{"paper":{"title":"Density Level Set Estimation on Manifolds with DBSCAN","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ML","authors_text":"Heinrich Jiang","submitted_at":"2017-03-10T01:28:15Z","abstract_excerpt":"We show that DBSCAN can estimate the connected components of the $\\lambda$-density level set $\\{ x : f(x) \\ge \\lambda\\}$ given $n$ i.i.d. samples from an unknown density $f$. We characterize the regularity of the level set boundaries using parameter $\\beta > 0$ and analyze the estimation error under the Hausdorff metric. When the data lies in $\\mathbb{R}^D$ we obtain a rate of $\\widetilde{O}(n^{-1/(2\\beta + D)})$, which matches known lower bounds up to logarithmic factors. When the data lies on an embedded unknown $d$-dimensional manifold in $\\mathbb{R}^D$, then we obtain a rate of $\\widetilde"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03503","kind":"arxiv","version":2},"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"}