Abstract
One of outstanding issues in brain network analysis is to extract common topological substructure shared by a group of individuals. Recently, methods to detect group-wise modular structure on graph Laplacians have been introduced. From the perspective of algebraic topology, the modules or clusters are the zeroth topology information of a topological space. Higher order topology information can be found in holes. In this study, we extend the concept of graph Laplacian to higher order Hodge Laplacian of weighted networks, and develop a group-level hole identification method via the Stiefel optimization. In experiments, we applied the proposed method to three synthetic data and Alzheimer’s disease neuroimaing initiative (ADNI) database. Experimental results showed that the coidentification of group-level hole structures helped to find the underlying topology information of brain networks that discriminate groups well.
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Acknowledgements
Data used in preparation of this article were obtained from the ADNI database http://adni.loni.usc.edu. This work is supported by NRF Grants funded by the Korean Government (No. 2013R1A1A2064593, No. 2016R1D1A1B03935463, No. 2015M3C7A1028926, No. 2017M3C7A1048079, No. 2016R1D1A1A02937497, No. 2017R1A5A1015626, and No. 2011-0030815), and NIH grant EB022856.
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Lee, H. et al. (2019). Coidentification of Group-Level Hole Structures in Brain Networks via Hodge Laplacian. In: Shen, D., et al. Medical Image Computing and Computer Assisted Intervention – MICCAI 2019. MICCAI 2019. Lecture Notes in Computer Science(), vol 11767. Springer, Cham. https://doi.org/10.1007/978-3-030-32251-9_74
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DOI: https://doi.org/10.1007/978-3-030-32251-9_74
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