Community Detection From Multiple Observations: From Product Graph Model to Brain Applications

This paper proposes a multilayer graph model for community detection based on multiple observations. This scenario is common when different estimators are used to infer graph edges from signals at the nodes, or when various signal measurements are taken. The multilayer network stacks these graph observations at different layers and links replica nodes at adjacent layers. This configuration corresponds to the Cartesian product between the ground truth graph and a path graph, where the number of nodes matches the number of observations. Using the algebraic structure of the Laplacian of the Cartesian multilayer network, we infer a subset of the eigenvectors of the true graph and perform community detection. Experimental results on synthetic graphs demonstrate the accuracy of the method, which outperforms state-of-the-art approaches in correctly detecting graph communities. Finally, we apply our method to distinguish between different brain networks derived from real EEG data collected during motor imagery experiments. We conclude that our approach is promising for identifying graph communities when multiple graph observations are available, and it shows potential for applications such as EEG-based motor imagery applications.