A PARAMETERIZED ALGORITHM TO EXPLORE FORMAL CONTEXTS WITH A TAXONOMY

Formal Concept Analysis (FCA) is a natural framework to learn from examples. Indeed, learning from examples results in sets of frequent concepts whose extent contains mostly these examples. In terms of association rules, the above learning strategy can be seen as searching the premises of rules where the consequence is set. In its most classical setting, FCA considers attributes as a non-ordered set. When attributes of the context are partially ordered to form a taxonomy, Conceptual Scaling allows the 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 algorithm, to learn rules in the presence of a taxonomy. It works on a non-completed context. The taxonomy is taken into account during the computation so as to remove all redundancies from intents. Simply changing one of its operations, this parameterized algorithm can compute various kinds of concept-based rules. We present instantiations of the parameterized algorithm to learn rules as well as to compute the set of frequent concepts.