{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,17]],"date-time":"2026-07-17T11:41:43Z","timestamp":1784288503370,"version":"3.55.0"},"reference-count":46,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"name":"ONR","award":["N00014-18-1-2142"],"award-info":[{"award-number":["N00014-18-1-2142"]}]},{"name":"ONR","award":["N00014-19-1-2404"],"award-info":[{"award-number":["N00014-19-1-2404"]}]},{"name":"ARO","award":["W911NF-18-1-0303"],"award-info":[{"award-number":["W911NF-18-1-0303"]}]},{"name":"NSF","award":["CAREER ECCS-1818571"],"award-info":[{"award-number":["CAREER ECCS-1818571"]}]},{"name":"NSF","award":["CCF-1806154"],"award-info":[{"award-number":["CCF-1806154"]}]},{"name":"NSF","award":["CCF-1901199"],"award-info":[{"award-number":["CCF-1901199"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Signal Process."],"published-print":{"date-parts":[[2021]]},"DOI":"10.1109\/tsp.2021.3051425","type":"journal-article","created":{"date-parts":[[2021,1,14]],"date-time":"2021-01-14T21:07:02Z","timestamp":1610658422000},"page":"867-877","source":"Crossref","is-referenced-by-count":21,"title":["Beyond Procrustes: Balancing-Free Gradient Descent for Asymmetric Low-Rank Matrix Sensing"],"prefix":"10.1109","volume":"69","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2532-0038","authenticated-orcid":false,"given":"Cong","family":"Ma","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuanxin","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6766-5459","authenticated-orcid":false,"given":"Yuejie","family":"Chi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"263","reference":[{"key":"ref39","first-page":"1233","article-title":"No spurious local minima in nonconvex low rank problems: A unified geometric analysis","author":"ge","year":"0","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref38","first-page":"2973","article-title":"Matrix completion has no spurious local minimum","author":"ge","year":"0","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1093\/imaiai\/iaz009"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2019.2937282"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-019-01363-6"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1016\/j.acha.2018.01.001"},{"key":"ref37","article-title":"Low-rank matrix recovery with composite optimization: Good conditioning and rapid convergence","author":"charisopoulos","year":"2019","journal-title":"arXiv 1904 10020"},{"key":"ref36","first-page":"384","article-title":"Algorithmic regularization in learning deep homogeneous models: Layers are automatically balanced","author":"du","year":"0","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2020.2992234"},{"key":"ref34","first-page":"5751","article-title":"Fast and sample efficient inductive matrix completion via multi-phase procrustes flow","author":"zhang","year":"0","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1137\/17M1150189"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2018.2835403"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2018.2832197"},{"key":"ref12","first-page":"4152","article-title":"Fast algorithms for robust PCA via gradient descent","author":"yi","year":"0","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref13","article-title":"Spectral methods for data science: A statistical perspective","author":"chen","year":"2020","journal-title":"arXiv 2012 08496"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1137\/070697835"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2017.2773497"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-009-9045-5"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1109\/JPROC.2009.2035722"},{"key":"ref18","first-page":"1665","article-title":"Restricted strong convexity and weighted matrix completion: Optimal bounds with noise","volume":"13","author":"negahban","year":"2012","journal-title":"J Mach Learn Res"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2011.2104999"},{"key":"ref28","article-title":"Fast low-rank estimation by projected gradient descent: General statistical and algorithmic guarantees","author":"chen","year":"2015","journal-title":"arXiv 1509 03025"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1109\/JSTSP.2016.2539100"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-019-09429-9"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2018.2821706"},{"key":"ref6","first-page":"530","article-title":"Dropping convexity for faster semi-definite optimization","author":"bhojanapalli","year":"0","journal-title":"Proc Conf Learn Theory"},{"key":"ref29","first-page":"1496","article-title":"Nonconvex matrix factorization from rank-one measurements","author":"li","year":"0","journal-title":"Proc 22nd Int Conf Artif Intell Statist"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-002-0352-8"},{"key":"ref8","first-page":"964","article-title":"Low-rank solutions of linear matrix equations via procrustes flow","author":"tu","year":"0","journal-title":"Proc Int Conf Mach Learn"},{"key":"ref7","first-page":"2757","article-title":"The non-convex Burer-Monteiro approach works on smooth semidefinite programs","author":"boumal","year":"0","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2010.2044061"},{"key":"ref9","article-title":"Convergence analysis for rectangular matrix completion using Burer-Monteiro factorization and gradient descent","author":"zheng","year":"2016","journal-title":"arXiv 1605 07051"},{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1109\/IEEECONF44664.2019.9048714"},{"key":"ref46","article-title":"Low-rank matrix recovery with scaled subgradient methods: Fast and robust convergence without the condition number","author":"tong","year":"2020","journal-title":"arXiv 2010 13364"},{"key":"ref20","first-page":"3413","article-title":"A simpler approach to matrix completion","volume":"12","author":"recht","year":"2011","journal-title":"J Mach Learn Res"},{"key":"ref45","article-title":"Accelerating ill-conditioned low-rank matrix estimation via scaled gradient descent","author":"tong","year":"2020","journal-title":"arXiv 2005 08898"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1214\/10-AOS850"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2014.2343623"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2019.2898663"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2010.2046205"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-019-00889-w"},{"key":"ref23","first-page":"109","article-title":"A convergent gradient descent algorithm for rank minimization and semidefinite programming from random linear measurements","author":"zheng","year":"0","journal-title":"Proc Adv Neural Inf Process Syst"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2020.3008876"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1145\/2488608.2488693"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1093\/imaiai\/iay003"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2015.25"}],"container-title":["IEEE Transactions on Signal Processing"],"original-title":[],"link":[{"URL":"https:\/\/ieeexplore.ieee.org\/ielam\/78\/9307529\/9321745-aam.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/78\/9307529\/09321745.pdf?arnumber=9321745","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,10]],"date-time":"2022-05-10T14:50:34Z","timestamp":1652194234000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/9321745\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"references-count":46,"URL":"https:\/\/doi.org\/10.1109\/tsp.2021.3051425","relation":{},"ISSN":["1053-587X","1941-0476"],"issn-type":[{"value":"1053-587X","type":"print"},{"value":"1941-0476","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021]]}}}