ALLSAT compressed with wildcards: Frequent Set Mining

TL;DR

This paper introduces a novel algorithm for efficiently finding all maximal frequent itemsets, enabling better compression of frequent set data using wildcards, with significant implications for Frequent Set Mining.

Contribution

The paper presents the Find-All-Facets algorithm that replaces hypergraph dualization with a more efficient method for identifying facets in simplicial complexes, enhancing FSM processing.

Findings

The new algorithm efficiently finds all facets of finite simplicial complexes.

It replaces costly hypergraph dualization with a faster minimal set calculation.

The approach significantly improves Frequent Set Mining compression techniques.

Abstract

Like any simplicial complex the simplicial complex of all frequent sets can be compressed with wildcards once the maximal frequent sets (=facets) are known. Namely, the task (a particular kind of ALLSAT problem) is achieved by the author's recent algorithm Facets-To-Faces. But how to get the facets in the first place? The novel algorithm Find-All-Facets determines all facets of any (decidable) finite simplicial complex by replacing costly hypergraph dualization (Dualize+Advance and its variants) with the cheaper calculation of the minimal members of certain set families. The latter task is sped up by Vertical Layout. While all of this concerns arbitrary simplicial complexes, the impact to Frequent Set Mining (FSM) seems particularly high.