Covariance shrinkage can assess and improve functional connectomes

Abstract

Connectomes derived from resting-state functional MRI scans have significantly benefited from the development of dedicated fMRI motion correction and denoising algorithms. But they are based on empirical correlations that can produce unreliable results in high dimension low sample size settings. A family of statistical estimators, the covariance shrinkage methods, could mitigate this issue. Unfortunately, these methods have rarely been used to correct functional connectomes and no extensive experiment has been conducted so far to compare the shrinkage methods available for this task. In this work, we propose to fix this issue by processing a benchmark dataset made of a thousand high-resolution resting-state fMRI scans provided by the Human Connectome Project to compare the ability of five prominent covariance shrinkage methods to produce reliable functional connectomes at different spatial resolutions and scans duration: the pioneer linear covariance shrinkage method introduced by Ledoit and Wolf, the Oracle Approximating Shrinkage, the QuEST method, the NERCOME method, and a recent analytical approximation of the QuEST approach. Our experiments establish that all covariance shrinkage methods significantly improve functional connectomes derived from short fMRI scans. The Oracle Approximating Shrinkage and the QuEST method produced the best results. Lastly, we present shrinkage intensity charts that can be used for designing and analyzing fMRI studies. These charts indicate that sparse connectomes are difficult to estimate from short fMRI scans, and they describe a range of settings where dynamic functional connectivity should not be computed.

Keywords: Covariance shrinkage; Dynamic connectivity; Resting-state fmri.