Free-sets: A condensed representation of Boolean data for the approximation of frequency queries

Given a large collection of transactions containing items, a basic common data mining problem is to extract the so-called frequent itemsets (i.e., sets 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 epsilon-adequate representations (H. Mannila and H. Toivonen, 1996. In Proc. of the Second International Conference on Knowledge Discovery and Data Mining (KDD'96), pp. 189-194). 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 on real dense data sets show a significant reduction of the size of the output when compared with standard frequent itemset extraction. Furthermore, the experiments show that the extraction of frequent free-sets is still possible when the extraction of frequent itemsets becomes intractable, and that the supports of the frequent free-sets can be used to approximate very closely the supports of the frequent itemsets. Finally, we consider the effect of this approximation on association rules ( a popular kind of patterns that can be derived from frequent itemsets) and show that the corresponding errors remain very low in practice.