An Efficient Algorithm for Decreasing the Granularity Levels of Attributes in Formal Concept Analysis

Abstract

In the formal concept analysis (FCA), a concept lattice represents the basic structure derived from Boolean data describing the relationships between objects and attributes. One of the basic problems of FCA is to control the structure of concept lattices to extract useful information. To explore a data set, sometimes we need to tune the structure of the corresponding concept lattice by merging a couple of finer attributes to a coarser attribute. The merged attribute can be interpreted as a coarser granularity level. In this paper, we propose an efficient algorithm called fold for decreasing the granularity levels of attributes. We analyzed and explored the relationships between concepts before and after decreasing the granularity level of an attribute. Based on those theoretical proofs, we propose an efficient method of classifying concepts to reduce the comparisons between the concepts compared with the original zoom-out algorithm. Moreover, we provide a preprocessing procedure to search for canonical generators and help restore the covering relation. We describe the algorithm completely, discuss time complexity issues, and present an experimental evaluation of its performance and comparison with the zoom-out algorithm. The theoretical and empirical analyses demonstrate the advantages of our algorithm when applied to various types of formal contexts.