2025/12/23 by Yoshihiro Maruyama, Maruyama, Yoshihiro
Computer Science · Mathematics · #Advanced Graph Neural Networks #Computational Geometry (cs.CG) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Homotopy and Cohomology in Algebraic Topology #Machine Learning (cs.LG) #Topological and Geometric Data Analysis
paper · doi:10.48550/arxiv.2512.20325
openalex publication_date 2025/12/23 · openalex created_date 2025/12/25 · openalex updated_date 2026/07/28
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.