2018/11/11 by Hyekyoung Lee, Moo K. Chung, Lee, Hyekyoung +11
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Medicine · #Algorithm #Alzheimer's disease research and treatments #Artificial intelligence #Betti number #Bioinformatics and Genomic Networks #Cluster analysis #Combinatorics #Complex network #Computer science #FOS: Biological sciences #Mathematics #Pattern recognition (psychology) #Persistent homology #Pure mathematics #Quantitative Methods (q-bio.QM) #Substructure #Topological and Geometric Data Analysis #Topological data analysis #Topology (electrical circuits) #q-bio.QM
paper · pdf · doi:10.48550/arxiv.1811.04355
published in arXiv (Cornell University) (Cornell University) · The paper is accepted for publication at the 7th Workshop on Computational Topology in Image Context (CTIC) (http://www.ctic2019.uma.es)
arxiv created 2018/11/11 · openalex publication_date 2018/11/11 · arxiv updated 2018/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Persistent homology has been applied to brain network analysis for finding\nthe shape of brain networks across multiple thresholds. In the persistent\nhomology, the shape of networks is often quantified by the sequence of\nk-dimensional holes and Betti numbers.The Betti numbers are more widely used\nthan holes themselves in topological brain network analysis. However, the holes\nshow the local connectivity of networks, and they can be very informative\nfeatures in analysis. In this study, we propose a new method of measuring\nnetwork differences based on the dissimilarity measure of harmonic holes (HHs).\nThe HHs, which represent the substructure of brain networks, are extracted by\nthe Hodge Laplacian of brain networks. We also find the most contributed HHs to\nthe network difference based on the HH dissimilarity. We applied our proposed\nmethod to clustering the networks of 4 groups, normal control (NC), stable and\nprogressive mild cognitive impairment (sMCI and pMCI), and Alzheimer's disease\n(AD). The results showed that the clustering performance of the proposed method\nwas better than that of network distances based on only the global change of\ntopology.\n