A Parameterized Algorithm for Exploring Concept Lattices

Abstract

Formal Concept Analysis (FCA) is a natural framework for learning from positive and negative examples. Indeed, learning from examples results in sets of frequent concepts whose extent contains only these examples. In terms of association rules, the above learning strategy can be seen as searching the premises of exact rules where the consequence is fixed. In its most classical setting, FCA considers attributes as a non-ordered set. When attributes of the context are ordered, Conceptual Scaling allows the related taxonomy to be taken into account by producing a context completed with all attributes deduced from the taxonomy. The drawback, however, is that concept intents contain redundant information. In this article, we propose a parameterized generalization of a previously proposed algorithm, in order to learn rules in the presence of a taxonomy. The taxonomy is taken into account during the computation so as to remove all redundancies from intents. Simply changing one component, this parameterized algorithm can compute various kinds of concept-based rules. We present instantiations of the parameterized algorithm for learning positive and negative rules.