A proposal for extending formal concept analysis to knowledge graphs

Abstract

Knowledge graphs offer a versatile knowledge representation, and have been studied under different forms, such as conceptual graphs or Datalog databases. With the rise of the Semantic Web, more and more data are available as knowledge graphs. FCA has been successful for analyzing, mining, learning, and exploring tabular data, and our aim is to help transpose those results to graph-based data. Previous FCA approaches have already addressed relational data, hence graphs, but with various limits. We propose G-FCA as an extension of FCA where the formal context is a knowledge graph based on n-ary relationships. The main contributions is the introduction of "n-ary concepts", i.e. concepts whose extents are n-ary relations of objects. Their intents, "projected graph patterns", mix relationships of different arities, objects, and variables. In this paper, we lay first theoretical results, in particular the existence of a concept lattice for each concept arity, and the role of relational projections to connect those different lattices.