12 citations · 35 across the 15 of their papers we have counts for
8 papers · 1 filter
Central limit theorems for the eigenvalues of graph Laplacians on data clouds
Chenghui Li, Nicolás García Trillos, Housen Li +1
Given i.i.d.\ samples from a distribution supported on a low dimensional manifold embedded in Eucliden space, we consider the graph Laplacian ope…
Minimax Rates for the Estimation of Eigenpairs of Weighted Laplace-Beltrami Operators on Manifolds
Nicolás García Trillos, Chenghui Li, Raghavendra Venkatraman
We study the problem of estimating eigenpairs of elliptic differential operators from samples of a distribution supported on a manifold . The operators discussed in the pape…
Fermat Distances: Metric Approximation, Spectral Convergence, and Clustering Algorithms
Nicolás García Trillos, Anna Little, Daniel McKenzie +1
We analyze the convergence properties of Fermat distances, a family of density-driven metrics defined on Riemannian manifolds with an associated probability measure. Fermat distanc…
Rates of Convergence for Regression with the Graph Poly-Laplacian
Nicolás García Trillos, Ryan Murray, Matthew Thorpe
In the (special) smoothing spline problem one considers a variational problem with a quadratic data fidelity penalty and Laplacian regularisation. Higher order regularity can be ob…
Clustering dynamics on graphs: from spectral clustering to mean shift through Fokker-Planck interpolation
Katy Craig, Nicolás García Trillos, Dejan Slepčev
In this work we build a unifying framework to interpolate between density-driven and geometry-based algorithms for data clustering, and specifically, to connect the mean shift algo…
Local Regularization of Noisy Point Clouds: Improved Global Geometric Estimates and Data Analysis
Nicolas Garcia Trillos, Daniel Sanz-Alonso, Ruiyi Yang
Several data analysis techniques employ similarity relationships between data points to uncover the intrinsic dimension and geometric structure of the underlying data-generating me…