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Graph clustering and semi-supervised learning of non-binary, temporal and geometric networks

Maximilien Dreveton 1
1 NEO - Network Engineering and Operations
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : The massive explosion of data collection led to a multi-disciplinary interest in the statistical inference of complex systems. In these systems, agents interact by pairs. Since similar agents tend to interact similarly, an important unsupervised learning problem consists of grouping the agents into communities or clusters based on the pairwise interactions. This thesis explore various aspects of this learning task.In particular, we study random graph models in which each node belong to a community (also called block) and the interactions between node pairs depend on the community structure. For those stochastic block models, we establish consistency thresholds for community recovery. These results allow for non-binary interactions, such as weighted, temporal or multiplex networks. In particular, it shows that in temporal networks with Markov interactions, consistent recovery of communities can be achieved for very sparse interactions, provided that the number of snapshots is large enough.We propose several algorithms for clustering temporal networks, such as spectral methods based on the persisting edges, or methods based on an online computation of the likelihood.We also study graph clustering in a semi-supervised setting. In this setting, an oracle provides the community memberships of a few nodes. This extra information helps to recover the community labels of the rest of the nodes.Finally, we investigate networks in which the nodes have a position in a metric space. In such geometric networks, we show that standard spectral methods (such as Spectral Clustering) fail at recovering the communities. We propose and analyze a spectral algorithm based on a higher-order eigenvector.
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Submitted on : Friday, May 13, 2022 - 9:55:32 AM
Last modification on : Saturday, May 14, 2022 - 3:31:39 AM


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  • HAL Id : tel-03667090, version 1



Maximilien Dreveton. Graph clustering and semi-supervised learning of non-binary, temporal and geometric networks. Artificial Intelligence [cs.AI]. Université Côte d'Azur, 2022. English. ⟨NNT : 2022COAZ4011⟩. ⟨tel-03667090⟩



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