Title: Topological Brain Network Distances,
Abstract: Existing brain network distances are often based on matrix norms. The
element-wise differences in the existing matrix norms may fail to capture
underlying topological differences. Further, matrix norms are sensitive to
outliers. A major disadvantage to element-wise distance calculations is that it
could be severely affected even by a small number of extreme edge weights. Thus
it is necessary to develop network distances that recognize topology. In this
paper, we provide a survey of bottleneck, Gromov-Hausdorff (GH) and
Kolmogorov-Smirnov (KS) distances that are adapted for brain networks, and
compare them against matrix-norm based network distances. Bottleneck and
GH-distances are often used in persistent homology. However, they were rarely
utilized to measure similarity between brain networks. KS-distance is recently
introduced to measure the similarity between networks across different
filtration values. The performance analysis was conducted using the random
network simulations with the ground truths. Using a twin imaging study, which
provides biological ground truth, we demonstrate that the KS distance has the
ability to determine heritability.