Molly Troxel, Kim Swarm, Robert Zembowicz, and Jan M. Zytkow
In this paper we analyze relationships between different forms of knowledge that can be discovered in the same data matrix (database): regularities, concept descriptions and conceptual clusters (hierarchies). These relationships, very important for our understanding of knowledge, have not received sufficient attention, neither in the domain of machine learning nor from the perspective of knowledge based systems. We argue for the basic role of regularities (law-like knowledge) and show how a subset of the discovered regularities, made of regularities which approximate logical equivalences, can be used to construct concept hierarchies. We show how each of those regularities leads to an element of the conceptual hierarchy and how those elements are linked to form elements of higher empirical contents. One-way implications can also contribute to the empirical contents of hierarchy elements. Next we show how to combine hierarchy elements into concept hierarchy. Different hierarchies are possible, leading to the question of choice between hierarchies, for which we provide our optimality criteria. The algorithm is illustrated by a walk-through application on the soybean database. We compare our results with results obtained earlier by the COBWEB clustering approach.