Finding Association Rules is a classical data mining task. The most critical part of Association Rules Mining is about finding the frequent itemsets in the database. Since the introduction of the famouse Apriori algorithm [14], many others have been proposed to find the frequent itemsets. Among all the algorithms, the approach of mining closed itemsets has arisen a lot of interests in data mining community, because the closed itemsets are the condensed representation of all the frequent itemsets. The algorithms taking this approach include TITANIC [8], CLOSET+ [6], DCI-Closed [4], FCI-Stream [3], GC-Tree [15], etc. While the above algorithms are trying to improve the performance of finding the Intents of Formal Concepts (in anther word, the closed itemsets), they missed another important information: the Extents of Formal Concepts. In this paper, we propose an online algorithm, TGC-Tree, which is adapted from the GC-Tree algorithm [15], that could be used to trace the closed itemsets(Intents) and the corresponding transaction sets(Extents) simultaneously in an incremental way.
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