Efficient Incremental Algorithm for Building Swiftly Concepts Lattices

Abstract

Efficient tool and platform for several areas, concept lattice are widely used in many fields of research. Dynamic environment requires an incremental algorithm to build formal concepts. It plays an essential role in the application of concept lattice. This paper presents a fast, efficient, incremental algorithm to compute formal concepts. Algorithmic complexity is studied both theoretically (in the worst case) and experimentally. It presents a complexity of at most (|M|.|G|.|L|) where M is set of attributes, G is set of objects and L is set of concepts of the lattice. Irrespective of the lattice, the algorithm computes incrementally all formal concepts without increasing time complexity. Algorithmic complexity of the most important incremental algorithms is compared theoretically, and an experimental study based on density/ sparseness of underlying formal contexts is performed with Norris' algorithm classified the most one efficient incremental in practice.