Persistence Spheres: Bi-Continuous Linear Representations of Persistence Diagrams. Some Early Stage Results.

Matteo Pegoraro
Proceedings of the Geometry, Topology, and Machine Learning Workshop, PMLR 325:251-261, 2026.

Abstract

In this extended abstract, we present ongoing work on a novel functional representation of persistence diagrams (PDs). Building on the approach of \citet{gotovac2025topological}, we model PDs as scalar fields on the sphere using the lift zonoid representation of finite integrable measures. Unlike their method, however, our construction yields a bi-continuous operator that is stable with respect to the 1-Wasserstein distance.

Cite this Paper

BibTeX
@InProceedings{pmlr-v325-pegoraro26a, title = {Persistence Spheres: Bi-Continuous Linear Representations of Persistence Diagrams. Some Early Stage Results.}, author = {Pegoraro, Matteo}, booktitle = {Proceedings of the Geometry, Topology, and Machine Learning Workshop}, pages = {251--261}, year = {2026}, editor = {Bleher, Michael and Jensen, Freya and Maier, Levin and Taha, Diaaeldin and Wienhard, Anna}, volume = {325}, series = {Proceedings of Machine Learning Research}, month = {10--14 Nov}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v325/main/assets/pegoraro26a/pegoraro26a.pdf}, url = {https://proceedings.mlr.press/v325/pegoraro26a.html}, abstract = {In this extended abstract, we present ongoing work on a novel functional representation of persistence diagrams (PDs). Building on the approach of \citet{gotovac2025topological}, we model PDs as scalar fields on the sphere using the lift zonoid representation of finite integrable measures. Unlike their method, however, our construction yields a bi-continuous operator that is stable with respect to the 1-Wasserstein distance.} }
Endnote
%0 Conference Paper %T Persistence Spheres: Bi-Continuous Linear Representations of Persistence Diagrams. Some Early Stage Results. %A Matteo Pegoraro %B Proceedings of the Geometry, Topology, and Machine Learning Workshop %C Proceedings of Machine Learning Research %D 2026 %E Michael Bleher %E Freya Jensen %E Levin Maier %E Diaaeldin Taha %E Anna Wienhard %F pmlr-v325-pegoraro26a %I PMLR %P 251--261 %U https://proceedings.mlr.press/v325/pegoraro26a.html %V 325 %X In this extended abstract, we present ongoing work on a novel functional representation of persistence diagrams (PDs). Building on the approach of \citet{gotovac2025topological}, we model PDs as scalar fields on the sphere using the lift zonoid representation of finite integrable measures. Unlike their method, however, our construction yields a bi-continuous operator that is stable with respect to the 1-Wasserstein distance.
APA
Pegoraro, M.. (2026). Persistence Spheres: Bi-Continuous Linear Representations of Persistence Diagrams. Some Early Stage Results.. Proceedings of the Geometry, Topology, and Machine Learning Workshop, in Proceedings of Machine Learning Research 325:251-261 Available from https://proceedings.mlr.press/v325/pegoraro26a.html.

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