Coalescent embedding in the hyperbolic space unsupervisedly discloses the hidden geometry of the brain

TL;DR

This study demonstrates that coalescent embedding in hyperbolic space can accurately uncover the hidden geometric structure of brain networks, revealing neuroanatomical organization and detecting pathological changes in Parkinson's Disease.

Contribution

It introduces the use of hyperbolic coalescent embedding to reconstruct brain network geometry and identify disease-related alterations without supervision.

Findings

Accurately reconstructs brain network geometry in hyperbolic space.

Reveals the relationship between network geometry and neuroanatomical lobes.

Detects geometrical changes associated with Parkinson's Disease.

Abstract

The human brain displays a complex network topology, whose structural organization is widely studied using diffusion tensor imaging. The original geometry from which emerges the network topology is known, as well as the localization of the network nodes in respect to the brain morphology and anatomy. One of the most challenging problems of current network science is to infer the latent geometry from the mere topology of a complex network. The human brain structural connectome represents the perfect benchmark to test algorithms aimed to solve this problem. Coalescent embedding was recently designed to map a complex network in the hyperbolic space, inferring the node angular coordinates. Here we show that this methodology is able to unsupervisedly reconstruct the latent geometry of the brain with an incredible accuracy and that the intrinsic geometry of the brain networks strongly relates to the lobes organization known in neuroanatomy. Furthermore, coalescent embedding allowed the detection of geometrical pathological changes in the connectomes of Parkinson's Disease patients. The present study represents the first evidence of brain networks' angular coalescence in the hyperbolic space, opening a completely new perspective, possibly towards the realization of latent geometry network markers for evaluation of brain disorders and pathologies.