Robust Barycenters of Persistence Diagrams
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915741925638144 |
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| author | Sisouk, Keanu Tanguy, Eloi Delon, Julie Tierny, Julien |
| author_facet | Sisouk, Keanu Tanguy, Eloi Delon, Julie Tierny, Julien |
| contents | This short paper presents a general approach for computing robust Wasserstein barycenters of persistence diagrams. The classical method consists in computing assignment arithmetic means after finding the optimal transport plans between the barycenter and the persistence diagrams. However, this procedure only works for the transportation cost related to the $q$-Wasserstein distance $W_q$ when $q=2$. We adapt an alternative fixed-point method to compute a barycenter diagram for generic transportation costs ($q > 1$), in particular those robust to outliers, $q \in (1,2)$. We show the utility of our work in two applications: \emph{(i)} the clustering of persistence diagrams on their metric space and \emph{(ii)} the dictionary encoding of persistence diagrams. In both scenarios, we demonstrate the added robustness to outliers provided by our generalized framework. Our Python implementation is available at this address: https://github.com/Keanu-Sisouk/RobustBarycenter . |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14904 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robust Barycenters of Persistence Diagrams Sisouk, Keanu Tanguy, Eloi Delon, Julie Tierny, Julien Machine Learning Computational Geometry This short paper presents a general approach for computing robust Wasserstein barycenters of persistence diagrams. The classical method consists in computing assignment arithmetic means after finding the optimal transport plans between the barycenter and the persistence diagrams. However, this procedure only works for the transportation cost related to the $q$-Wasserstein distance $W_q$ when $q=2$. We adapt an alternative fixed-point method to compute a barycenter diagram for generic transportation costs ($q > 1$), in particular those robust to outliers, $q \in (1,2)$. We show the utility of our work in two applications: \emph{(i)} the clustering of persistence diagrams on their metric space and \emph{(ii)} the dictionary encoding of persistence diagrams. In both scenarios, we demonstrate the added robustness to outliers provided by our generalized framework. Our Python implementation is available at this address: https://github.com/Keanu-Sisouk/RobustBarycenter . |
| title | Robust Barycenters of Persistence Diagrams |
| topic | Machine Learning Computational Geometry |
| url | https://arxiv.org/abs/2509.14904 |