Generating frequent itemsets incrementally: two novel approaches based on Galois lattice theory

Galois (concept) lattice theory has been successfully applied to the resolution of the association rule problem in data mining. In particular, structural results about lattices have been used in the design of efficient procedures for mining the frequent patterns (itemsets) in a transaction database. As transaction databases are often dynamic, we propose a detailed study of the incremental aspects in lattice construction to support effective procedures for incremental mining of frequent closed itemsets (FCIs). Based on a set of descriptive results about lattice substructures involved in incremental updates, the paper presents a novel algorithm for lattice construction that only explores limited parts of a lattice for updating. Two new methods for incremental FCI mining are studied: the first one inherits its extensive search strategy from a classical lattice method, whereas the second one applies the new lattice construction strategy to the itemset mining context. Unlike batch techniques based on FCIs, both methods avoid rebuilding from scratch the FCI family whenever new transactions are added to the database and/or when the minimal support is changed.