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Persistent Homology for High-dimensional Data Based on Spectral Methods
May 9, 2024, 4:42 a.m. | Sebastian Damrich, Philipp Berens, Dmitry Kobak
cs.LG updates on arXiv.org arxiv.org
Abstract: Persistent homology is a popular computational tool for analyzing the topology of point clouds, such as the presence of loops or voids. However, many real-world datasets with low intrinsic dimensionality reside in an ambient space of much higher dimensionality. We show that in this case traditional persistent homology becomes very sensitive to noise and fails to detect the correct topology. The same holds true for existing refinements of persistent homology. As a remedy, we find …
abstract ambient arxiv case computational cs.lg data datasets dimensionality however intrinsic loops low math.at popular show space tool topology type world
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