Abstract

Data mining has become a key research area in database after Agrawal and Sirkant introduced association rules in data mining and proposed Apriori for mining association. However, most of the works focuses on finding patterns on itemsets, especially associations between items. With the fast development of high technologies and large scale of information collection tools, the need for data mining has gone far beyond association mining. In this thesis, a new framework is established that largely extends the current existing data mining field. While the traditional data mining problems can be viewed as computing itemset lattice, vet another equal important data mining problem is mining circumstance which forms a second lattice: circumstance lattice. In itemset lattice, extensive work is done to introduce constraints in correlations mining and algorithms for computing different useful correlation queries are provided. For the new concept of circumstance mining, a close relationship is set up between computing circumstance lattice and data cube. Several algorithms, including new algorithms and modification of existing data cube algorithms, are given to answer circumstance mining queries. Finally, algorithms for the dual mining on bilattices--from itemset lattice to circumstance lattice and back, or vise versa are presented to compute the Armstrong Basis for a given transaction database.