From Graphs to Manifolds - Weak and Strong Pointwise Consistency of Graph Laplacians
Abstract
In the machine learning community it is generally believed that graph Laplacians corresponding to a finite sample of data points converge to a continuous Laplace operator if the sample size increases. Even though this assertion serves as a justification for many Laplacian-based algorithms, so far only some aspects of this claim have been rigorously proved. In this paper we close this gap by establishing the strong pointwise consistency of a family of graph Laplacians with data- dependent weights to some weighted Laplace operator. Our investigation also includes the important case where the data lies on a submanifold of ${\mathbb R}^{d}$ .
Cite
Text
Hein et al. "From Graphs to Manifolds - Weak and Strong Pointwise Consistency of Graph Laplacians." Annual Conference on Computational Learning Theory, 2005. doi:10.1007/11503415_32Markdown
[Hein et al. "From Graphs to Manifolds - Weak and Strong Pointwise Consistency of Graph Laplacians." Annual Conference on Computational Learning Theory, 2005.](https://mlanthology.org/colt/2005/hein2005colt-graphs/) doi:10.1007/11503415_32BibTeX
@inproceedings{hein2005colt-graphs,
title = {{From Graphs to Manifolds - Weak and Strong Pointwise Consistency of Graph Laplacians}},
author = {Hein, Matthias and Audibert, Jean-Yves and von Luxburg, Ulrike},
booktitle = {Annual Conference on Computational Learning Theory},
year = {2005},
pages = {470-485},
doi = {10.1007/11503415_32},
url = {https://mlanthology.org/colt/2005/hein2005colt-graphs/}
}