The reverse doubling construction

Abstract

It is well known inside the Formal Concept Analysis (FCA) community that a concept lattice could have an exponential size in the data. Hence, the size of concept lattices is a critical issue in the presence of large real-life data sets. In this paper, we propose to investigate factor lattices as a tool to get meaningful parts of the whole lattice. These factor lattices have been widely studied from the early theory of lattices to more recent work in the FCA field. This paper contains two parts. The first one gives background about lattice theory and formal concept analysis, and mainly compatible sub-contexts, arrow-closed sub-contexts and congruence relations. The second part presents a new decomposition called “reverse doubling construction” that exploits the above three notions used for the doubling convex construction investigated by Day. Theoretical results and their proofs are given as well as an illustrative example.