Abstract
Cycles or loops in a network embed higher-order interactions beyond pairwise relations. The cycles are essential for the parallel processing of information and enable feedback loops. Despite the fundamental importance of cycles in understanding the higher-order connectivity, identifying and extracting them are computationally prohibitive. This paper proposes a novel persistent homology-based framework for extracting and modelling cycles in brain networks using the Hodge Laplacian. The method is applied in discriminating the functional brain networks of males and females. The code for modeling cycles through the Hodge Laplacian is provided in https://github.com/laplcebeltrami/hodge.
This study is funded by NIH R01 EB022856, EB02875, NSF MDS-2010778.
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Dakurah, S., Anand, D.V., Chen, Z., Chung, M.K. (2022). Modelling Cycles in Brain Networks with the Hodge Laplacian. In: Wang, L., Dou, Q., Fletcher, P.T., Speidel, S., Li, S. (eds) Medical Image Computing and Computer Assisted Intervention – MICCAI 2022. MICCAI 2022. Lecture Notes in Computer Science, vol 13431. Springer, Cham. https://doi.org/10.1007/978-3-031-16431-6_31
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