Detecting Differences Between Correlation-Matrix Populations due to Single-variable Perturbations, with Application to Resting State fMRI

Correlation matrices are widely used to analyze the interdependence of variables in various real-world scenarios. Often, a perturbation in a few variables leads to mild differences in many correlation coefficients associated with these variables. We propose an efficient low-dimensional model that characterizes these differences as a product of single-variable effects. We develop methods for point estimation, confidence intervals, and hypothesis testing for this model. Importantly, our methods can account for both the variability in individual correlation matrices and for within-group variability. In simulations, our model shows increased power compared to competing approaches. We use the model to analyze resting-state functional MRI correlation matrices in patients with transient global amnesia and healthy controls. Our model detects significant decreases in synchronization for the patient population in several brain regions, which could not have been detected using previous methods without prior knowledge. Our methods are available in the open-source package \emph{github.com/itamarfaran/corrpops}.