{"paper":{"title":"Scalable Nuclear-norm Minimization by Subspace Pursuit Proximal Riemannian Gradient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"cs.LG","authors_text":"Anton van den Hengel, Dong Xu, Junbin Gao, Mingkui Tan, Qinfeng Shi, Shijie Xiao","submitted_at":"2015-03-10T09:42:17Z","abstract_excerpt":"Nuclear-norm regularization plays a vital role in many learning tasks, such as low-rank matrix recovery (MR), and low-rank representation (LRR). Solving this problem directly can be computationally expensive due to the unknown rank of variables or large-rank singular value decompositions (SVDs). To address this, we propose a proximal Riemannian gradient (PRG) scheme which can efficiently solve trace-norm regularized problems defined on real-algebraic variety $\\mMLr$ of real matrices of rank at most $r$. Based on PRG, we further present a simple and novel subspace pursuit (SP) paradigm for gene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02828","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"}