Aspects of topological approaches for data science
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- 1 January 2022
- journal article
- research article
- Published by American Institute of Mathematical Sciences (AIMS) in Foundations of Data Science
- Vol. 4 (2) , 165-216
Abstract
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.Keywords
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