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Basic metric geometry of the bottleneck distance

Basic metric geometry of the bottleneck distance
Basic metric geometry of the bottleneck distance

Given a metric pair (X,A), i.e. a metric space X and a distinguished closed set A ⊂ X, one may construct in a functorial way a pointed pseudometric space D∞(X,A) of persistence diagrams equipped with the bottleneck distance. We investigate the basic metric properties of the spaces D∞(X,A) and obtain characterizations of their metrizability, completeness, separability, and geodesicity.

Bottleneck distance, metric pair, persistence diagram
0002-9939
3575-3591
Che, Mauricio
06168f22-25c1-48f2-8719-75c6da381594
Galaz-García, Fernando
629d488b-6be6-46a4-a224-c513b53a4934
Guijarro, Luis
b1f6921c-f690-4437-b851-82b7f61784db
Solis, Ingrid Membrillo
c458faf5-8cdb-4618-ba90-f8a90209f20a
Valiunas, Motiejus
23b32cdf-14c1-409c-9fc7-d53b54623233
Che, Mauricio
06168f22-25c1-48f2-8719-75c6da381594
Galaz-García, Fernando
629d488b-6be6-46a4-a224-c513b53a4934
Guijarro, Luis
b1f6921c-f690-4437-b851-82b7f61784db
Solis, Ingrid Membrillo
c458faf5-8cdb-4618-ba90-f8a90209f20a
Valiunas, Motiejus
23b32cdf-14c1-409c-9fc7-d53b54623233

Che, Mauricio, Galaz-García, Fernando, Guijarro, Luis, Solis, Ingrid Membrillo and Valiunas, Motiejus (2024) Basic metric geometry of the bottleneck distance. Proceedings of the American Mathematical Society, 152 (8), 3575-3591. (doi:10.1090/proc/16776).

Record type: Article

Abstract

Given a metric pair (X,A), i.e. a metric space X and a distinguished closed set A ⊂ X, one may construct in a functorial way a pointed pseudometric space D∞(X,A) of persistence diagrams equipped with the bottleneck distance. We investigate the basic metric properties of the spaces D∞(X,A) and obtain characterizations of their metrizability, completeness, separability, and geodesicity.

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2205.09718v2 - Accepted Manuscript
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More information

Accepted/In Press date: 4 January 2024
e-pub ahead of print date: 12 June 2024
Published date: August 2024
Additional Information: Publisher Copyright: © 2024 American Mathematical Society.
Keywords: Bottleneck distance, metric pair, persistence diagram
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Identifiers

Local EPrints ID: 493396
URI: http://eprints.soton.ac.uk/id/eprint/493396
DOI: doi:10.1090/proc/16776
ISSN: 0002-9939
PURE UUID: 962ae77c-a91e-4e66-be0b-78e2f88e248c
ORCID for Ingrid Membrillo Solis: ORCID iD orcid.org/0000-0002-9209-3042
ORCID for Motiejus Valiunas: ORCID iD orcid.org/0000-0003-1519-6643

Catalogue record

Date deposited: 02 Sep 2024 16:50
Last modified: 03 Sep 2024 02:00

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Contributors

Author: Mauricio Che
Author: Fernando Galaz-García
Author: Luis Guijarro
Author: Ingrid Membrillo Solis ORCID iD
Author: Motiejus Valiunas ORCID iD

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