Characterizing trees in property-oriented concept lattices

Abstract

Property-oriented concept lattices are systems of conceptual clusters called property-oriented concepts, which are partially ordered by the subconcept/superconcept relationships. Property-oriented concept lattices are basic structures used in formal concept analysis. In general, a property-oriented concept lattice may contain overlapping clusters and is not to be a tree construction. Additionally, tree-like classification schemes are appealing and are produced by several clustering methods. In this paper, we present necessary and sufficient conditions on input data for the output property-oriented concept lattice to form a tree after one removes its greatest element. After applying to input data for which the associated property-oriented concept lattice is a tree, we present an algorithm for computing property-oriented concept lattices.