Generic Association Rule Bases: Are They so Succinct?

In knowledge mining, current trend is witnessing the emergence of a growing number of works towards defining “concise and lossless” representations. One main motivation behind is: tagging a unified framework for drastically reducing large sized sets of association rules. In this context, generic bases of association rules – whose backbone is the conjunction of the concepts of minimal generator and closed itemset (CI) – constituted so far irreducible compact nuclei of association rules. However, the inherent absence of a unique minimal generator (MG) associated to a given CI offers an “ideal” gap towards a tougher redundancy removal even from generic bases of association rules. In this paper, we adopt the succinct system of minimal generators (SSMG), newly redefined in [1], to be an exact representation of the MG set. Then, we incorporate the SSMG into the framework of generic bases to only maintain the succinct generic association rules. After that, we give a thorough formal study of the related inference mechanisms allowing to derive all redundant association rules starting from succinct ones. Finally, an experimental study shows that our approach makes it possible to eliminate without information loss an important number of redundant generic association rules and thus, to only present succinct and informative ones to users.