Abstract:Given i.i.d. observations uniformly distributed on a closed submanifold of the Euclidean space, we study higher-order generalizations of graph Laplacians, so-called Hodge Laplacians on graphs, as approximations of the Laplace-Beltrami operator on differential forms. Our main result is a high-probability error bound for the associated Dirichlet forms. This bound improves existing Dirichlet form error bounds for graph Laplacians in the context of Laplacian Eigenmaps, and it provides insights into the Betti numbers studied in topological data analysis and the complementing positive part of the spectrum.
From: Martin Wahl [view email]
[v1]
Fri, 4 Apr 2025 13:18:32 UTC (30 KB)
[v2]
Fri, 17 Jul 2026 09:01:18 UTC (3,539 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。