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arXiv · 2106.02538

Bottleneck Profiles and Discrete Prokhorov Metrics for Persistence Diagrams

Paweł Dłotko·Niklas Hellmer
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Abstract

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 shortcomings of these metrics and show a way to investigate them in a systematic way by introducing bottleneck profiles. This leads to a notion of discrete Prokhorov metrics for persistence diagrams as a generalization of the Bottleneck distance. They satisfy a stability result and bounds with respect to Wasserstein metrics. We provide algorithms to compute the newly introduced quantities and end with an discussion about experiments.

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Paweł Dłotko, Niklas Hellmer. 2021-06-04. Bottleneck Profiles and Discrete Prokhorov Metrics for Persistence Diagrams. https://doi.org/10.1007/s00454-023-00498-w

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