Structures of frequent itemsets and classifying structures of association rule set by order relations. (10th April 2015) - Tran, Anh; Truong, Tin; Le, Bac
This paper shows a mathematical foundation for almost important features in the problem of discovering knowledge by association rules. The sets of itemsets and association rules are partitioned into disjoint classes by two appropriate equivalence relations based on closures. The structure and unique representation of frequent itemsets are figured out through their generators and corresponding eliminable itemsets. Due to this structure, each equivalence rule class is split into different sets of basic and consequence rules according to an order relation. Indeed, the basic set comprises minimal elements (basic rules) whose forms are explicitly showed. Then, we propose operators to non-repeatedly deduce all consequence rules by adding, deleting or moving appropriate eliminable itemsets in both sides of basic rules. Further, we show that mining association rules based on a new order relation, min relation, is better than four other ones in terms of reductions in the time to extract basic rules, their cardinalities and rule lengths. These theoretical results are proven to be reliable. Experimental study on many benchmark databases shows the efficiency of the corresponding algorithms. Our approach (e.g., the partitions of the frequent itemset and association rule sets) is suitable to deal with big data because it can be exploited in parallel and distributed environment.