Characterizing functional dependencies in formal concept analysis with pattern structures

Abstract

Computing functional dependencies from a relation is an important database topic, with many applications in database management, reverse engineering and query optimization. Whereas it has been deeply investigated in those fields, strong links exist with the mathematical framework of Formal Concept Analysis. Considering the discovery of functional dependencies, it is indeed known that a relation can be expressed as the binary relation of a formal context, whose implications are equivalent to those dependencies. However, this leads to a new data representation that is quadratic in the number of objects w.r.t. the original data. Here, we present an alternative avoiding such a data representation and show how to characterize functional dependencies using the formalism of pattern structures, an extension of classical FCA to handle complex data. We also show how another class of dependencies can be characterized with that framework, namely, degenerated multivalued dependencies. Finally, we discuss and compare the performances of our new approach in a series of experiments on classical benchmark datasets.