Fused graphical lasso for brain networks with symmetries

TL;DR

This paper introduces the symmetric graphical lasso, a novel method for inferring brain connectivity networks from fMRI data that explicitly models hemispherical symmetries, improving understanding of brain structure and disorders.

Contribution

The paper proposes a fused graphical lasso with symmetry constraints and an efficient optimization algorithm to jointly learn brain networks and their symmetrical properties.

Findings

Successfully applied to real fMRI data from healthy and affected subjects.

Revealed differences in symmetry structures between healthy and disordered brains.

Demonstrated robustness of the method across different detrending techniques.

Abstract

Neuroimaging is the growing area of neuroscience devoted to produce data with the goal of capturing processes and dynamics of the human brain. We consider the problem of inferring the brain connectivity network from time dependent functional magnetic resonance imaging (fMRI) scans. To this aim we propose the symmetric graphical lasso, a penalized likelihood method with a fused type penalty function that takes into explicit account the natural symmetrical structure of the brain. Symmetric graphical lasso allows one to learn simultaneously both the network structure and a set of symmetries across the two hemispheres. We implement an alternating directions method of multipliers algorithm to solve the corresponding convex optimization problem. Furthermore, we apply our methods to estimate the brain networks of two subjects, one healthy and the other affected by a mental disorder, and to compare them with respect to their symmetric structure. The method applies once the temporal dependence characterising fMRI data has been accounted for and we compare the impact on the analysis of different detrending techniques on the estimated brain networks.