Topological Distances Between Brain Networks

Introduction Many existing brain network distances are based on matrix norms. The element-wise differences may fail to capture underlying topological differences. Further, matrix norms are sensitive to outliers. A few extreme edge weights may severely affect the distance. There is a need to develop network distances that recognize topology. We introduce Gromov-Hausdorff (GH) and KolmogorovSmirnov (KS) distances. GH-distance is often used in persistent homology based brain network models. The superior performance of KS-distance is contrasted against matrix norms and GH-distance in simulations with the ground truths. The KS-distance is then applied in characterizing the multimodal MRI and DTI study of maltreated children.