{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/interpolating-convex-and-non-convex-tensor","title":"Interpolating Convex and Non-Convex Tensor Decompositions via the Subspace Norm","arxiv_id":"1503.05479","date":"2015-03-18","proceeding":"NeurIPS 2015 12","authors":["Qinqing Zheng","Ryota Tomioka"],"abstract":"We consider the problem of recovering a low-rank tensor from its noisy\nobservation. Previous work has shown a recovery guarantee with signal to noise\nratio $O(n^{\\lceil K/2 \\rceil /2})$ for recovering a $K$th order rank one\ntensor of size $n\\times \\cdots \\times n$ by recursive unfolding. In this paper,\nwe first improve this bound to $O(n^{K/4})$ by a much simpler approach, but\nwith a more careful analysis. Then we propose a new norm called the subspace\nnorm, which is based on the Kronecker products of factors obtained by the\nproposed simple estimator. The imposed Kronecker structure allows us to show a\nnearly ideal $O(\\sqrt{n}+\\sqrt{H^{K-1}})$ bound, in which the parameter $H$\ncontrols the blend from the non-convex estimator to mode-wise nuclear norm\nminimization. Furthermore, we empirically demonstrate that the subspace norm\nachieves the nearly ideal denoising performance even with $H=O(1)$.","url_abs":"http://arxiv.org/abs/1503.05479v2","url_pdf":"http://arxiv.org/pdf/1503.05479v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"interpolating-convex-and-non-convex-tensor","repo_url":"https://github.com/enosair/tensor-subspace-norm","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"denoising","task_name":"Denoising"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}