Cubes of Concepts: Multi-dimensional Exploration of Multi-valued Contexts

A number of information systems offer a limited exploration in that users can only navigate from one object to another object, e.g. navigating from folder to folder in file systems, or from page to page on the Web. An advantage of conceptual information systems is to provide navigation from concept to concept, and therefore from set of objects to set of objects. The main contribution of this paper is to push the exploration capability one step further, by providing navigation from set of concepts to set of concepts. Those sets of concepts are structured along a number of dimensions, thus forming a cube of concepts. We describe a number of representations of concepts, such as sets of objects, multisets of values, and aggregated values. We apply our approach to multi-valued contexts, which stand at an intermediate position between many-valued contexts and logical contexts. We explain how users can navigate from one cube of concepts to another. We show that this navigation includes and extends both conceptual navigation and OLAP operations on cubes.