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 enhanced version of the classical binary data descriptions based on the distinction of several mutually related formal contexts. Key Words: Galois lattices, conceptual scaling, lattice constructing algorithms, relational information. 1

Abstract 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, knowledge bases, 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. Therefore, several attempts have been made to introduce relations into the formal concept analysis field which otherwise generated a large number of knowl-edge discovery methods and tools. However, the proposed approaches invariably look at relations as an intra-concept construct, typically relating two parts of the concept description, and therefore can only lead to the discovery of coarse-grained patterns. As an approach towards the discovery of finer-grain relational concepts, we propose to enhance the classical (object × attribute) data representations with a new dimension that is made out of inter-object links (e.g., spouse, friend, manager-of, etc.). Consequently, the discovered concepts are linked by relations which, like

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, knowledge bases, 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 nal results eased. Therefore, several attempts have been made to introduce relations into the formal concept analysis eld which otherwise generated a large number of knowl-edge discovery methods and tools. However, the proposed approaches invariably look at relations as an intra-concept construct, typically relating two parts of the concept description, and therefore can only lead to the discovery of coarse-grained patterns. As an approach towards the discovery of ner-grain relational concepts, we propose to enhance the classical (object attribute) data representations with a new dimen-sion that is made out of inter-object links (e.g., spouse, friend, manager-of, etc.).

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. Therefore, several attempts have been made to introduce relations into the formal concept analysis field which otherwise generated a large number of knowledge discovery methods and tools. However, the proposed approaches invariably look at relations as an intra-concept construct, typically relating two parts of the concept description, and therefore can only lead to the discovery of coarse-grained patterns. As an approach towards the discovery of finer-grain relational concepts, we propose to enhance the classical (object x attribute) data representations with a new dimension that is made out of inter-object links (e.g., spouse, friend, manager-of, etc.). Consequently, the discovered concepts are linked by relations which, like associations in conceptual data models such as the entity-relation diagrams, abstract from existing links between concept instances. The borders for the application of the relational mining task are provided by what we call a relational context family, a set of binary data tables representing individuals of various sorts (e.g., human beings, companies, vehicles, etc.) related by additional binary relations 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 a method for constructing concepts 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.