6 citations · 7 across the 3 of their papers we have counts for
4 papers
Density Sensitive Bifiltered Dowker Complexes via Total Weight
Niklas Hellmer, Jan Spaliński
In this paper, we introduce new density-sensitive bifiltrations for data using the framework of Dowker complexes. Previously, Dowker complexes were studied to address directional o…
When Do Two Distributions Yield the Same Expected Euler Characteristic Curve in the Thermodynamic Limit?
Tobias Fleckenstein, Niklas Hellmer
Let be a probability distribution on which admits a bounded density. We investigate the Euler characteristic of the Čech complex on points sampled from i…
Topology-Driven Goodness-of-Fit Tests in Arbitrary Dimensions
Paweł Dłotko, Niklas Hellmer, Łukasz Stettner +1
This paper adopts a tool from computational topology, the Euler characteristic curve (ECC) of a sample, to perform one- and two-sample goodness of fit tests. We call our procedure…
Bottleneck Profiles and Discrete Prokhorov Metrics for Persistence Diagrams
Paweł Dłotko, Niklas Hellmer
In topological data analysis (TDA), persistence diagrams have been a succesful tool. To compare them, Wasserstein and Bottleneck distances are commonly used. We address the shortco…