Efficient assessment of formal concept stability in the Galois lattice

Abstract

Formal concept analysis (FCA) is a mathematical tool for analyzing data and formally representing conceptual knowledge. Under this formalism, the concept stability metric can be used in many applications: community detection, pattern selection in noisy data, patient care trajectories, and biclusters of similar objects, etc. However, computing the stability is a #P-complete problem. Therefore, most existing studies have focused either on estimating this metric using some heuristics or by proposing recursive approaches to assess the exact value of the stability. In this paper, we introduce an algorithm called the Exact Stability Computing for Galois Lattice Esc-Gl for computing the stability of a formal concept given the underlying partial relation. Based on the lower cover of a given concept, the algorithm can improve scalability and reduce computational complexity. Our experiments performed on large benchmark datasets from the FCA field show that our contributions sharply outperform all the pioneering approaches of the dedicated literature.