Abstract
This paper proposes a novel topological learning framework that integrates networks of different sizes and topology through persistent homology. Such challenging task is made possible through the introduction of a computationally efficient topological loss. The use of the proposed loss bypasses the intrinsic computational bottleneck associated with matching networks. We validate the method in extensive statistical simulations to assess its effectiveness when discriminating networks with different topology. The method is further demonstrated in a twin brain imaging study where we determine if brain networks are genetically heritable. The challenge here is due to the difficulty of overlaying the topologically different functional brain networks obtained from resting-state functional MRI onto the template structural brain network obtained through diffusion MRI.
Funding Statement
This study is funded by NIH Grants R01 EB022856, EB02875, and NSF Grant MDS-2010778.
Acknowledgments
We thank Hernando Ombao of King Abdullah University of Science and Technology (KAUST) for discussion on brain network modeling. We thank Gary Shiu of University of Wisconsin–Madison for discussion on stability theorem. We thank Li Shen of University of Pennsylvania for providing the template structural brain network used in our twin brain imaging study. We thank Shih-Gu Huang of National University of Singapore for providing fMRI preprocessing support.
Citation
Tananun Songdechakraiwut. Moo K. Chung. "Topological learning for brain networks." Ann. Appl. Stat. 17 (1) 403 - 433, March 2023. https://doi.org/10.1214/22-AOAS1633
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