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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.16682 |
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| _version_ | 1866911219999309824 |
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| author | Eryilmaz, Omer Bahadir Katar, Cihan Little, Max A. |
| author_facet | Eryilmaz, Omer Bahadir Katar, Cihan Little, Max A. |
| contents | We introduce ellipsoidal filtration, a novel method for persistent homology, and demonstrate its effectiveness in denoising recurrent signals. Unlike standard Rips filtrations, which use isotropic neighbourhoods and ignore the signal's direction of evolution, our approach constructs ellipsoids aligned with local gradients to capture trajectory flow. The death scale of the most persistent H_1 feature defines a data-driven neighbourhood for averaging. Experiments on synthetic signals show that our method achieves better noise reduction than both topological and moving-average filters, especially for low-amplitude components. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_16682 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ellipsoidal Filtration for Topological Denoising of Recurrent Signals Eryilmaz, Omer Bahadir Katar, Cihan Little, Max A. Computational Geometry 55N31, 55U10, 68T10 We introduce ellipsoidal filtration, a novel method for persistent homology, and demonstrate its effectiveness in denoising recurrent signals. Unlike standard Rips filtrations, which use isotropic neighbourhoods and ignore the signal's direction of evolution, our approach constructs ellipsoids aligned with local gradients to capture trajectory flow. The death scale of the most persistent H_1 feature defines a data-driven neighbourhood for averaging. Experiments on synthetic signals show that our method achieves better noise reduction than both topological and moving-average filters, especially for low-amplitude components. |
| title | Ellipsoidal Filtration for Topological Denoising of Recurrent Signals |
| topic | Computational Geometry 55N31, 55U10, 68T10 |
| url | https://arxiv.org/abs/2510.16682 |