{"ID":2825824,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.20325","arxiv_id":"2512.20325","title":"Top-K Exterior Power Persistent Homology: Algorithm, Structure, and Stability","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.","short_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 mo...","url_abs":"https://arxiv.org/abs/2512.20325","url_pdf":"https://arxiv.org/pdf/2512.20325v1","authors":"[\"Yoshihiro Maruyama\"]","published":"2025-12-23T12:49:44Z","proceeding":"cs.CG","tasks":"[\"cs.CG\",\"cs.DM\",\"cs.LG\"]","methods":"[\"Generative Adversarial Network\"]","has_code":false}