Closed frequent itemsets mining and structuring association rules based on Q-analysis

Association rule discovering is one of the most important procedures in data mining. Lattice theory paradigm has been successfully used for the association rule mining. In particular, the theoretical foundation based on the field of Galois lattice has been used in the design of efficient algorithm for mining the frequent itemsets in transactional database. In this paper we describe a formal framework for the problem of mining closed frequent itemsets, where theoretical foundation is based on the algebraic topology. By means of Q-analysis and according to intrinsic q-values, an approximative closed frequent itemsets can be extracted. In data mining process, a large number of association rules are discovered. In this paper we also show how the algebraic topology-theoretic framework can be used to organize association rules by means of metarules.