Distributed three-way formal concept analysis for large formal contexts

Abstract

Three-way concept analysis (3WCA) is a framework based on Formal concept analysis and three-way decisions is used in the field of knowledge discovery to solve uncertainties in many domains like machine learning, data mining and software engineering. The 3WCA requires both the formal context and its complement context for generating concepts and constructing the concept lattice. In three-way concept analysis, data are analyzed using two types of concept lattices constructed using classical formal concept analysis (FCA) algorithms: object-induced (OE) concept lattices and attribute-induced (AE) concept lattices. The existing formal concept analysis algorithms focus on the sequential generation of OE and AE concepts rather than finding them in parallel and cannot process large datasets efficiently. The main contribution of this paper is that we propose a novel parallel algorithm for concept generation and construction of the three way concept lattice for knowledge discovery and representation in large datasets. Aiming to construct an efficient algorithm for 3WCA, this paper primarily discusses the existing algorithms for concept generation. Further we develop an efficient algorithm for OE and AE concept generation and lattice construction. Extensive experiments are conducted on various datasets to evaluate the efficiency of the proposed algorithm. Both the experimental and statistical results demonstrate the efficacy of the algorithm on larger datasets. Also the proposed algorithm can significantly decrease the time required for OE/AE concept generation and lattice construction compared to the existing classical FCA algorithms.