数据科学拓扑方法的各个方面。

IF 1.7 Q2 MATHEMATICS, APPLIED Foundations of data science (Springfield, Mo.) Pub Date : 2022-06-01 DOI:10.3934/fods.2022002

Jelena Grbić, Jie Wu, Kelin Xia, Guo-Wei Wei

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摘要

我们建立了一种新理论，通过同时适用于点云数据和图数据（包括超越成对交互的网络），统一了数据科学拓扑方法的各个方面。我们将简单复合物和超图概括为超超图，并建立了超超图同源性作为简单同源性的扩展。在应用的推动下，我们还引入了超持久同源性。

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ASPECTS OF TOPOLOGICAL APPROACHES FOR DATA SCIENCE.

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.

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