{"paper":{"title":"Efficient Point-to-Subspace Query in $\\ell^1$: Theory and Applications in Computer Vision","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["cs.CV","stat.AP"],"primary_cat":"stat.ML","authors_text":"John Wright, Ju Sun, Yuqian Zhang","submitted_at":"2012-11-05T04:15:25Z","abstract_excerpt":"Motivated by vision tasks such as robust face and object recognition, we consider the following general problem: given a collection of low-dimensional linear subspaces in a high-dimensional ambient (image) space and a query point (image), efficiently determine the nearest subspace to the query in $\\ell^1$ distance. We show in theory that Cauchy random embedding of the objects into significantly-lower-dimensional spaces helps preserve the identity of the nearest subspace with constant probability. This offers the possibility of efficiently selecting several candidates for accurate search. We sk"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0757","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"}