Paper: Sebastian Rudolph, Christian Săcărea, Diana Troancă, Conceptual Navigation for Polyadic Formal Concept Analysis, Proceedings of the 4th International Workshop on Artificial Intelligence for Knowledge Management (AI4KM 2016), pp. 35-41 New York, USA
Abstract: Formal Concept Analysis (FCA) is a mathematically inspired field of knowledge representation with wide applications in knowledge discovery and decision support. Polyadic FCA is an extension of classical FCA that instead of a binary uses an n-ary incidence relation to define formal concepts, i.e. data clusters in which all elements are interrelated.
We consider a paradigm for navigating the space of concepts, based on so-called membership constraints. We present an implementation for the cases n ∈ {2, 3, 4} using an encoding into answer set programming (ASP) allowing us to exploit optimization strategies offered by ASP. For the case n = 3, we compare this implementation to a second strategy that uses exhaustive search in the concept set, which is precomputed by an existing tool. We evaluate the implementation strategies in terms of performance. Finally, we discuss the limitations of each approach and the possibility of generalizations to n-ary datasets.
Keywords: Formal Concept Analysis, Polyadic FCA, navigating the space of concepts, membership constraints, answer set programming