  Recent studies on frequent itemset mining algorithms resulted in significant
performance improvements. However, if the minimal support threshold is set too
low, or the data is highly correlated, the number of frequent itemsets itself
can be prohibitively large. To overcome this problem, recently several
proposals have been made to construct a concise representation of the frequent
itemsets, instead of mining all frequent itemsets. The main goal of this paper
is to identify redundancies in the set of all frequent itemsets and to exploit
these redundancies in order to reduce the result of a mining operation. We
present deduction rules to derive tight bounds on the support of candidate
itemsets. We show how the deduction rules allow for constructing a minimal
representation for all frequent itemsets. We also present connections between
our proposal and recent proposals for concise representations and we give the
results of experiments on real-life datasets that show the effectiveness of the
deduction rules. In fact, the experiments even show that in many cases, first
mining the concise representation, and then creating the frequent itemsets from
this representation outperforms existing frequent set mining algorithms.
