{"paper":{"title":"Error estimation of weighted nonlocal Laplacian on random point cloud","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Bao Wang, Stanley J. Osher, Zuoqiang Shi","submitted_at":"2018-09-23T16:04:02Z","abstract_excerpt":"We analyze the convergence of the weighted nonlocal Laplacian (WNLL) on high dimensional randomly distributed data. The analysis reveals the importance of the scaling weight $\\mu \\sim P|/|S|$ with $|P|$ and $|S|$ be the number of entire and labeled data, respectively. The result gives a theoretical foundation of WNLL for high dimensional data interpolation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08622","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}