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Espace intrinsèque d'un graphe et recherche de communautés.

Alain Lelu 1, 2, 3 Martine Cadot 4
1 KIWI - Knowledge Information and Web Intelligence
LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
4 ABC - Machine Learning and Computational Biology
LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : Determining the number of relevant dimensions in the eigen-space of a graph Laplacian matrix is a central issue in many spectral graph-mining applications. We tackle here the problem of finding out the "right" dimensionality of Laplacian matrices, especially those often encountered in the domains of social or biological graphs: the ones underlying large, sparse, unoriented and unweighted graphs, often endowed with a power-law degree distribution. We present here the application of a randomization test to this problem. After a small introductive example, we validate our approach first on an artificial sparse and scale-free graph, with two intermingled clusters, then on two real-world social graphs ("Football-league", "Mexican Politician Network"), where the actual, intrinsic dimensions appear to be 10 and 2 respectively ; we illustrate the optimality of the transformed dataspaces both visually and numerically, by means of a densitybased clustering technique and a decision tree.
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https://hal.archives-ouvertes.fr/hal-00641128
Contributor : Martine Cadot <>
Submitted on : Monday, November 14, 2011 - 10:35:54 PM
Last modification on : Friday, April 2, 2021 - 3:33:25 AM

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  • HAL Id : hal-00641128, version 1

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Alain Lelu, Martine Cadot. Espace intrinsèque d'un graphe et recherche de communautés.. Revue I3 - Information Interaction Intelligence, Cépaduès, 2011, 2011 (1), pp.1-25. ⟨hal-00641128⟩

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