The code in this repository reproduces the experimental results on convergence rates for k-nearest neighbor graph infinity Laplacians from our paper
Bungert, Calder, and Roith. Uniform Convergence Rates for Lipschitz Learning on Graphs. IMA Journal of Numerical Analysis, 2022.
Feel free to use it and please refer to our paper when doing so.
@article{bungert2022uniform,
author = {Bungert, Leon and Calder, Jeff and Roith, Tim},
title = {Uniform convergence rates for Lipschitz learning on graphs},
journal = {IMA Journal of Numerical Analysis},
year = {2022},
month = {09},
doi = {10.1093/imanum/drac048}
}
The Python package GraphLearning is required to run the experiments. Install with
pip install graphlearning
The script aronsson_experiment.py runs convergence rate experiments, to see the usage run
python aronsson_experiment.py -h
The bash script all_experiments.sh contains the commands for running all experiments from our paper. The results of the experiments are saved in .csv files in the results folder. To generate the plots and figures from the paper run
python generate_plots.py
All figures are saved in the figures folder.
Our code verifies our convergence proofs for solutions of the graph infinity Laplacian equation
on a point cloud with constraint set
to an Absolutely Minimizing Lipschitz Extension on the continuum domain
with constraint set
, i.e., a solution of
where is the geodesic Lipschitz constant.
The relative scaling of the graph bandwidth to the resolution of the graph
, defined as Hausdorff distance between
and
can be set with the
-b option in all_experiments.sh.