Weighted persistent homology

Gregory Bell; Austin Lawson; Joshua Martin; James Rudzinski; Clifford Smyth

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.

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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

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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

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