Aspects of topological approaches for data science-Reference-Cited by-同舟云学术

Aspects of topological approaches for data science

Published:2022 Issue:2 Volume:4 Page:165
ISSN:2639-8001
Container-title:Foundations of Data Science
language:
Short-container-title:FoDS

Author:

Grbić Jelena¹,Wu Jie²³,Xia Kelin⁴,Wei Guo-Wei⁵

Affiliation:

1. School of Mathematical Sciences, University of Southampton, Southampton, UK

2. School of Mathematical Sciences, Center of Topology and Geometry based Technology, Hebei Normal University, Yuhua District, Shijiazhuang, Hebei, 050024 China

3. Yanqi Lake Beijing Institute of Mathematica Sciences, Yanqihu, Huairou District, Beijing, 101408 China

4. School of Physical and Mathematical Sciences, Nanyang Technological University, SPMS-MAS-05-18, 21 Nanyang Link, 1, Singapore 63737

5. Department of Mathematics, Department of Computer Science and Engineering, Department of Biochemistry and Molecular Biology, Michigan State University, MI 48824, USA

Abstract

<p style='text-indent:20px;'>We establish a new theory which unifies various aspects of topological approaches for data science, by being applicable both to point cloud data and to graph data, including networks beyond pairwise interactions. We generalize simplicial complexes and hypergraphs to super-hypergraphs and establish super-hypergraph homology as an extension of simplicial homology. Driven by applications, we also introduce super-persistent homology.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

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