{"paper":{"title":"Topological analysis of scalar fields with outliers","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"cs.CG","authors_text":"Fengtao Fan, Fr\\'ed\\'eric Chazal, Micka\\\"el Buchet, Steve Y. Oudot, Tamal K. Dey, Yusu Wang","submitted_at":"2014-12-04T14:41:56Z","abstract_excerpt":"Given a real-valued function $f$ defined over a manifold $M$ embedded in $\\mathbb{R}^d$, we are interested in recovering structural information about $f$ from the sole information of its values on a finite sample $P$. Existing methods provide approximation to the persistence diagram of $f$ when geometric noise and functional noise are bounded. However, they fail in the presence of aberrant values, also called outliers, both in theory and practice.\n  We propose a new algorithm that deals with outliers. We handle aberrant functional values with a method inspired from the k-nearest neighbors regr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1680","kind":"arxiv","version":3},"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"}