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Efficient and Robust Topological Data Analysis on Metric Spaces

Mickael Buchet 1 Frederic Chazal 1 Steve Y. Oudot 1 Donald R. Sheehy 1
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : We extend the notion of the distance to a measure from Euclidean space to probability measures on general metric spaces as a way to do topological data analysis in a way that is robust to noise and outliers. We then give an efficient way to approximate the sub-level sets of this function by a union of metric balls and extend previous results on sparse Rips filtrations to this setting. This robust and efficient approach to topological data analysis is illustrated with several examples from an implementation.
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Preprints, Working Papers, ...
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Contributor : Frédéric Chazal Connect in order to contact the contributor
Submitted on : Friday, June 7, 2013 - 3:41:19 PM
Last modification on : Friday, February 23, 2018 - 2:20:13 PM

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  • HAL Id : hal-00831729, version 1
  • ARXIV : 1306.0039



Mickael Buchet, Frederic Chazal, Steve Y. Oudot, Donald R. Sheehy. Efficient and Robust Topological Data Analysis on Metric Spaces. 2013. ⟨hal-00831729⟩



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