Sparse Dowker Nerves

Abstract

We propose sparse versions of filtered simplicial complexes used to compte persistent homology of point clouds and of networks. In particular we extend a slight variation of the Sparse Čech Complex of Cavanna, Jahanseir and Sheehy from point clouds in Cartesian space to point clouds in arbitrary metric spaces. Along the way we formulate interleaving in terms of strict $2$-categories, and we introduce the concept of Dowker dissimilarities that can be considered as a common generalization of metric spaces and networks.

25 pages

References in corpus (2)

• Strong Collapse for Persistence
• Universality of the Homotopy Interleaving Distance

Cited by in corpus (3)

• Metric Comparisons of Relations
• Sparse Filtered Nerves
• Sparse Nerves in Practice