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inria-00508462, version 1

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

Mehdi Kaytoue (Author to contact preferably) a1, Sergei O. Kuznetsov () 2, Zainab Assaghir () 1, Amedeo Napoli () 1

N° RR-7353 (2010)

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.

  • a –  LORIA
  • 1:  ORPAILLEUR (INRIA Lorraine - LORIA)
  • INRIA – CNRS : UMR7503 – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
  • 2:  Department of Applied Mathematics - State University Higher School of Economics
  • State University Higher School of Economics
  • Domain : Computer Science/Artificial Intelligence
  • Keywords : formal concept analysis – similarity – tolerance – information fusion
  • Internal note : RR-7353
 
  • inria-00508462, version 1
  • oai:hal.inria.fr:inria-00508462
  • From: 
  • Submitted on: Thursday, 3 February 2011 07:00:18
  • Updated on: Thursday, 3 February 2011 07:00:18