{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/local-angles-and-dimension-estimation-from","title":"Local angles and dimension estimation from data on manifolds","arxiv_id":"1805.01577","date":"2018-05-04","proceeding":null,"authors":["Mateo Díaz","Adolfo J. Quiroz","Mauricio Velasco"],"abstract":"For data living in a manifold $M\\subseteq \\mathbb{R}^m$ and a point $p\\in M$\nwe consider a statistic $U_{k,n}$ which estimates the variance of the angle\nbetween pairs of vectors $X_i-p$ and $X_j-p$, for data points $X_i$, $X_j$,\nnear $p$, and evaluate this statistic as a tool for estimation of the intrinsic\ndimension of $M$ at $p$. Consistency of the local dimension estimator is\nestablished and the asymptotic distribution of $U_{k,n}$ is found under minimal\nregularity assumptions. Performance of the proposed methodology is compared\nagainst state-of-the-art methods on simulated data.","url_abs":"http://arxiv.org/abs/1805.01577v1","url_pdf":"http://arxiv.org/pdf/1805.01577v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"local-angles-and-dimension-estimation-from","repo_url":"https://github.com/mateodd25/ANOVA_dimension_estimator","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}