{"paper":{"title":"Parameter-free Topology Inference and Sparsification for Data on Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"cs.CG","authors_text":"Tamal K. Dey, Yusu Wang, Zhe Dong","submitted_at":"2015-05-24T17:44:06Z","abstract_excerpt":"In topology inference from data, current approaches face two major problems. One concerns the selection of a correct parameter to build an appropriate complex on top of the data points; the other involves with the typical `large' size of this complex. We address these two issues in the context of inferring homology from sample points of a smooth manifold of known dimension sitting in an Euclidean space $\\mathbb{R}^k$. We show that, for a sample size of $n$ points, we can identify a set of $O(n^2)$ points (as opposed to $O(n^{\\lceil \\frac{k}{2}\\rceil})$ Voronoi vertices) approximating a subset "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06462","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"}