{"paper":{"title":"New Null Space Results and Recovery Thresholds for Matrix Rank Minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.ML"],"primary_cat":"math.OC","authors_text":"Babak Hassibi, Samet Oymak","submitted_at":"2010-11-29T18:46:08Z","abstract_excerpt":"Nuclear norm minimization (NNM) has recently gained significant attention for its use in rank minimization problems. Similar to compressed sensing, using null space characterizations, recovery thresholds for NNM have been studied in \\cite{arxiv,Recht_Xu_Hassibi}. However simulations show that the thresholds are far from optimal, especially in the low rank region. In this paper we apply the recent analysis of Stojnic for compressed sensing \\cite{mihailo} to the null space conditions of NNM. The resulting thresholds are significantly better and in particular our weak threshold appears to match w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.6326","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"}