{"paper":{"title":"Metric embedding with outliers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anastasios Sidiropoulos, Yusu Wang","submitted_at":"2015-08-14T18:38:05Z","abstract_excerpt":"We initiate the study of metric embeddings with \\emph{outliers}. Given some metric space $(X,\\rho)$ we wish to find a small set of outlier points $K \\subset X$ and either an isometric or a low-distortion embedding of $(X\\setminus K,\\rho)$ into some target metric space. This is a natural problem that captures scenarios where a small fraction of points in the input corresponds to noise.\n  For the case of isometric embeddings we derive polynomial-time approximation algorithms for minimizing the number of outliers when the target space is an ultrametric, a tree metric, or constant-dimensional Eucl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03600","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"}