When concepts point at other concepts: the case of UML diagram reconstruction

Relational datasets, i.e., datasets in which individuals are described both by their own features and by their relations to other individuals, arise from various sources such as databases, both relational and object-oriented, or software models, e.g., UML class diagrams. When processing such complex datasets, it is of prime importance for an analysis tool to hold as much as possible to the initial format so that the semantics is preserved and the interpretation of the final results eased. There have been several attempts to introduce relations into the Galois lattice and formal concept analysis fields. We propose a novel approach to this problem which relies on an extension of the classical binary data descriptions based on the distinction of several mutually related formal contexts. As we impose no restrictions on the relations in the dataset, a major challenge is the processing of relational loops among data items. We present an approach for constructing lattices on top of circular descriptions which is based on an iterative approximation of the final solution. The underlying construction methods are illustrated through their application to the restructuring of class hierarchies in object-oriented software engineering, which are described in UML.