Restructuring Iceberg Lattice For Multilevel Analysis

We introduce the hierarchy called MLIL for multilevel iceberg concept lattices, and show their use in data mining in very large transactional database, with ordered attributes. MLIL is a restructuring of the iceberg lattice, which respects the hierarchical levels of the itemsets after having plunged unwanted background knowledge at the output, and which are explicit by the order relation on the attributes. MLIL also serve as a new condensed representation of frequent itemsets for multilevel analysis, as a starting point for computing bases of generalized association rules, and as a visualization method for generalized association rules. MLIL is based on the lattice structure of the antichains lattice of the order on the attributes, and on the iceberg lattices and both are based on the theory of Formal Concept Analysis, a mathematical theory with applications in data analysis, information retrieval, and knowledge discovery.