Parallel Computation of Closed Itemsets and Implication Rule Bases

Abstract

Formal concept analysis has been successfully applied as a data mining framework whereby target patterns come in the form of intent families and implication bases. Since their extraction is a challenging task, especially for large datasets, parallel techniques should be helpful in reducing the computational effort and increasing the scalability of the approach. In this paper we describe a way to parallelize a recent divide-and-conquer method computing both the intents and the Duquenne-Guiges implication basis of dataset. Wile intents admit a straightforward computation, adding the basis — whose definition is recursive — poses harder problems, in particular, for parallel design. A first, and by no means final, solution relies on a partition of the basis that allows the crucial and inherently sequential step of redundancy removal to be nevertheless split into parallel subtasks. A prototype implementation of our method, called ParCIM, shows a nearly linear acceleration w.r.t. its sequential counter-part.