Authors:
Jean-François Viaud
1
;
Karell Bertet
1
;
Christophe Demko
1
and
Rokia Missaoui
2
Affiliations:
1
University of La Rochelle, France
;
2
University of Quebec in Outaouais, Canada
Keyword(s):
Concept Lattice, Congruence Relation, Factor Lattice, Arrow Relation, Arrow Closed Subcontext, Compatible Subcontext, Doubling Convex.
Related
Ontology
Subjects/Areas/Topics:
Artificial Intelligence
;
Clustering and Classification Methods
;
Computational Intelligence
;
Concept Mining
;
Evolutionary Computing
;
Foundations of Knowledge Discovery in Databases
;
Knowledge Discovery and Information Retrieval
;
Knowledge-Based Systems
;
Machine Learning
;
Soft Computing
;
Symbolic Systems
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.