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Espace intrinsèque d'un graphe et recherche de communautés

Alain Lelu 1, 2 Martine Cadot 3
1 KIWI - Knowledge Information and Web Intelligence
LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
3 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 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. We validate our approach first on an artificial sparse and power-law type graph, with two intermingled clusters, then on a real-world social graph ("Football-league"), where the actual, intrinsic dimension appears to be 11 ; we illustrate the optimality of this transformed dataspace both visually and numerically, by means of a density-based clustering technique and a decision tree.
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Alain Lelu, Martine Cadot. Espace intrinsèque d'un graphe et recherche de communautés. Première conférence sur les Modèles et l'Analyse des Réseaux : Approches Mathématiques et Informatique - MARAMI 2010, Oct 2010, Toulouse, France. pp.1. ⟨hal-00516865⟩

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