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Characterizing functional dependencies in formal concept analysis with pattern structures

Identifieur interne : 000D74 ( Main/Exploration ); précédent : 000D73; suivant : 000D75

Characterizing functional dependencies in formal concept analysis with pattern structures

Auteurs : Jaume Baixeries [Espagne] ; Mehdi Kaytoue [France] ; Amedeo Napoli [France]

Source :

RBID : Hal:hal-01101107

English descriptors

Abstract

Computing functional dependencies from a relation is an impor-tant 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 For-mal 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. How-ever, 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 depen-dencies. Finally, we discuss and compare the performances of our new approach in a series of experiments on classical benchmark datasets.

Url:
DOI: 10.1007/s10472-014-9400-3


Affiliations:


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Le document en format XML

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<idno type="IdRef">067077927</idno>
<idno type="RNSR">198912571S</idno>
<idno type="IdUnivLorraine">[UL]RSI--</idno>
<orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName>
<orgName type="acronym">LORIA</orgName>
<date type="start">2012-01-01</date>
<desc>
<address>
<addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr</ref>
</desc>
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<relation active="#struct-413289" type="direct"></relation>
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<idno type="IdUnivLorraine">[UL]100--</idno>
<orgName>Université de Lorraine</orgName>
<orgName type="acronym">UL</orgName>
<date type="start">2012-01-01</date>
<desc>
<address>
<addrLine>34 cours Léopold - CS 25233 - 54052 Nancy cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.univ-lorraine.fr/</ref>
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<idno type="IdRef">02636817X</idno>
<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
<desc>
<address>
<country key="FR"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
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<country>France</country>
<placeName>
<settlement type="city">Nancy</settlement>
<settlement type="city">Metz</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Université de Lorraine</orgName>
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<idno type="DOI">10.1007/s10472-014-9400-3</idno>
<series>
<title level="j">Annals of Mathematics and Artificial Intelligence</title>
<idno type="ISSN">1012-2443</idno>
<imprint>
<date type="datePub">2014</date>
</imprint>
</series>
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<keywords scheme="mix" xml:lang="en">
<term>Association rules</term>
<term>attribute implications</term>
<term>data dependencies</term>
<term>formal concept analysis</term>
<term>pattern structures</term>
</keywords>
</textClass>
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<front>
<div type="abstract" xml:lang="en">Computing functional dependencies from a relation is an impor-tant 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 For-mal 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. How-ever, 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 depen-dencies. Finally, we discuss and compare the performances of our new approach in a series of experiments on classical benchmark datasets.</div>
</front>
</TEI>
<affiliations>
<list>
<country>
<li>Espagne</li>
<li>France</li>
</country>
<region>
<li>Auvergne-Rhône-Alpes</li>
<li>Grand Est</li>
<li>Lorraine (région)</li>
<li>Rhône-Alpes</li>
</region>
<settlement>
<li>Lyon</li>
<li>Metz</li>
<li>Nancy</li>
</settlement>
<orgName>
<li>Université Claude Bernard Lyon 1</li>
<li>Université de Lorraine</li>
<li>Université de Lyon</li>
</orgName>
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<country name="Espagne">
<noRegion>
<name sortKey="Baixeries, Jaume" sort="Baixeries, Jaume" uniqKey="Baixeries J" first="Jaume" last="Baixeries">Jaume Baixeries</name>
</noRegion>
</country>
<country name="France">
<region name="Auvergne-Rhône-Alpes">
<name sortKey="Kaytoue, Mehdi" sort="Kaytoue, Mehdi" uniqKey="Kaytoue M" first="Mehdi" last="Kaytoue">Mehdi Kaytoue</name>
</region>
<name sortKey="Napoli, Amedeo" sort="Napoli, Amedeo" uniqKey="Napoli A" first="Amedeo" last="Napoli">Amedeo Napoli</name>
</country>
</tree>
</affiliations>
</record>

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