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arXiv · 2507.23762

Path representations in multiparameter persistent homology

Xudong Sun·René Corbet·Carsten Marr
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Abstract

Multiparameter persistence module can capture more topological differences across data instances compared to using a single parameter, where the well-studied matching distance investigates the distance along a straight line in the multiparameter space that gives the biggest difference. We propose to generalize the straight line to a monotone path filtration and offer software implementations.

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Xudong Sun, René Corbet, Carsten Marr. 2025-07-31. Path representations in multiparameter persistent homology. https://arxiv.org/abs/2507.23762

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