A Fast Algorithm for Building the Hasse Diagram of a Galois Lattice

Formal concept analysis and Galois lattices in general are increasingly used for large contexts that are automatically generated. As the size of the resulting datasets may grow considerably, it becomes essential to keep the algorithmic complexity of the analysis procedures as low as possible. This paper presents an e cient algorithm that computes the Hasse diagram of a Galois lattice from the lattice ground set, i.e., the set of all concepts. The algorithm performs an element-wise completion of the lattice according to a linear extension of the lattice order. This requires only a limited number of comparisons between concepts and therefore makes the global algorithm very e cient. In fact, its asymptotic time complexity is almost linear in the number of concepts. Consequently, the joint use of our algorithm with an e cient procedure for concept generation yields a complete procedure for building the Galois lattice.