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Published in:
2009 | OriginalPaper | Chapter
A Unified Hierarchy for Functional Dependencies, Conditional Functional Dependencies and Association Rules
Authors : Raoul Medina, Lhouari Nourine
Published in: Formal Concept Analysis
Publisher: Springer Berlin Heidelberg
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Conditional Functional Dependencies (CFDs) are Functional Dependencies (FDs) that hold on a fragment relation of the original relation. In this paper, we show the hierarchy between FDs, CFDs and Association Rules (ARs): FDs are the union of CFDs while CFDs are the union of ARs. We also show the link between Approximate Functional Dependencies (AFDs) and approximate ARs. In this paper, we show that all those dependencies are indeed structurally the same and can be unified into a single hierarchy of dependencies. A benefit of this hierarchy is that existing algorithms which discover ARs could be adapted to discover any kind of dependencies and, moreover, generate a reduced set of dependencies. We also establish the link between the problem of finding equivalent pattern tableaux of a CFD and the problem of finding keys of a relation.