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A Unified Hierarchy for Functional Dependencies, Conditional Functional Dependencies and Association Rules

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Formal Concept Analysis (ICFCA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5548))

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Abstract

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.

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Author information

Authors and Affiliations

  1. Université Blaise Pascal – LIMOS, Campus des Cézeaux, 63173, Aubière Cedex, France

    Raoul Medina & Lhouari Nourine

Authors
  1. Raoul Medina
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  2. Lhouari Nourine
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Editor information

Editors and Affiliations

  1. Irisa/Ifsic, Université de Rennes 1, Campus Universitaire de Beaulieu, 35042, Rennes cedex, France

    Sébastien Ferré

  2. Institut AIFB, Universität Karlsruhe (TH), 76128, Karlsruhe, Germany

    Sebastian Rudolph

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Medina, R., Nourine, L. (2009). A Unified Hierarchy for Functional Dependencies, Conditional Functional Dependencies and Association Rules. In: Ferré, S., Rudolph, S. (eds) Formal Concept Analysis. ICFCA 2009. Lecture Notes in Computer Science(), vol 5548. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01815-2_9

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  • DOI: https://doi.org/10.1007/978-3-642-01815-2_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-01814-5

  • Online ISBN: 978-3-642-01815-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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