Convergence Rate of the Symmetrically Normalized Graph Laplacian

Details Convergence Rate of the Symmetrically Normalized Graph Laplacian Convergence Rate of the Symmetrically Normalized Graph Laplacian

2011-01-07

arxiv.org/abs/1101.1428v1

Mathematics

Differential Geometry

Scientific paper

This short note aims at (re)proving that the symmetrically normalized graph
Laplacian $L=\Id - D^{-1/2}WD^{-1/2}$ (from a graph defined from a Gaussian
weighting kernel on a sampled smooth manifold) converges towards the continuous
Manifold Laplacian when the sampling become infinitely dense. The convergence
rate with respect to the number of samples $N$ is $O(1/N)$.

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