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Jul, 2023
Fermat距离:度量逼近、谱收敛和聚类算法
Fermat Distances: Metric Approximation, Spectral Convergence, and Clustering Algorithms
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Nicolás García Trillos, Anna Little, Daniel McKenzie, James M. Murphy
TL;DR
通过引入几何和统计的论点,我们证明了在渐近意义下样本驱动的 Fermat 距离收敛于连续距离,并展示了离散图拉普拉斯算子和对应的连续算子的收敛情况和有效性。
Abstract
We analyze the convergence properties of
fermat distances
, a family of density-driven metrics defined on
riemannian manifolds
with an associated probability measure.
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