A Geometric Approach to Brain Network Connectivity

We present an exploratory data analysis tool for visualizing and formal testing of the symmetric positive definite matrices (e.g., covariance, spectral and coherence matrices) in a multi-subject experimental setting. Our work is motivated by our clinical collaborator’s interest to determine association between functional brain connectivity (as measured by coherence) and patients’ response to treatment. For each study participant, the geometric surface boxplot (GSBox) is developed to characterize the distribution of coherence matrices through the median matrix and the 50% most central region of the data. The GSBox will also be used to detect the outlier coherence matrices as in the classical boxplot. To investigate the treatment effect, we develop a rank-based nonparametric approach to test for significant differences in coherence matrices between treatment and control groups. The proposed method is applied to a study on infantile spasms to determine the potential impact of functional brain connectivity on the infants’ response to treatment. Supplementary materials for this article are available online.