Reconstructing the Geometry of Random Geometric Graphs

[2402.09591] Reconstructing the Geometry of Random Geometric Graphs Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2402.09591 (cs) [Submitted on 14 Feb 2024 ( v1 ), last revised 8 Apr 2026 (this version, v3)] Title: Reconstructing the Geometry of Random Geometric Graphs Authors: Han Huang , Pakawut Jiradilok , Elchanan Mossel View a PDF of the paper titled Reconstructing the Geometry of Random Geometric Graphs, by Han Huang and 2 other authors View PDF HTML (experimental) 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. Comments: Polish the introduction section; include an example for non-identifiability in the setting with step function (hard-disc random geometric graph model) Subjects: Machine Learning (cs.LG) ; Probability (math.PR) Cite as: arXiv:2402.09591 [cs.LG] (or arXiv:2402.09591v3 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2402.09591 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Han Huang [ view email ] [v1] Wed, 14 Feb 2024 21:34:44 UTC (71 KB) [v2] Tue, 11 Jun 2024 01:50:34 UTC (72 KB) [v3] Wed, 8 Apr 2026 22:24:10 UTC (2,754 KB) Full-text links: Access Paper: View a PDF of the paper titled Reconstructing the Geometry of Random Geometric Graphs, by Han Huang and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2024-02 Change to browse by: cs math math.PR References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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