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Some Links Between Formal Concept Analysis and Graph Mining

Michel Liquière 1
1 COCONUT - Agents, Apprentissage, Contraintes
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : This chapter presents a formal model to learning from examples represented by labelled graphs. This formal model is based upon lattice theory and in particular Galois lattices. We widen the domain of formal concept analysis, by the use of the Galois lattices model with structural descriptions of examples and concepts. The operational implementation of our model, called "Graal" (for GRAph And Learning) constructs a Galois lattice for any description language provided that the operations of comparison and generalization are determined for that language. These operations exist in the case of labelled graphs satisfying an partial order relation (homomorphism). This paper is concerned as well with the known problems regarding propositionalization (i.e. the transformation of a structural description in a propositional description). Using classical lattice results, we have a formal model for the transformation of a structural machine learning problem into a propositional one.
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Submitted on : Friday, March 16, 2007 - 2:38:56 PM
Last modification on : Monday, January 11, 2021 - 5:24:06 PM
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Michel Liquière. Some Links Between Formal Concept Analysis and Graph Mining. Cook, Diane J. / Holder, Lawrence B. Mining Graph Data, John Wiley & Sons, pp.227-252, 2006, ISBN-10: 0471731900 ISBN-13: 978-0471731900. ⟨lirmm-00137035⟩

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