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Abstract In this work, we focus on explicitly nonlinear relationships in functional networks. We introduce a technique using normalized mutual information (NMI) that calculates the nonlinear relationship between different brain regions. We demonstrate our proposed approach using simulated data and then apply it to a dataset previously studied by Damaraju et al. This resting‐state fMRI data included 151 schizophrenia patients and 163 age‐ and gender‐matched healthy controls. We first decomposed these data using group independent component analysis (ICA) and yielded 47 functionally relevant intrinsic connectivity networks. Our analysis showed a modularized nonlinear relationship among brain functional networks that was particularly noticeable in the sensory and visual cortex. Interestingly, the modularity appears both meaningful and distinct from that revealed by the linear approach. Group analysis identified significant differences in explicitly nonlinear functional network connectivity (FNC) between schizophrenia patients and healthy controls, particularly in the visual cortex, with controls showing more nonlinearity (i.e., higher normalized mutual information between time courses with linear relationships removed) in most cases. Certain domains, including subcortical and auditory, showed relatively less nonlinear FNC (i.e., lower normalized mutual information), whereas links between the visual and other domains showed evidence of substantial nonlinear and modular properties. Overall, these results suggest that quantifying nonlinear dependencies of functional connectivity may provide a complementary and potentially important tool for studying brain function by exposing relevant variation that is typically ignored. Beyond this, we propose a method that captures both linear and nonlinear effects in a “boosted” approach. This method increases the sensitivity to group differences compared to the standard linear approach, at the cost of being unable to separate linear and nonlinear effects. 

Abstract Resting‐state functional network connectivity (rsFNC) has shown utility for identifying characteristic functional brain patterns in individuals with psychiatric and mood disorders, providing a promising avenue for biomarker development. However, several factors have precluded widespread clinical adoption of rsFNC diagnostics, namely a lack of standardized approaches for capturing comparable and reproducible imaging markers across individuals, as well as the disagreement on the amount of data required to robustly detect intrinsic connectivity networks (ICNs) and diagnostically relevant patterns of rsFNC at the individual subject level. Recently, spatially constrained independent component analysis (scICA) has been proposed as an automated method for extracting ICNs standardized to a chosen network template while still preserving individual variation. Leveraging the scICA methodology, which solves the former challenge of standardized neuroimaging markers, we investigate the latter challenge of identifying a minimally sufficient data length for clinical applications of resting‐state fMRI (rsfMRI). Using a dataset containing rsfMRI scans of individuals with schizophrenia and controls (M = 310) as well as simulated rsfMRI, we evaluated the robustness of ICN and rsFNC estimates at both the subject‐ and group‐level, as well as the performance of diagnostic classification, with respect to the length of the rsfMRI time course. We found individual estimates of ICNs and rsFNC from the full‐length (5 min) reference time course were sufficiently approximated with just 3–3.5 min of data (r = 0.85, 0.88, respectively), and significant differences in group‐average rsFNC could be sufficiently approximated with even less data, just 2 min (r = 0.86). These results from the shorter clinical data were largely consistent with the results from validation experiments using longer time series from both simulated (30 min) and real‐world (14 min) datasets, in which estimates of subject‐level FNC were reliably estimated with 3–5 min of data. Moreover, in the real‐world data we found rsFNC and ICN estimates generated across the full range of data lengths (0.5–14 min) more reliably matched those generated from the first 5 min of scan time than those generated from the last 5 min, suggesting increased influence of “late scan” noise factors such as fatigue or drowsiness may limit the reliability of FNC from data collected after 10+ min of scan time, further supporting the notion of shorter scans. Lastly, a diagnostic classification model trained on just 2 min of data retained 97%–98% classification accuracy relative to that of the full‐length reference model. Our results suggest that, when decomposed with scICA, rsfMRI scans of just 2–5 min show good clinical utility without significant loss of individual FNC information of longer scan lengths.