{"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/faster-fast-tensor-completion-with-nonconvex","title":"FasTer: Fast Tensor Completion with Nonconvex Regularization","arxiv_id":"1807.08725","date":"2018-07-23","proceeding":null,"authors":["Quanming Yao","James T. Kwok","Bo Han"],"abstract":"Low-rank tensor completion problem aims to recover a tensor from limited\nobservations, which has many real-world applications. Due to the easy\noptimization, the convex overlapping nuclear norm has been popularly used for\ntensor completion. However, it over-penalizes top singular values and lead to\nbiased estimations. In this paper, we propose to use the nonconvex regularizer,\nwhich can less penalize large singular values, instead of the convex one for\ntensor completion. However, as the new regularizer is nonconvex and overlapped\nwith each other, existing algorithms are either too slow or suffer from the\nhuge memory cost. To address these issues, we develop an efficient and scalable\nalgorithm, which is based on the proximal average (PA) algorithm, for\nreal-world problems. Compared with the direct usage of PA algorithm, the\nproposed algorithm runs orders faster and needs orders less space. We further\nspeed up the proposed algorithm with the acceleration technique, and show the\nconvergence to critical points is still guaranteed. Experimental comparisons of\nthe proposed approach are made with various other tensor completion approaches.\nEmpirical results show that the proposed algorithm is very fast and can produce\nmuch better recovery performance.","url_abs":"http://arxiv.org/abs/1807.08725v3","url_pdf":"http://arxiv.org/pdf/1807.08725v3.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":"faster-fast-tensor-completion-with-nonconvex","repo_url":"https://github.com/quanmingyao/FasTer","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"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}