Poincaré Embedding Reveals Edge-Based Functional Networks of the Brain

Abstract

Many approaches have been applied to fMRI data in order to understand the network organization of the brain. While the majority of these works defines networks as a collection of regions (i.e., nodes), there is ample evidence that defining networks as a collection of connections between regions (i.e., edges) offers numerous advantages, including a natural way of grouping regions into multiple networks. Here, we proposed a framework for creating edge-based networks from resting-state functional connectivity data. This framework relies on a novel embedding approach—based on the Poincaré embedding—to handle the large number of edges found in fMRI data (e.g., $O(N^2)$). We applied this framework to resting-state fMRI data from the Human Connectome Project and compared the resultant networks to networks derived from clustering nodes and from previously proposed methods for clustering edges. While previous methods for clustering edges failed to discover a valuable network representation of the human brain, the edge-based networks derived from clustering the Poincaré embedding showed clear and interpretable functional networks. Overall, our framework provides a novel tool for characterizing the functional network organization of the brain.