Attribute reduction in formal decision contexts and its application to finite topological spaces

Attribute reduction in formal decision contexts has become one of the key issues in the research and development of formal concept analysis (FCA) and its applications. As far as we know, however, most of the existing reduction methods for formal decision contexts are time-consuming especially for the large-scale data. This paper investigates the attribute reduction method for large-scale formal decision contexts. The computation of a discernibility matrix is an important step in the development of the corresponding reduction method. A simple and powerful method to efficiently calculate the discernibility matrix of formal decision contexts is first presented. In addition, a heuristic algorithm for searching the optimal reduct is then proposed. Thirdly, as an application of the new results, we discuss the problem of finding the minimal subbases of finite topological spaces. It has shown that the method of attribute reduction in formal decision contexts can be used to obtain all the minimal subbases of a finite topological space. Furthermore, we present an algorithm for computing the minimal subbase of a topological space, based on the attribute reduction method proposed in this paper. Finally, two groups of experiments are carried out on some large-scale data sets to verify the effectiveness of the proposed algorithms.