Espace intrinsèque d'un graphe et recherche de communautés
Résumé
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.
Origine | Fichiers produits par l'(les) auteur(s) |
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