An Analysis of the Convergence of Graph Laplacians
Abstract
Existing approaches to analyzing the asymptotics of graph Laplacians typically assume a well-behaved kernel function with smoothness assumptions. We remove the smoothness assumption and generalize the analysis of graph Laplacians to include previously unstudied graphs including kNN graphs. We also introduce a kernel-free framework to analyze graph constructions with shrinking neighborhoods in general and apply it to analyze locally linear embedding (LLE). We also describe how, for a given limit operator, desirable properties such as a convergent spectrum and sparseness can be achieved by choosing the appropriate graph construction.
Cite
Text
Ting et al. "An Analysis of the Convergence of Graph Laplacians." International Conference on Machine Learning, 2010.Markdown
[Ting et al. "An Analysis of the Convergence of Graph Laplacians." International Conference on Machine Learning, 2010.](https://mlanthology.org/icml/2010/ting2010icml-analysis/)BibTeX
@inproceedings{ting2010icml-analysis,
title = {{An Analysis of the Convergence of Graph Laplacians}},
author = {Ting, Daniel and Huang, Ling and Jordan, Michael I.},
booktitle = {International Conference on Machine Learning},
year = {2010},
pages = {1079-1086},
url = {https://mlanthology.org/icml/2010/ting2010icml-analysis/}
}