Granularity of attributes in formal concept analysis

We propose a method to control the structure of concept lattices derived from Boolean data. Concept lattices represent the basic structure utilized in formal concept analysis. Their structure is of primary importance for the analysis and understanding of the input data. Our method enables to control the structure of the derived concept lattice by specifying granularity levels of attributes, thus in a sense by focusing the lenses through which we perceive and conceptually carve up the world. The granularity levels are chosen by a user based on his expertise and experimentation with the data. If the resulting formal concepts are too specific and there is a large number of them, the user can choose to use a coarser level of granularity. The resulting formal concepts are then less specific and can be seen as resulting from a zoom-out. In a similar way, one may perform a zoom-in to obtain finer, more specific formal concepts. The paper presents a basic study of this topic. We describe the motivations, the method, a theoretical insight, zoom-in and zoom-out algorithms, and experiments demonstrating the method.