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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.20954 |
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| _version_ | 1866917105283104768 |
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| author | Minian, Elias Gabriel |
| author_facet | Minian, Elias Gabriel |
| contents | We introduce a subsampling method for topological data analysis based on strong collapses of simplicial complexes. Given a point cloud and a scale parameter $δ$, we construct a subsampling that preserves both global and local topological features while significantly reducing computational complexity of persistent homology calculations. We illustrate the effectiveness of our approach through experiments on synthetic and real datasets, showing improved persistence approximations compared to other subsampling techniques. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20954 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $δ$-core subsampling, strong collapses and TDA Minian, Elias Gabriel Computational Geometry Data Structures and Algorithms Algebraic Topology 55N31, 62R40, 68U05 We introduce a subsampling method for topological data analysis based on strong collapses of simplicial complexes. Given a point cloud and a scale parameter $δ$, we construct a subsampling that preserves both global and local topological features while significantly reducing computational complexity of persistent homology calculations. We illustrate the effectiveness of our approach through experiments on synthetic and real datasets, showing improved persistence approximations compared to other subsampling techniques. |
| title | $δ$-core subsampling, strong collapses and TDA |
| topic | Computational Geometry Data Structures and Algorithms Algebraic Topology 55N31, 62R40, 68U05 |
| url | https://arxiv.org/abs/2511.20954 |