Formal concept analysis over attributes with levels of granularity

Formal concept analysis (FCA) is a method of exploratory analysis of object-attribute data tables. The two main outputs are a hierarchical structure of clusters (so-called formal concepts) and a non-redundant basis of so-called attribute implications. An important topic in FCA is to cope with a possibly large number of resulting clusters. We propose a method to control the number of clusters by means of specification of a granularity level of attributes. A user selects an appropriate level of granularity of each attribute. If the corresponding set of clusters is too large, the user can select a lower level of granularity for appropriate attributes. The resulting set of clusters is then smaller and can be seen as a rougher version of the original set of clusters. If the corresponding set of clusters is too small, the user can select a finer level of granularity for appropriate attributes. The resulting set of clusters is then larger and can be seen as a refinement of the original set of clusters. The paper presents a preliminary study on this topic. We describe the motivations, the method, basic theoretical insight, and experiments demonstrating the method