A fast incremental algorithm for constructing concept lattices

• Necessary and sufficient conditions for an attribute set to be a new intent.
• The procedure of searching for canonical generators is improved.
• We prove that the number of children of any concept has an upper bound.
• The procedure of updating the upper neighbors of a new concept is improved.
• An efficient incremental algorithm for constructing concept lattices is proposed.

Incremental algorithms for constructing concept lattices can update a concept lattice according to new objects added to the formal context. In this paper, we propose an efficient incremental algorithm for concept lattice construction. The algorithm, called FastAddIntent, results as a modification of AddIntent in which we improve two fundamental procedures including searching for canonical generators and fixing the covering relation. We describe the algorithm completely, prove correctness of our improvements, discuss time complexity issues, and present an experimental evaluation of its performance and comparison with AddIntent. Theoretical and empirical analyses show the advantages of our algorithm when applied to large or (and) dense formal contexts.