30 citations · 180 across the 40 of their papers we have counts for
4 papers · 1 filter
Improved spectral convergence rates for graph Laplacians on epsilon-graphs and k-NN graphs
Jeff Calder, Nicolas Garcia Trillos
In this paper we improve the spectral convergence rates for graph-based approximations of Laplace-Beltrami operators constructed from random data. We utilize regularity of the cont…
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…
Geometric structure of graph Laplacian embeddings
Nicolas Garcia Trillos, Franca Hoffmann, Bamdad Hosseini
We analyze the spectral clustering procedure for identifying coarse structure in a data set , and in particular study the geometry of graph Laplacian embeddings wh…
A maximum principle argument for the uniform convergence of graph Laplacian regressors
Nicolas Garcia Trillos, Ryan Murray
This paper investigates the use of methods from partial differential equations and the Calculus of variations to study learning problems that are regularized using graph Laplacians…