Finite Confluences and Closed Pattern Mining

TL;DR

This paper introduces confluences, a weaker partial order than lattices, to extend closed pattern mining and formal concept analysis, enabling reduction of pattern spaces while preserving closure properties.

Contribution

It proposes confluences as a new structure for pattern mining, extending formal concept analysis to reduce pattern spaces without losing closure operator characteristics.

Findings

Confluences preserve key closure properties despite being weaker than lattices.

Reducing pattern spaces via confluences simplifies analysis while maintaining essential closure information.

The approach offers a new perspective on reducing pattern and concept spaces in data analysis.

Abstract

The purpose of this article is to propose and investigate a partial order structure weaker than the lattice structure and which have nice properties regarding closure operators. We extend accordingly closed pattern mining and formal concept analysis to such structures we further call confluences. The primary motivation for investigating these structures is that it allows to reduce a lattice to a part whose elements are connected, as in some graph, still preserving a useful characterization of closure operators. Our investigation also considers how reducing one of the lattice involved in a Galois connection affects the structure of the closure operators ranges. When extending this way formal concept analysis we will focus on the intensional space, i.e. in reducing the pattern language, while recent investigations rather explored the reduction of the extensional space to connected elements.