Given a large set of data, a common data mining problem is to extract the frequent patterns occurring in this set. The idea presented in this paper is to extract a condensed representation of the frequent patterns called disjunction-free sets, instead of extracting the whole frequent pattern collection. We show that this condensed representation can be used to regenerate all frequent patterns and their exact frequencies.

Frequent association rules (e.g., A∧B⇒C to say that when properties A and B are true in a record then, C tends to be also true) have become a popular way to summarize huge datasets. The last 5 years, there has been a lot of research on association rule mining and more precisely, the tractable discovery of interesting rules among the frequent ones. We consider now the problem of mining association rules that may involve negations e.g., A∧B⇒⌝C or ⌝A∧B⇒C. Mining such rules is difficult and remains an open problem. We identify several possibilities for a tractable approach in practical cases. Among others, we discuss the active use of constraints. We propose a generic algorithm and discuss the use of constraints to mine the generalized sets from which rules with negations can be derived.