
Lipschitz regularity of graph Laplacians on random data clouds
In this paper we study Lipschitz regularity of elliptic PDEs on geometri...
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Error estimates for spectral convergence of the graph Laplacian on random geometric graphs towards the LaplaceBeltrami operator
We study the convergence of the graph Laplacian of a random geometric gr...
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Eigenconvergence of Gaussian kernelized graph Laplacian by manifold heat interpolation
This work studies the spectral convergence of graph Laplacian to the Lap...
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From graph cuts to isoperimetric inequalities: Convergence rates of Cheeger cuts on data clouds
In this work we study statistical properties of graphbased clustering a...
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Pseudolikelihoodbased Mestimation of random graphs with dependent edges and parameter vectors of increasing dimension
An important question in statistical network analysis is how to estimate...
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On the infinitedimensional QR algorithm
Spectral computations of infinitedimensional operators are notoriously ...
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Automorphisms and isogeny graphs of abelian varieties, with applications to the superspecial Richelot isogeny graph
We investigate special structures due to automorphisms in isogeny graphs...
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Improved spectral convergence rates for graph Laplacians on epsilongraphs and kNN graphs
In this paper we improve the spectral convergence rates for graphbased approximations of LaplaceBeltrami operators constructed from random data. We utilize regularity of the continuum eigenfunctions and strong pointwise consistency results to prove that spectral convergence rates are the same as the pointwise consistency rates for graph Laplacians. In particular, for an optimal choice of the graph connectivity ε, our results show that the eigenvalues and eigenvectors of the graph Laplacian converge to those of the LaplaceBeltrami operator at a rate of O(n^1/(m+4)), up to log factors, where m is the manifold dimension and n is the number of vertices in the graph. Our approach is general and allows us to analyze a large variety of graph constructions that include εgraphs and kNN graphs.
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