Dynamic concept reduction methods based on local information

Abstract

Knowledge reduction is one of the core research issues in formal concept analysis. As a new technique of knowledge reduction, concept reduction has received increasing attention recently. One typical method of calculating concept reducts is based on representative concept matrix (RC-matrix, for short), which can obtain all concept reducts. However, it is confronted with the following challenges: (1) before the construction of the RC-matrix, all concepts of the formal context need to be calculated, which is both time and space consuming; (2) there is a lot of redundant information in the constructed RC-matrix, which is not helpful to calculate the concept reducts; (3) when the data changes dynamically, the concept reducts need to be calculated for scratch. To address these issues, dynamic concept reduction methods based on local information are proposed in this paper. Firstly, the characteristics of the minimal elements (with respect to set inclusion) in the RC-matrix are analyzed, and all the minimal elements are directly labeled from the formal context; secondly, the advantage of local information is taken to construct each minimal elements of the RC-matrix, from which all the concept reducts can be obtained; besides, a new simplified version of RC-matrix, named as Type-I minimal RC-matrix, is further constructed to compute one concept reduct; and finally, when data dynamically changes, the connections between concept reducts of the original formal context and those of the new one are analyzed, consequently, two dynamic concept reduction algorithms are proposed.