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Topological data analysis and topological deep learning beyond persistent homology: a review

Crossref DOI link: https://doi.org/10.1007/s10462-025-11462-w

Published Online: 2025-12-21

Update policy: https://doi.org/10.1007/springer_crossmark_policy

Authors

Su, Zhe https://orcid.org/0000-0003-3499-6814
Liu, Xiang https://orcid.org/0000-0001-6046-1405
Hamdan, Layal Bou

Maroulas, Vasileios https://orcid.org/0000-0002-3412-6766
Wu, Jie https://orcid.org/0000-0003-2445-6750
Carlsson, Gunnar

Wei, Guo-Wei https://orcid.org/0000-0002-5781-2937
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Text and Data Mining valid from 2025-12-21

Version of Record valid from 2026-01-14
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Article History

Received: 18 July 2025

Accepted: 2 December 2025

First Online: 21 December 2025

Declarations

:

: The authors declare no Conflict of interest.