{"paper":{"title":"Generalized Singular Value Thresholding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.NA","math.NA"],"primary_cat":"cs.CV","authors_text":"Canyi Lu, Changbo Zhu, Chunyan Xu, Shuicheng Yan, Zhouchen Lin","submitted_at":"2014-12-06T13:08:29Z","abstract_excerpt":"This work studies the Generalized Singular Value Thresholding (GSVT) operator ${\\text{Prox}}_{g}^{{\\sigma}}(\\cdot)$, \\begin{equation*}\n  {\\text{Prox}}_{g}^{{\\sigma}}(B)=\\arg\\min\\limits_{X}\\sum_{i=1}^{m}g(\\sigma_{i}(X)) + \\frac{1}{2}||X-B||_{F}^{2}, \\end{equation*} associated with a nonconvex function $g$ defined on the singular values of $X$. We prove that GSVT can be obtained by performing the proximal operator of $g$ (denoted as $\\text{Prox}_g(\\cdot)$) on the singular values since $\\text{Prox}_g(\\cdot)$ is monotone when $g$ is lower bounded. If the nonconvex $g$ satisfies some conditions (ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2231","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"}