Comparing Functional Connectivity Matrices: A Geometry-Aware Approach applied to Participant Identification

Abstract

Understanding the correlation structure associated with multiple brain measurements informs about potential "functional groupings" and network organization. The correlation structure can be conveniently captured in a matrix format that summarizes the relationships among a set of brain measurements involving two regions, for example. Such functional connectivity matrix is an important component of many types of investigation focusing on network-level properties of the brain, including clustering brain states, characterizing dynamic functional states, performing participant identification (so-called "fingerprinting") understanding how tasks reconfigure brain networks, and inter-subject correlation analysis. In these investigations, some notion of proximity or similarity of functional connectivity matrices is employed, such as their Euclidean distance or Pearson correlation (by correlating the matrix entries). Here, we propose the use of a geodesic distance metric that reflects the underlying non-Euclidean geometry of functional correlation matrices. The approach is evaluated in the context of participant identification (fingerprinting): given a participant's functional connectivity matrix based on resting-state or task data, how effectively can the participant be identified? Using geodesic distance, identification accuracy was over 95% on resting-state data, and exceeded the Pearson correlation approach by 20%. For whole-cortex regions, accuracy improved on a range of tasks by between 2% and as much as 20%. We also investigated identification using pairs of subnetworks (say, dorsal attention plus default mode), and particular combinations improved accuracy over whole-cortex participant identification by over 10%. The geodesic distance also outperformed Pearson correlation when the former employed a fourth of the data as the latter. Finally, we suggest that low-dimensional distance visualizations based on the geodesic approach help uncover the geometry of task functional connectivity in relation to that during resting-state. We propose that the use of the geodesic distance is an effective way to compare the correlation structure of the brain across a broad range of studies.

Functional connectivity of EEG is subject-specific, associated with phenotype, and different from fMRI

“…(delta, r = 0.052, p = 0.19; theta, r = 0.078, p = 0.58; alpha, r = 0.103, p = 0.45; beta, r = 0.102, p = 0.89, broadband, r = 0.12, p = 0.75). We confirm these findings using three other measures of similarity, image intraclass correlation coefficient (I2C2) ( Shou et al, 2013 ), Multiscale Graph Correlation (MGC) algorithm ( Shen et al, 2018 ; Vogelsteinetal., 2019 ) and geodesic distance ( Venkatesh etal., 2020 ) (see Supplement ). Given these results and the distinct clusters of connectivity shown in Fig.…”

Typicality of Functional Connectivity robustly captures motion artifacts in rs-fMRI across datasets, atlases and preprocessing pipelines

“…Instead of TFC, we also tried a method based on Euclidean L 2 distance (Ponsoda et al, 2017) from the typical FC matrix and mean geodesic distance from the cohort (Venkatesh et al, 2020). Unlike TFC measure, which shows significant both Spearman and Pearson quality-motion correlations, the correlations of L 2 distance with motion were significant only for Pearson correlation (r F D P = 0.22, p = 0.003) because this relationship was driven mainly by outliers.…”

Brainprints: identifying individuals from magnetoencephalograms

“…For example, functional connectivity at different bands has been used to identify twins from other participants [17]. Other feature similarity function m(·, ·) may also be used to improve accuracy [38]. Figure S1: Layout of the sensors for FST, HP, and SEN data (306-channel Elekta Neuromag system).…”