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2018 Weighted persistent homology
Shiquan Ren, Chengyuan Wu, Jie Wu
Rocky Mountain J. Math. 48(8): 2661-2687 (2018). DOI: 10.1216/RMJ-2018-48-8-2661

Abstract

In this paper, we develop the theory of weighted persistent homology. In 1990, Dawson was the first to study in depth the homology of weighted simplicial complexes. We generalize the definitions of weighted simplicial complex and the homology of weighted simplicial complex to allow weights in an integral domain $R$. Then, we study the resulting weighted persistent homology. We show that weighted persistent homology can distinguish between filtrations that ordinary persistent homology does not distinguish. For example, if there is a point considered as special, weighted persistent homology can tell when a cycle containing the point is formed or has disappeared.

Citation

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Shiquan Ren. Chengyuan Wu. Jie Wu. "Weighted persistent homology." Rocky Mountain J. Math. 48 (8) 2661 - 2687, 2018. https://doi.org/10.1216/RMJ-2018-48-8-2661

Information

Published: 2018
First available in Project Euclid: 30 December 2018

zbMATH: 06999279
MathSciNet: MR3894998
Digital Object Identifier: 10.1216/RMJ-2018-48-8-2661

Subjects:
Primary: 55N35, 55U10
Secondary: 55N99

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 8 • 2018
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