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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.26068 |
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| _version_ | 1866908999600832512 |
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| author | Kalinowski, Alexander |
| author_facet | Kalinowski, Alexander |
| contents | We study detection of collapse in high-dimensional point clouds, where mass concentrates near a lower-dimensional set relative to a non-collapsed geometry. We propose persistent homology-based test statistics under two well-studied filtrations, with cutoffs calibrated under a broad set of non-collapsed reference models. We benchmark power across three alternative collapse mechanisms (linear/spectral, nonlinear-support, and contamination/heterogeneity) and distill the results into a mechanism map guiding the choice of filtration and statistic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26068 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Calibrated Persistent Homology Tests for High-dimensional Collapse Detection Kalinowski, Alexander Computational Geometry We study detection of collapse in high-dimensional point clouds, where mass concentrates near a lower-dimensional set relative to a non-collapsed geometry. We propose persistent homology-based test statistics under two well-studied filtrations, with cutoffs calibrated under a broad set of non-collapsed reference models. We benchmark power across three alternative collapse mechanisms (linear/spectral, nonlinear-support, and contamination/heterogeneity) and distill the results into a mechanism map guiding the choice of filtration and statistic. |
| title | Calibrated Persistent Homology Tests for High-dimensional Collapse Detection |
| topic | Computational Geometry |
| url | https://arxiv.org/abs/2604.26068 |