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E. Attar, A. Pigeau, and M. Gelgon, A Decentralized and Robust Approach to Estimating a Probabilistic Mixture Model for Structuring Distributed Data, 2011 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology, pp.22-27, 2011.
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URL : https://hal.archives-ouvertes.fr/hal-00595300

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. Réduction-de-modèles-de-mélange-en-utilisant-la-technique-de-goldberger, Les ellipses continues et pointillées représentent respectivement les modèles de f et g La figure (a) montre la première étape de l'algorithme où les divergences entre les composantes de f et g sont calculées. La meilleure correspondance obtenue m, consiste à associer, par exemple, l'ensemble {f 1 , f 2 , f 3 } à g 1 et les composantes restantes à g 2 . La figure (b) présente les mises à jour des paramètres de modèle réduit g en se basant sur la fonction de correspondance m, et en, p.50

. Exemple, Les ellipses continues et pointillées représentent respectivement les modèles de f et g. La figure (a) contient les composantes originales de distribution de Student Dans la figure (b), chaque composante Student est approximée par un mélange de gaussiennes de P = 3 composantes. L'optimisation du critère de match bound consiste à chercher la meilleure fonction de correspondance m entre les composantes de f et g, d'une façon à minimiser la sommation de la divergence de KL, Ici, les flèches montrent la fonction de correspondance m obtenue implicitement par la méthode match bound entre les

. Santes-f-ip-et-g-jp, après avoir lié les composantes f i avec les composantes g i selon m. La figure (c) représente la mise à jour de composantes du modèle réduit g. Les paramètres du modèle g sont calculés à partir de ceux du modèle f selon la fonction m, p.54

. Cette-figure-présente-le-modèle-f-et-le-modèle-réduit-g-obtenu, Elle illustre aussi les données générées à partir de chaque composante f i de f . Les ellipses uniques sont les composantes f i de f , et les ellipses multiples sont les composantes g j de g, p.58

.. Cette-figure-est-extraite-de, Elle montre bien le changement de topologie après l'application du protocole de cyclon (une implémentation de PSS) sur le noeud 2. Le noeud 2 après avoir choisi aléatoirement son voisin 9, il lui envoie la liste {2, 0, 6} et il reçoit également un autre ensemble {0, 5, 7}. Puis les deux noeuds mettent à jour leurs listes de voisins, p.79

.. Schéma-générale-de-notre-algorithme-proposé, abord, des modèles de mélange sont estimés localement sur chaque site. Puis, ces modèles sont échangés et agrégés avec les modèles voisins, en utilisant un protocole de communication gossip. Notre méthode inclut une étape de détection et d'élimination des modèles non fiables dans le processus d'agrégation

.. Cette-figure-présente-une-partie-du-graphe, Les ellipses en pointillé sur chaque noeud représentent les modèles correspondants Le noeud (1) possède ici une liste de 6 voisins. Nous allons voir après, comment est obtenu le modèle global sur cet exemple, p.86

. Ensuite, =. Échantillons-composés-chacun-de-s-taille-modèles-À-partir-de-l-'ensemble-m-voisin, and M. .. {m-1,, Pour chaque échantillon, un algorithme itératif est appliqué pour améliorer sa qualité, en éliminant les modèles non fiables. Cet algorithme consiste à comparer la similarité entre les modèles M j ? M voisin et ceux dans S t . Puis les modèles M j les plus proches sont sélectionnés pour former à nouveau l'échantillon S t . La convergence est réalisée lorsque tous les échantillons deviennent stables, p.91