43 citations · 238 across the 28 of their papers we have counts for
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math.MG2019★ 26 cited
Rips complexes as nerves and a Functorial Dowker-Nerve Diagram
Žiga Virk
Using ideas of the Dowker duality we prove that the Rips complex at scale is homotopy equivalent to the nerve of a cover consisting of sets of prescribed diameter. We then deve…
math.MG2019★ 8 cited
The Space of Persistence Diagrams on Points Coarsely Embeds into Hilbert Space
Atish Mitra, Žiga Virk
We prove that the space of persistence diagrams on points (with the bottleneck or a Wasserstein distance) coarsely embeds into Hilbert space by showing it is of asymptotic dime…
cs.CG2019★ 3 cited
Topological Data Analysis in Information Space
Herbert Edelsbrunner, Ziga Virk, Hubert Wagner
Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images repre…