Reconstructing the Geometry of Random Geometric Graphs (Extended Abstract)

Han Huang, Pakawut Jiradilok, Elchanan Mossel
Proceedings of Thirty Seventh Conference on Learning Theory, PMLR 247:2519-2521, 2024.

Abstract

Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance, independently among pairs. In this work we show how to efficiently reconstruct the geometry of the underlying space from the sampled graph under the {\em manifold} assumption, i.e., assuming that the underlying space is a low dimensional manifold and that the connection probability is a strictly decreasing function of the Euclidean distance between the points in a given embedding of the manifold in $\mathbb{R}^N$. Our work complements a large body of work on manifold learning, where the goal is to recover a manifold from sampled points sampled in the manifold along with their (approximate) distance

Cite this Paper

BibTeX
@InProceedings{pmlr-v247-huang24c, title = {Reconstructing the Geometry of Random Geometric Graphs (Extended Abstract)}, author = {Huang, Han and Jiradilok, Pakawut and Mossel, Elchanan}, booktitle = {Proceedings of Thirty Seventh Conference on Learning Theory}, pages = {2519--2521}, year = {2024}, editor = {Agrawal, Shipra and Roth, Aaron}, volume = {247}, series = {Proceedings of Machine Learning Research}, month = {30 Jun--03 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v247/huang24c/huang24c.pdf}, url = {https://proceedings.mlr.press/v247/huang24c.html}, abstract = {Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance, independently among pairs. In this work we show how to efficiently reconstruct the geometry of the underlying space from the sampled graph under the {\em manifold} assumption, i.e., assuming that the underlying space is a low dimensional manifold and that the connection probability is a strictly decreasing function of the Euclidean distance between the points in a given embedding of the manifold in $\mathbb{R}^N$. Our work complements a large body of work on manifold learning, where the goal is to recover a manifold from sampled points sampled in the manifold along with their (approximate) distance} }
Endnote
%0 Conference Paper %T Reconstructing the Geometry of Random Geometric Graphs (Extended Abstract) %A Han Huang %A Pakawut Jiradilok %A Elchanan Mossel %B Proceedings of Thirty Seventh Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2024 %E Shipra Agrawal %E Aaron Roth %F pmlr-v247-huang24c %I PMLR %P 2519--2521 %U https://proceedings.mlr.press/v247/huang24c.html %V 247 %X Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance, independently among pairs. In this work we show how to efficiently reconstruct the geometry of the underlying space from the sampled graph under the {\em manifold} assumption, i.e., assuming that the underlying space is a low dimensional manifold and that the connection probability is a strictly decreasing function of the Euclidean distance between the points in a given embedding of the manifold in $\mathbb{R}^N$. Our work complements a large body of work on manifold learning, where the goal is to recover a manifold from sampled points sampled in the manifold along with their (approximate) distance
APA
Huang, H., Jiradilok, P. & Mossel, E.. (2024). Reconstructing the Geometry of Random Geometric Graphs (Extended Abstract). Proceedings of Thirty Seventh Conference on Learning Theory, in Proceedings of Machine Learning Research 247:2519-2521 Available from https://proceedings.mlr.press/v247/huang24c.html.

Related Material