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arXiv · 2604.26068

Calibrated Persistent Homology Tests for High-dimensional Collapse Detection

Alexander Kalinowski
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Abstract

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.

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Alexander Kalinowski. 2026-04-28. Calibrated Persistent Homology Tests for High-dimensional Collapse Detection. https://arxiv.org/abs/2604.26068

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