Concept lattice compression in incomplete contexts based on K-medoids clustering

Incomplete contexts are a kind of formal contexts in which information about the relationship between some objects and attributes is not available or is lost. Knowledge discovery in incomplete contexts is of interest because such databases are frequently encountered in the real world. The existing work has proposed an approach to construct the approximate concept lattice of an incomplete context. Generally speaking, however, the huge nodes in the approximate concept lattice make the obtained conceptual knowledge difficult to be understood and weaken the efficiency of the related decision-making analysis as well. Motivated by this problem, this paper puts forward a method to compress the approximate concept lattice using K-medoids clustering. To be more concrete, firstly we discuss the accuracy measure of approximate concepts in incomplete contexts. Secondly, the similarity measure between approximate concepts is presented via the importance degrees of an object and an attribute. And then the approximate concepts of an incomplete context are clustered by means of K-medoids clustering. Moreover, we define the so-called K-deletion transformation to achieve the task of compressing the approximate concept lattice. Finally, we conduct some experiments to perform a robustness analysis of the proposed clustering method with respect to the parameters and K, and show the average rate of compression of approximate concept lattice.