Sparse Dowker nerves
Sparse Dowker nerves
复制标题
稀疏的道克神经
DOI：
10.1007/s41468-019-00028-9
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
N. Blaser
中科院分区：
文献类型：
--
作者：
M. Brun;N. Blaser
We propose sparse versions of filtered simplicial complexes used to compute persistent homology of point clouds and of networks. In particular, we extend the Sparse Čech Complex of Cavanna et al. (A geometric perspective on sparse filtrations. CoRR, arXiv:1506.03797, 2015) from point clouds in convex metric spaces to point clouds in arbitrary metric spaces. Along the way we formulate interleaving in terms of strict 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2$$\end{document}-categories, and we introduce the concept of Dowker dissimilarities that can be considered as a common generalization of metric spaces and networks.
We propose sparse versions of filtered simplicial complexes used to compute persistent homology of point clouds and of networks. In particular, we extend the Sparse Čech Complex of Cavanna et al. (A geometric perspective on sparse filtrations. CoRR, arXiv:1506.03797, 2015) from point clouds in convex metric spaces to point clouds in arbitrary metric spaces. Along the way we formulate interleaving in terms of strict 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2$$\end{document}-categories, and we introduce the concept of Dowker dissimilarities that can be considered as a common generalization of metric spaces and networks.