English(EN) First-order asymptotic expansions for spectral convergence of normalized graph Laplacians constructed from samples on manifolds

新方法扩展了流形上图拉普拉斯算子的谱收敛性分析

作者 PulseAugur 编辑部 · [1 个来源] · 2026-11-11 05:00

研究人员开发了一种方法，可以推导出归一化图拉普拉斯算子特征值和特征向量的一阶渐近展开。这些展开式是从黎曼流形上的样本构建的，并包含余项的集中不等式，从而建立了弱收敛结果。该分析的特点是不需要特征值的重数一假设，从而扩大了其在特征值重数可能重复的流形上的适用性。 AI

排序理由这是一篇研究论文，详细介绍了一种用于分析图拉普拉斯算子新数学方法。[lever_c_demoted from research: ic=1 ai=0.4]

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arXiv stat.ML TIER_1 English(EN) · Eunseong Bae, Wolfgang Polonik · 2026-11-11 05:00

流形上样本构建的归一化图拉普拉斯算子的谱收敛的一阶渐近展开

arXiv:2611.13623v1 Announce Type: cross Abstract: Under i.i.d. uniform sampling from a closed Riemannian manifold embedded in Euclidean space, we derive first-order asymptotic expansions for the eigenvalues and eigenvectors of symmetrically normalized graph Laplacians constructed…