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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
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Abstract |
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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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Keywords
persistent homology, weighted persistent homology,
stability, Vietoris–Rips complex, Čech complex,
interleaving, bottleneck distance, persistence diagram
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Mathematical Subject Classification 2010
Primary: 55N35
Secondary: 55U99, 68U10
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Milestones
Received: 9 June 2018
Revised: 20 September 2018
Accepted: 29 November 2018
Published: 22 May 2019
Communicated by Józef H. Przytycki
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Authors |
| Gregory Bell | |
| Department of Mathematics and
Statistics The University of North Carolina at Greensboro Greensboro, NC United States |
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| Austin Lawson | |
| Department of Mathematics and
Statistics The University of North Carolina at Greensboro Mount Airy, NC United States |
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| Joshua Martin | |
| Department of Mathematics and
Statistics The University of North Carolina at Greensboro Greensboro, NC United States |
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| James Rudzinski | |
| Department of Mathematics and
Statistics The University of North Carolina at Greensboro Greensboro, NC United States |
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| Clifford Smyth | |
| Department of Mathematics and
Statistics The University of North Carolina at Greensboro Greensboro, NC United States |
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