Stable Overlapping Replicator Dynamics for Brain Community Detection

A fundamental means for understanding the brain's organizational structure is to group its spatially disparate regions into functional subnetworks based on their interactions. Most community detection techniques are designed for generating partitions, but certain brain regions are known to interact with multiple subnetworks. Thus, the brain's underlying subnetworks necessarily overlap. In this paper, we propose a technique for identifying overlapping subnetworks from weighted graphs with statistical control over false node inclusion. Our technique improves upon the replicator dynamics formulation by incorporating a graph augmentation strategy to enable subnetwork overlaps, and a graph incrementation scheme for merging subnetworks that might be falsely split by replicator dynamics due to its stringent mutual similarity criterion in defining subnetworks. To statistically control for inclusion of false nodes into the detected subnetworks, we further present a procedure for integrating stability selection into our subnetwork identification technique. We refer to the resulting technique as stable overlapping replicator dynamics (SORD). Our experiments on synthetic data show significantly higher accuracy in subnetwork identification with SORD than several state-of-the-art techniques. We also demonstrate higher test-retest reliability in multiple network measures on the Human Connectome Project data. Further, we illustrate that SORD enables identification of neuroanatomically-meaningful subnetworks and network hubs.