Abstract
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. Thus it is necessary to develop network distances that recognize topology. In this paper, we introduce Gromov-Hausdorff (GH) and Kolmogorov-Smirnov (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 random network simulations with the ground truths. The KS-distance is then applied in characterizing the multimodal MRI and DTI study of maltreated children.
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Acknowledgements
This work is supported by NIH Grants MH61285, MH68858, MH84051, UL1TR000427, Brain Initiative Grant EB022856 and Basic Science Research Program through the National Research Foundation (NRF) of Korea (NRF-2016R1D1A1B03935463). M.K.C. would like to thank professor A.M. Mathai of McGill University for asking to prove the convergence of KS test in a homework. That homework motivated the construction of KS-distance for graphs.
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Chung, M.K., Lee, H., Solo, V., Davidson, R.J., Pollak, S.D. (2017). Topological Distances Between Brain Networks. In: Wu, G., Laurienti, P., Bonilha, L., Munsell, B. (eds) Connectomics in NeuroImaging. CNI 2017. Lecture Notes in Computer Science(), vol 10511. Springer, Cham. https://doi.org/10.1007/978-3-319-67159-8_19
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