{"paper":{"title":"ABCDepth: efficient algorithm for Tukey depth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Milan Merkle, Milica Bogicevic","submitted_at":"2016-03-17T18:47:30Z","abstract_excerpt":"We present a new algorithm for Tukey (halfspace) depth level sets and its implementation. Given $d$-dimensional data set for any $d\\geq 2$, the algorithm is based on representation of level sets as intersections of balls in $R^d$, and can be easily adapted to related depths (Type D, Zuo and Serfling (Ann. Stat. {\\bf 28} (2000), 461--482)). The algorithm complexity is $O(dn^2 + n^2\\log{n})$ where $n$ is the data set size. Examples with real and synthetic data show that the algorithm is much faster than other implemented algorithms and that it can accept thousands of multidimensional observation"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05609","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"}