Choosing the Parameter of the Fermat Distance: Navigating Geometry and Noise
Abstract
The Fermat distance has been recently established as a valuable tool for machine learning tasks when a natural distance is not directly available to the practitioner or to improve the results given by Euclidean distances by exploiting the geometrical and statistical properties of the dataset. This distance depends on a parameter $\alpha$ that significantly affects the performance of subsequent tasks. Ideally, the value of $\alpha$ should be large enough to navigate the geometric intricacies inherent to the problem. At the same time, it should remain restrained enough to avoid any deleterious effects stemming from noise during the distance estimation process. We study both theoretically and through simulations how to select this parameter.
Cite
Text
Chazal et al. "Choosing the Parameter of the Fermat Distance: Navigating Geometry and Noise." Transactions on Machine Learning Research, 2024.Markdown
[Chazal et al. "Choosing the Parameter of the Fermat Distance: Navigating Geometry and Noise." Transactions on Machine Learning Research, 2024.](https://mlanthology.org/tmlr/2024/chazal2024tmlr-choosing/)BibTeX
@article{chazal2024tmlr-choosing,
title = {{Choosing the Parameter of the Fermat Distance: Navigating Geometry and Noise}},
author = {Chazal, Frederic and Ferraris, Laure and Groisman, Pablo and Jonckheere, Matthieu and Pascal, Frederic and Sapienza, Facundo Fabián},
journal = {Transactions on Machine Learning Research},
year = {2024},
url = {https://mlanthology.org/tmlr/2024/chazal2024tmlr-choosing/}
}