The Phd thesis defense of Maximilien Dreveton will take place on April, 6th, 2022 at 14:00 CET in room Euler violet at Inria Sophia Antipolis. You can also attend by Zoom.
Title: “Graph clustering and semi-supervised learning of non-binary, temporal and geometric networks”
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 belongs 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.
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.
