Phase Angle Spatial Embedding (PhASE) - A Kernel Method for Studying the Topology of the Human Functional Connectome.

Modern resting-state functional magnetic resonance imaging (rs-fMRI) provides a wealth of information about the inherent functional connectivity of the human brain. However, understanding the role of negative correlations and the nonlinear topology of rs-fMRI remains a challenge. To address these challenges, we propose a novel graph embedding technique, phase angle spatial embedding (PhASE), to study the " intrinsic geometry" of the functional connectome. PhASE both incorporates negative correlations as well as reformulates the connectome modularity problem as a kernel two-sample test, using a kernel method that induces a maximum mean discrepancy (MMD) in a reproducing kernel Hilbert space (RKHS). By solving a graph partition that maximizes this MMD, PhASE identifies the most functionally distinct brain modules. As a test case, we analyzed a public rs-fMRI dataset to compare male and female connectomes using PhASE and minimum spanning tree inferential statistics. These results show statistically significant differences between male and female resting-state brain networks, demonstrating PhASE to be a robust tool for connectome analysis.