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The goal of data mining is to discover important associations among items such that the presence of some items in a transaction will imply the presence of some other items. To achieve this purpose, Agrawal and his co-workers proposed several mining algorithms based on the concept of large itemsets to find association rules in transaction data (Agrawal et al., 1993a) (Agrawal et al., 1993b) (Agrawal & Srikant, 1994) (Agrawal & Srikant, 1995). They divided the mining process into two phases. In the first phase, frequent (large) itemsets are found based on the counts by scanning the transaction data. In the second phase, association rules were induced from the large itemsets found in the first phase. After that, several other approaches were also proposed (Fukuda et al., 1996) (Han & Fu, 1995) (Mannila et al., 1994) (Park et al., 1997) (Srikant & Agrawal, 1996) (Han et al., 2000) (Li et al., 2003). Many of the above algorithms for mining association rules from transactions were executed in level-wise processes. That is, itemsets containing single items were processed first, then itemsets with two items were processed, then the process was repeated, continuously adding one more item each time, until some criteria were met. These algorithms usually considered the database size static and focused on batch mining. In real-world applications, however, new records are usually inserted into databases, and designing a mining algorithm that can maintain association rules as a database grows is thus critically important. When new records are added to databases, the original association rules may become invalid, or new implicitly valid rules may appear in the resulting updated databases (Cheung et al., 1996) (Cheung et al., 1997) (Lin & Lee, 1998) (Sarda & Srinivas, 1998) (Zhang, 1999). In these situations, conventional batch-mining algorithms must re-process the entire updated databases to find final association rules. Cheung and his co-workers thus proposed an incremental mining algorithm, called FUP (Fast UPdate algorithm) (Cheung et al., 1996), for incrementally maintaining mined association rules and avoiding the shortcomings mentioned above. The FUP algorithm modified the Apriori mining algorithm (Agrawal & Srikant, 1994) and adopted the pruning techniques used in the DHP (Direct Hashing and Pruning) algorithm (Park et al., 1997). It first calculated large itemsets mainly from newly O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg

Mining Multiple-level Association Rules Based on Pre-large Concepts