Year: 2024
Type: preprint
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 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) distances.
Source: arXiv (Cornell University)
Authors: Huang, Han, Jiradilok, Pakawut, Mossel, Elchanan
Institutions: University of Missouri, Massachusetts Institute of Technology
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4391912451