Since the first studies in functional connectivity, Pearson’s correlation has been the primary tool to determine relatedness between the activity of different brain locations. Over the years, concern over the information neglected by correlation pushed toward using different measures accounting for non-linearity. However, some studies suggest that, at the typical observation scale, a linear description of the brain captures a vast majority of the information. Therefore, we measured the fraction of information that would be lost using a linear description and which regions would be affected the most. We considered fMRI, EEG, iEEG, and single unit spikes to assess how the observation scale impacts the amount of non-linearity. We observe that the information loss is reduced for modalities with large temporal or spatial averaging (fMRI and EEG) and gains relevance on more fine descriptions of the activity (iEEG and single unit spikes). We conclude that for most human applications, Pearson’s correlation coefficient adequately describes pairwise interactions in time series from current recording techniques.
Significance Statement
In neuroimaging, as in other complex systems fields, the increasing interest in network inference by statistical dependencies (i.e. functional connectivity) invites advanced ways to quantify it. Various nonlinear measures, ultimately the Mutual Information, are used as alternatives to conventional linear Pearson’s correlation coefficient. We systematically assess the amount and reliability of detectable non-linearity of brain functional connectivity across imaging modalities and spatial scales. We demonstrate more pronounced nonlinearity in micro-scale recordings, while rather limited and unreliable in more accessible, noninvasive, large-scale modalities: functional magnetic resonance imaging and scalp electro-physiology. This fundamentally supports the use of robust and easily interpretable linear tools in large-scale neuroimaging, and important insights concerning the microscale connectivity nonlinearity, including the link to brain state dynamics.
