数据科学的拓扑方法的各个方面。
ASPECTS OF TOPOLOGICAL APPROACHES FOR DATA SCIENCE.
作者信息
Grbić Jelena, Wu Jie, Xia Kelin, Wei Guo-Wei
机构信息
School of Mathematical Sciences, University of Southampton, Southampton, UK.
School of Mathematical Sciences, Center of Topology and Geometry based Technology, Hebei Normal University, Yuhua District, Shijiazhuang, Hebei, 050024 China.
出版信息
Found Data Sci. 2022 Jun;4(2):165-216. doi: 10.3934/fods.2022002.
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.
摘要
我们建立了一种新理论，该理论统一了数据科学拓扑方法的各个方面，既适用于点云数据，也适用于图数据，包括超越成对相互作用的网络。我们将单纯复形和超图推广到超超图，并建立超超图同调作为单纯同调的扩展。受应用驱动，我们还引入了超持久同调。
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