Abstract.Given a large collection of transactions containing items, a basic common data mining problem is to extract the so-called frequent itemsets (i.e., set of items appearing in at least a given number of transactions). In this paper, we propose a structure called free-sets, from which we can approximate any itemset support (i.e., the number of transactions containing the itemset) and we formalize this notion in the framework of -adequate representation [10].We show that frequent free-sets can be efficiently extracted using pruning strategies developed for frequent itemset discovery, and that they can be used to approximate the support of any frequent itemset. Experiments run on real dense data sets show a significant reduction of the size of the output when compared with standard frequent itemsets extraction. Furthermore, the experiments show that the extraction of frequent free-sets is still possible when the extraction of frequent itemsets becomes intractable. Finally, we show that the error made when approximating frequent itemset support remains very low in practice.

Solving inductive queries which have to return complete collections of patterns satisfying a given predicate has been studied extensively the last few years. The specific problem of frequent set mining from potentially huge boolean matrices has given rise to tens of efficient solvers. Frequent sets are indeed useful for many data mining tasks, including the popular association rule mining task but also feature construction, association-based classification, clustering, etc. The research in this area has been boosted by the fascinating concept of condensed representations w.r.t. frequency queries. Such representations can be used to support the discovery of every frequent set and its support without looking back at the data. Interestingly, the size of condensed representations can be several orders of magnitude smaller than the size of frequent set collections. Most of the proposals concern exact representations while it is also possible to consider approximated ones, i.e., to trade computational complexity with a bounded approximation on the computed support values. This paper surveys the core concepts used in the recent works on condensed representation for frequent sets.

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. Moreover, this regeneration can be performed without any access to the original data. Practical experiments show that this representation can be extracted very efficiently even in difficult cases. We compared it with another representation of frequent patterns previously investigated in the literature called frequent closed sets. In nearly all experiments we have run, the disjunction-free sets have been extracted much more efficiently than frequent closed sets.