Vol. 12, No. 5, 2019

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Weighted persistent homology

Gregory Bell, Austin Lawson, Joshua Martin, James Rudzinski and Clifford Smyth

Vol. 12 (2019), No. 5, 823–837
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.

Keywords
persistent homology, weighted persistent homology, stability, Vietoris–Rips complex, Čech complex, interleaving, bottleneck distance, persistence diagram
Mathematical Subject Classification 2010
Primary: 55N35
Secondary: 55U99, 68U10
Milestones
Received: 9 June 2018
Revised: 20 September 2018
Accepted: 29 November 2018
Published: 22 May 2019

Communicated by Józef H. Przytycki
Authors
Gregory Bell
Department of Mathematics and Statistics
The University of North Carolina at Greensboro
Greensboro, NC
United States
Austin Lawson
Department of Mathematics and Statistics
The University of North Carolina at Greensboro
Mount Airy, NC
United States
Joshua Martin
Department of Mathematics and Statistics
The University of North Carolina at Greensboro
Greensboro, NC
United States
James Rudzinski
Department of Mathematics and Statistics
The University of North Carolina at Greensboro
Greensboro, NC
United States
Clifford Smyth
Department of Mathematics and Statistics
The University of North Carolina at Greensboro
Greensboro, NC
United States