Random matrix theory tools for the predictive analysis of functional magnetic resonance imaging examinations

Random matrix theory (RMT) is an increasingly useful tool for understanding large, complex systems. Prior studies have examined functional magnetic resonance imaging (fMRI) scans using tools from RMT, with some success. However, RMT computations are highly sensitive to a number of analytic choices, and the robustness of findings involving RMT remains in question. We systematically investigate the usefulness of RMT on a wide variety of fMRI datasets using a rigorous predictive framework.

We develop open-source software to efficiently compute RMT features from fMRI images and examine the cross-validated predictive potential of eigenvalue and RMT-based features ("eigenfeatures") with classic machine-learning classifiers. We systematically vary pre-processing extent, normalization procedures, RMT unfolding procedures, and feature selection and compare the impact of these analytic choices on the distributions of cross-validated prediction performance for each combination of dataset binary classification task, classifier, and feature. To deal with class imbalance, we use the area under the receiver operating characteristic curve (AUROC) as the main performance metric.

Across all classification tasks and analytic choices, we find RMT- and eigenvalue-based "eigenfeatures" to have predictive utility more often than not (82.4% of median $$; median AUROC range across classification tasks 0.47 to 0.64). Simple baseline reductions on source timeseries, by contrast, were less useful (58.8% of median $$, median AUROC range across classification tasks 0.42 to 0.62). Additionally, eigenfeature AUROC distributions were overall more right-tailed than baseline features, suggesting greater predictive potential. However, performance distributions were wide and often significantly affected by analytic choices.

Eigenfeatures clearly have potential for understanding fMRI functional connectivity in a wide variety of scenarios. The utility of these features is strongly dependent on analytic decisions, suggesting caution when interpreting past and future studies applying RMT to fMRI. However, our study demonstrates that the inclusion of RMT statistics in fMRI investigations could improve prediction performances across a wide variety of phenomena.