The Optimal Factorization Based On Three-Way Concept Lattices

Formal concept analysis(FCA)was put forward in 1982 by German mathematician Wille,it is a useful tool for data analysis and rules acquisition.Three-way concept analysis(3WCA)is the theory of combining FCA with Three-way decisions to study formal contexts.Nowadays,formal concept analysis and three-way concept analysis have been widely used in the fields of machine learning,data mining and information retrieval.In this paper,based on three-way concept analysis and factor analysis,we treated three-way concepts as optimal factors,and gave the optimal factorization of the corresponding formal contexts.Furthermore,we obtained the optimal factor concepts,which can realize our purpose of depict all the information in the formal context by fewer three-way concepts of this context.1.We firstly define the factorization and optimal factorization based on object(attribute)-induced three-way concept lattices,and discuss the existence and optimality of factors,and research the mandatory factors and approximate factorization.2.We present the relationship between the factorization of object(attribute)-induced three-way concept lattices and the factorization based on classical concept lattices respectively.3.We give the construction algorithms of optimal factors based on object(attribute)-induced three-way concept lattices.