On Computing the Minimal Generator Family for Concept Lattices and Icebergs

Minimal generators (ormingen) constitute a remarkable part of the closure space landscape since they are the antipodes of the closures, i.e., minimal sets in the underlying equivalence relation over the powerset of the ground set. As such, they appear in both theoretical and practical problem settings related to closures that stem from fields as diverging as graph theory, database design and data mining. In FCA, though, they have been almost ignored, a fact that has motivated our long-term study of the underlying structures under different perspectives. This paper is a two-fold contribution to the study of mingen families associated to a context or, equivalently, a closure space. On the one hand, it sheds light on the evolution of the family upon increases in the context attribute set (e.g., for purposes of interactive data exploration). On the other hand, it proposes a novel method for computing the mingen family that, although based on incremental lattice construction, is intended to be run in a batch mode. Theoretical and empirical evidence witnessing the potential of our approach is provided.