An Improved Incremental Algorithm for Constructing Concept Lattices

The concept lattice produced from a binary relation has been proved useful for many applications. How to construct it efficiently is a difficult but challenging task. In this article, the authors present an improved incremental algorithm, which, through tracking the most general concept with the same attributes in the intent of the newly-added object for each concept in the original concept lattice, greatly reduces the judgement of a concept to be an old node or not by comparing its common attributes to that of its parent concepts; furthermore, the improved algorithm limits the search space of parents of a newly added concept to the parent nodes of the corresponding generator and consequently improves the execution speed of the algorithm. Complexity analysis is given in the end to demonstrate the effectiveness of our new algorithm.