2021/02/17 by Moo K. Chung, Alexander Smith, Chung, Moo K. +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Algebraic Topology (math.AT) #Bioinformatics and Genomic Networks #Computational Geometry (cs.CG) #FOS: Biological sciences #FOS: Computer and information sciences #FOS: Mathematics #Neurons and Cognition (q-bio.NC) #Topological and Geometric Data Analysis #cs.CG #math.AT #q-bio.NC
paper · pdf · doi:10.48550/arxiv.2102.08623
arxiv created 2021/02/17 · openalex publication_date 2021/02/17 · arxiv updated 2021/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Almost all statistical and machine learning methods in analyzing brain networks rely on distances and loss functions, which are mostly Euclidean or matrix norms. The Euclidean or matrix distances may fail to capture underlying subtle topological differences in brain networks. Further, Euclidean distances are sensitive to outliers. A few extreme edge weights may severely affect the distance. Thus it is necessary to use distances and loss functions that recognize topology of data. In this review paper, we survey various topological distance and loss functions from topological data analysis (TDA) and persistent homology that can be used in brain network analysis more effectively. Although there are many recent brain imaging studies that are based on TDA methods, possibly due to the lack of method awareness, TDA has not taken as the mainstream tool in brain imaging field yet. The main purpose of this paper is provide the relevant technical survey of these powerful tools that are immediately applicable to brain network data.