Hierarchies of Conceptual Scales

Formal Concept Analysis allows to derive conceptual hierarchies from data tables. Formal Concept Analysis is applied in various domains, e. g., data analysis, information retrieval, and knowledge discovery in databases. In order to deal with increasing sizes of the data tables (and to allow more complex data structures than just binary attributes), conceptual scales have been developed. They are considered as metadata which structure the data conceptually. But in large applications, the number of conceptual scales increases as well. Techniques are needed which support the navigation of the user also on this meta-level of conceptual scales. In this paper, we attack this problem by extending the set of scales by hierarchically ordered higher level scales and by introducing a visualization technique called nested scaling. We extend the two-level architecture of Formal Concept Analysis (the data table plus one level of conceptual scales) to a many-level architecture with a cascading system of conceptual scales. The approach also allows to use representation techniques of Formal Concept Analysis for the visualization of thesauri and ontologies.