Group-Wise Functional Community Detection through Joint Laplacian Diagonalization

There is a growing conviction that the understanding of the brain function can come through a deeper knowledge of the network connectivity between different brain areas. Resting state Functional Magnetic Resonance Imaging (rs-fMRI) is becoming one of the most important imaging modality widely used to understand network functionality. However, due to the variability at subject scale, mapping common networks across individuals is by now a real challenge. In this work we present a novel approach to group-wise community detection, i.e. identification of functional coherent sub-graphs across multiple subjects. This approach is based on a joint diagonalization of two or more graph Laplacians, aiming at finding a common eigenspace across individuals, over which clustering in fewer dimension can then be applied. This allows to identify common sub-networks across different graphs. We applied our method to rs-fMRI dataset of mouse brain finding most important sub-networks recently described in literature.