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arXiv · 1709.00097

Weighted Persistent Homology

Greg Bell·Austin Lawson·Joshua Martin·James Rudzinski·Clifford Smyth
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Abstract

We introduce weighted versions of the classical \v{C}ech and Vietoris-Rips complexes. We show that a version of the Vietoris-Rips Lemma holds for these weighted complexes and that they enjoy appropriate stability properties. We also give some preliminary applications of these weighted complexes.

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Greg Bell, Austin Lawson, Joshua Martin, James Rudzinski, Clifford Smyth. 2017-08-31. Weighted Persistent Homology. https://doi.org/10.2140/involve.2019.12.823

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