Embedding Tolerance Relations in Concept Lattices - An application in Information Fusion

Mehdi Kaytoue 1, * Sergei O. Kuznetsov 2 Zainab Assaghir 1 Amedeo Napoli 1
* Corresponding author
1 ORPAILLEUR - Knowledge representation, reasonning
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : Formal Concept Analysis (FCA) is a well founded mathematical framework used for conceptual classification and knowledge management. Given a binary table describing a relation between objects and attributes, FCA consists in building a set of concepts organized by a subsumption relation within a concept lattice. Accordingly, FCA requires to transform complex data, e.g. numbers, intervals, graphs, into binary data leading to loss of information and poor interpretability of object classes. In this paper, we propose a pre-processing method producing binary data from complex data taking advantage of similarity between objects. As a result, the concept lattice is composed of classes being maximal sets of pairwise similar objects. This method is based on FCA and on a formalization of similarity as a tolerance relation (reflexive and symmetric). It applies to complex object descriptions and especially here to interval data. Moreover, it can be applied to any kind of structured data for which a similarity can be defined (sequences, graphs, etc.). Finally, an application highlights that the resulting concept lattice plays an important role in information fusion problem, as illustrated with a real-world example in agronomy.
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Submitted on : Thursday, February 3, 2011 - 7:00:18 AM
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Mehdi Kaytoue, Sergei O. Kuznetsov, Zainab Assaghir, Amedeo Napoli. Embedding Tolerance Relations in Concept Lattices - An application in Information Fusion. [Research Report] RR-7353, INRIA. 2010, pp.23. ⟨inria-00508462⟩

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