Attribute Selection using Contranominal Scales

Abstract: Formal Concept Analysis (FCA) allows to analyze binary data by deriving concepts and ordering them in lattices. One of the main goals of FCA is to enable humans to comprehend the information that is encapsulated in the data; however, the large size of concept lattices is a limiting factor for the feasibility of understanding the underlying structural properties. The size of such a lattice depends on the number of subcontexts in the corresponding formal context that are isomorphic to a contranominal scale of high dimension. In this work, we propose the algorithm ContraFinder that enables the computation of all contranominal scales of a given formal context. Leveraging this algorithm, we introduce delta-adjusting, a novel approach in order to decrease the number of contranominal scales in a formal context by the selection of an appropriate attribute subset. We demonstrate that delta-adjusting a context reduces the size of the hereby emerging sub-semilattice and that the implication set is restricted to meaningful implications. This is evaluated with respect to its associated knowledge by means of a classification task. Hence, our proposed technique strongly improves understandability while preserving important conceptual structures.