Graph-FCA: An extension of formal concept analysis to knowledge graphs

摘要

Knowledge graphs offer a versatile knowledge representation, and have been studied under different forms, such as conceptual graphs or RDF graphs in the Semantic Web. A challenge is to discover conceptual structures in those graphs, in the same way as Formal Concept Analysis (FCA) discovers conceptual structures in tables. FCA has been successful for analysing, mining, learning, and exploring tabular data, and our aim is to help transpose those results to graph-based data. Previous several FCA approaches have already addressed relational data, hence graphs, but with various limits. We propose Graph-FCA as an extension of FCA where a dataset is a hypergraph instead of a binary table. We show that it can be formalized simply by replacing objects by tuples of objects. This leads to the notion of "n-ary concept", whose extent is an n-ary relation of objects, and whose intent is a "projected graph pattern". In this paper, we formally reconstruct the fundamental results of FCA for knowledge graphs. We describe in detail the representation of hypergraphs, and the operations on them, as they are much more complex than the sets of attributes that they extend. We also propose an algorithm based on a notion of "pattern basis" to generate and display n-ary concepts in a more efficient and more compact way. We explore a few use cases, in order to study the feasibility and usefulness of Graph-FCA. We consider two use cases: workflow patterns in cooking recipes and linguistic structures from parse trees. In addition, we report on experiments about quantitative aspects of the approach. (C) 2019 Published by Elsevier B.V.