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2019 Weighted persistent homology
Gregory Bell, Austin Lawson, Joshua Martin, James Rudzinski, Clifford Smyth
Involve 12(5): 823-837 (2019). DOI: 10.2140/involve.2019.12.823

Abstract

We introduce weighted versions of the classical Čech 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.

Citation

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Gregory Bell. Austin Lawson. Joshua Martin. James Rudzinski. Clifford Smyth. "Weighted persistent homology." Involve 12 (5) 823 - 837, 2019. https://doi.org/10.2140/involve.2019.12.823

Information

Received: 9 June 2018; Revised: 20 September 2018; Accepted: 29 November 2018; Published: 2019
First available in Project Euclid: 29 May 2019

zbMATH: 07072556
MathSciNet: MR3954298
Digital Object Identifier: 10.2140/involve.2019.12.823

Subjects:
Primary: 55N35
Secondary: 55U99 , 68U10

Keywords: bottleneck distance , Čech complex , interleaving , persistence diagram , Persistent homology , stability , Vietoris–Rips complex , weighted persistent homology

Rights: Copyright © 2019 Mathematical Sciences Publishers

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Vol.12 • No. 5 • 2019
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