Clustering by Deep Latent Position Model with Graph Convolutional Network

Dingge Liang (1, 2) , Marco Corneli (3, 2) , Charles Bouveyron (3, 2) , Pierre Latouche (4)

1 UniCA - Université Côte d'Azur
2 MAASAI - Modèles et algorithmes pour l’intelligence artificielle
3 LJAD - Laboratoire Jean Alexandre Dieudonné
4 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5

With the significant increase of interactions between individuals through numeric means, clustering of vertices in graphs has become a fundamental approach for analyzing large and complex networks. In this work, we propose the deep latent position model (DeepLPM), an end-to-end generative clustering approach which combines the widely used latent position model (LPM) for network analysis with a graph convolutional network (GCN) encoding strategy. Moreover, an original estimation algorithm is introduced to integrate the explicit optimization of the posterior clustering probabilities via variational inference and the implicit optimization using stochastic gradient descent for graph reconstruction. Numerical experiments on simulated scenarios highlight the ability of DeepLPM to self-penalize the evidence lower bound for selecting the intrinsic dimension of the latent space and the number of clusters, demonstrating its clustering capabilities compared to state-of-the-art methods. Finally, DeepLPM is further applied to an ecclesiastical network in Merovingian Gaul and to a citation network Cora to illustrate the practical interest in exploring large and complex real-world networks.

Mots clés: Network Analysis; Graph Clustering; Unsupervised Deep Learning; Graph Neural Networks

Domaines: Intelligence artificielle [cs.AI]; Réseaux sociaux et d'information [cs.SI]; Applications [stat.AP]

Dingge Liang, Marco Corneli, Charles Bouveyron, Pierre Latouche. Clustering by Deep Latent Position Model with Graph Convolutional Network. 2022. ⟨hal-03629104⟩