Dynamical Persistent Homology via Wasserstein Gradient Flow
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
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| _version_ | 1866916508674818048 |
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| author | Wang, Minghua Xu, Jinhui |
| author_facet | Wang, Minghua Xu, Jinhui |
| contents | In this study, we introduce novel methodologies designed to adapt original data in response to the dynamics of persistence diagrams along Wasserstein gradient flows. Our research focuses on the development of algorithms that translate variations in persistence diagrams back into the data space. This advancement enables direct manipulation of the data, guided by observed changes in persistence diagrams, offering a powerful tool for data analysis and interpretation in the context of topological data analysis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03806 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamical Persistent Homology via Wasserstein Gradient Flow Wang, Minghua Xu, Jinhui Algebraic Topology Computational Geometry In this study, we introduce novel methodologies designed to adapt original data in response to the dynamics of persistence diagrams along Wasserstein gradient flows. Our research focuses on the development of algorithms that translate variations in persistence diagrams back into the data space. This advancement enables direct manipulation of the data, guided by observed changes in persistence diagrams, offering a powerful tool for data analysis and interpretation in the context of topological data analysis. |
| title | Dynamical Persistent Homology via Wasserstein Gradient Flow |
| topic | Algebraic Topology Computational Geometry |
| url | https://arxiv.org/abs/2412.03806 |