Symmetries in itemset mining

Abstract

In this paper, we describe a new framework for breaking symmetries in itemset mining problems. Symmetries are permutations between items that leave invariant the transaction database. Such kind of structural knowledge induces a partition of the search space into equivalent classes of symmetrical itemsets. Our proposed framework aims to reduce the search space of possible interesting itemsets by detecting and breaking symmetries between items. Firstly, we address symmetry discovery in transaction databases. Secondly, we propose two different approaches to break symmetries in a preprocessing step by rewriting the transaction database. This approach can be seen as an original extension of the symmetry breaking framework widely used in propositional satisfiability and constraint satisfaction problems. Finally, we show that Apriori-like algorithms can be enhanced by dynamic symmetry reasoning. Our experiments clearly show that several itemset mining instances taken from the available datasets contain such symmetries. We also provide experimental evidence that breaking such symmetries reduces the size of the output on some families of instances.