check all items or itemsets are frequent up-to-date k-patterns (k ≥ 1) or not. This strategy could reduce the execution time. The second pruning strategy is used for checking whether the itemsets will be frequent up-to-date k-patterns (k ≥ 3) or not. This strategy may prune some candidates to continue to be checked. That is, we reduce the number of candidates. Third, we propose an extension of the formula for deciding the valid appearance time of the pattern to avoid getting unreasonable results. Thus, our approach is faster than the UDP algorithm to find all frequent up-to-date patterns. Moreover, our approach can avoid getting unreasonable results. From our simulation results, we show that our Earliest-Time-Point approach is more efficient than the UDP algorithm.

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
　1.1 Mining Association Rules . . . . . . . . . . . . . . . . . . . . . . . . . 1
　1.2 Temporal Data Mining . . . . . . . . . . . . . . . . . . . . . . . . . . 2
　　1.2.1 Pattern Discovery Technique for Temporal Data . . . . . . . . 3
　　1.2.2 Challenges for Temporal Data Mining . . . . . . . . . . . . . . 4
　　1.2.3 The Concept of Up-to-Date Patterns . . . . . . . . . . . . . . 5
　1.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
　1.4 Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
　1.5 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
　1.6 Organization of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . 12
2. A Survey of Data Mining Algorithms . . . . . . . . . . . . . . . . . 13
　2.1 The Apriori Algorithm for Association Rules Mining . . . . . . . . . 14
　2.2 The FP-tree Structure and the FP-growth Algorithm . . . . . . . . . 16
　2.3 The FUFP-tree Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 17
　2.4 The UDP-Tree Construction Algorithm and the UDP-Growth Mining Algorithm … 19
　　2.4.1 Up-to-Date Patterns . . . . . . . . . . . . . . . . . . . . . . . 19
　　2.4.2 The UDP-Tree Construction Algorithm . . . . . . . . . . . . . 20
　　　2.4.2.1 The Construction Algorithm . . . . . . . . . . . . . . 20
　　2.4.3 The UDP-Growth Mining Algorithm . . . . . . . . . . . . . . 23
　　　2.4.3.1 The Mining Algorithm . . . . . . . . . . . . . . . . . 23
3. The Earliest-Time-Point Approach . . . . . . . . . . . . . . . . . . . 26
　3.1 Defi nitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
　3.2 The Tree Construction Algorithm with the Pruning Strategy . . . . . 28
　　3.2.1 Step 1: Scan the Database to Find Out the Timelist and the Count of Each Item … 29
　　3.2.2 Step 2: Find the Frequent 1-Patterns (L1) and Short-lifetime 1-Itemsets (SL1) … 31
　　3.2.3 Step 3: Examine the Items which are Stored in SL1 to Find Up-to-date 1-Patterns with Their Actual Lifetime…32
　　3.2.4 Step 4: Create the Header Table from Up-to-date 1-Patterns . 37
　　3.2.5 Step 5: Retain Items from Original Database by the Header Table within Their Corresponding Lifetime… 37
　　3.2.6 Step 6: Construct the Tree . . . . . . . . . . . . . . . . . . . . 39
　3.3 The Mining Algorithm with the Pruning Strategy . . . . . . . . . . . 43
　　3.3.1 Step 1: Deal with the Items in the Header Table One by One and Bottom-up … 44
　　3.3.2 Step 2: Form a Conditional Tree of Item I . . . . . . . . . . . 44
　　3.3.3 Step 3: Generate the Candidate Up-to-Date 2-Patterns . . . . 44
　　3.3.4 Step 4: Retain the Up-to-Date 2-Patterns within Their Corresponding Lifetime into L2 … 45
　　3.3.5 Step 5: Find Up-to-Date k-Patterns (k ≥ 3) within Their Corresponding Lifetime into Lk … 53
　3.4 Extension of the Formula . . . . . . . . . . . . . . . . . . . . . . . . . 56
　3.5 A Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4. Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
　4.1 The Performance Model . . . . . . . . . . . . . . . . . . . . . . . . . 63
　4.2 Experiment Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
　5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
　5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

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