TT-Miner: Topology-Transaction Miner for Mining Closed Itemset

Mining frequent closed itemsets (FCIs) from transaction databases is a fundamental problem in many data mining applications. All the enumeration algorithms enumerate FCIs by adding a singleton item to an itemset and then checking whether it is closure. In order to reduce enumerations, we enumerate FCIs by adding an itemset to the existing FCI itemset. To this end, we first analyze a binary relation on the set of itemsets in transaction databases, show co-occurrence relation among items, and prove that the relation is reflexive and transitive. Next, we use the relation to construct a topology for the set of itemsets and prove that all FCIs are included in the topology. Then, we construct a topology-transaction tree (TT-tree) and provide a topology-transaction miner (TT-Miner) algorithm for enumerating FCIs in the TT-tree. Finally, an extensive experimental evaluation on a number of real and synthetic databases shows that the TT-Miner is an efficient and scalable algorithm compared with the previous methods.