A framework for incremental generation of closed itemsets

Association rule mining from a transaction database (TDB) requires the detection of frequently occurring patterns, called frequent itemsets (FIs), whereby the number of FIs may be potentially huge. Recent approaches for FI mining use the closed itemset paradigm to limit the mining effort to a subset of the entire FI family, the frequent closed itemsets (FCIs). We show here how FCIs can be mined incrementally yet efficiently whenever a new transaction is added to a database whose mining results are available. Our approach for mining FIs in dynamic databases relies on recent results about lattice incremental restructuring and lattice construction. The fundamentals of the incremental FCI mining task are discussed and its reduction to the problem of lattice update, via the CI family, is made explicit. The related structural results underlie two algorithms for updating the set of FCIs of a given TDB upon the insertion of a new transaction. A straightforward method searches for necessary completions throughout the entire CI family, whereas a second method exploits lattice properties to limit the search to CIs which share at least one item with the new transaction. Efficient implementations of the parsimonious method is discussed in the paper together with a set of results from a preliminary study of the method's practical performances.