Revisiting Pattern Structure Projections

TL;DR

This paper introduces o-projections for pattern structures in formal concept analysis, generalizing existing projections to simplify complex data analysis while preserving key properties, and explores their algebraic structure.

Contribution

It proposes a new class of projections called o-projections, extending the capabilities of pattern structures in FCA for complex data analysis.

Findings

O-projections form a semilattice structure.

O-projections preserve properties of original pattern structure projections.

Discussion of the relationship between o-projections and representation contexts.

Abstract

Formal concept analysis (FCA) is a well-founded method for data analysis and has many applications in data mining. Pattern structures is an extension of FCA for dealing with complex data such as sequences or graphs. However the computational complexity of computing with pattern structures is high and projections of pattern structures were introduced for simplifying computation. In this paper we introduce o-projections of pattern structures, a generalization of projections which defines a wider class of projections preserving the properties of the original approach. Moreover, we show that o-projections form a semilattice and we discuss the correspondence between o-projections and the representation contexts of o-projected pattern structures. KEYWORDS: formal concept analysis, pattern structures, representation contexts, projections