Concepts of neighbors and their application to instance-based learning on relational data

Knowledge graphs and other forms of relational data have become a widespread kind of data, and powerful methods to analyze and learn from them are needed. Formal Concept Analysis (FCA) is a mathematical framework for the analysis of symbolic datasets, which has been extended to graphs and relational data, like Graph-FCA. It encompasses various tasks such as pattern mining or machine learning, but its application generally relies on the computation of a concept lattice whose size can be exponential with the number of instances. We propose to follow an instance-based approach where the learning effort is delayed until a new instance comes in, and an inference task is set. This is the approach adopted in k-Nearest Neighbors, and this relies on a distance between instances. We define a conceptual distance based on FCA concepts, and from there the notion of concepts of neighbors, which can be used as a basis for instance-based reasoning. Those definitions are given for both classical FCA and Graph-FCA. We provide efficient algorithms for computing concepts of neighbors, and we demonstrate their inference capabilities by presenting three different applications: query relaxation, knowledge graph completion, and relation extraction.