Concept Lattices Constrained by Attribute Dependencies

The input data to formal concept analysis consist of a collection of objects, a collection of attributes, and a table describing a relationship between objects and attributes (so-called formal context). Very often, there is an additional information about the objects and/or attributes available. In the analysis of the data, the additional information should be taken into account. We consider a particular form of the additional information. The information is in the form of particular attribute dependencies. The primary interpretation of the dependencies is to express a kind of relative importance of attributes. We introduce the notion of a formal concept compatible with the attribute dependencies. The main gain of considering only compatible formal concepts and disregarding formal concepts which are not compatible is the reduction of the number of resulting formal concepts. This leads to a more comprehensible structure of formal concepts (clusters) extracted from the input data. We illustrate our approach by examples.