79 research outputs found
Sparse Dowker Nerves
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 \v{C}ech 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
-categories, and we introduce the concept of Dowker dissimilarities that can
be considered as a common generalization of metric spaces and networks.Comment: 25 page
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