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arXiv · 2512.20325

Top-K Exterior Power Persistent Homology: Algorithm, Structure, and Stability

Yoshihiro Maruyama
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Abstract

Exterior powers play important roles in persistent homology in computational geometry. In the present paper we study the problem of extracting the $K$ longest intervals of the exterior-power layers of a tame persistence module. We prove a structural decomposition theorem that organizes the exterior-power layers into monotone per-anchor streams with explicit multiplicities, enabling a best-first algorithm. We also show that the Top-$K$ length vector is $2$-Lipschitz under bottleneck perturbations of the input barcode, and prove a comparison-model lower bound. Our experiments confirm the theory, showing speedups over full enumeration in high overlap cases. By enabling efficient extraction of the most prominent features, our approach makes higher-order persistence feasible for large datasets and thus broadly applicable to machine learning, data science, and scientific computing.

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Yoshihiro Maruyama. 2025-12-23. Top-K Exterior Power Persistent Homology: Algorithm, Structure, and Stability. https://arxiv.org/abs/2512.20325

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