{"id":"https://openalex.org/W3013334753","doi":"https://doi.org/10.1109/ieeeconf44664.2019.9048714","title":"Beyond Procrustes: Balancing-free Gradient Descent for Asymmetric Low-Rank Matrix Sensing","display_name":"Beyond Procrustes: Balancing-free Gradient Descent for Asymmetric Low-Rank Matrix Sensing","publication_year":2019,"publication_date":"2019-11-01","ids":{"openalex":"https://openalex.org/W3013334753","doi":"https://doi.org/10.1109/ieeeconf44664.2019.9048714","mag":"3013334753"},"language":"en","primary_location":{"id":"doi:10.1109/ieeeconf44664.2019.9048714","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ieeeconf44664.2019.9048714","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 53rd Asilomar Conference on Signals, Systems, and Computers","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074490643","display_name":"Cong Ma","orcid":"https://orcid.org/0000-0003-2532-0038"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Cong Ma","raw_affiliation_strings":["Princeton University,Department of Operations Research and Financial Engineering","Department of Operations Research and Financial Engineering, Princeton University"],"affiliations":[{"raw_affiliation_string":"Princeton University,Department of Operations Research and Financial Engineering","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Department of Operations Research and Financial Engineering, Princeton University","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011866457","display_name":"Yuan\u2010Xin Li","orcid":"https://orcid.org/0000-0003-4136-0961"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yuanxin Li","raw_affiliation_strings":["Carnegie Mellon University,Department of Electrical and Computer Engineering","Department of Electrical and Computer Engineering, Carnegie Mellon University"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University,Department of Electrical and Computer Engineering","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053809095","display_name":"Yuejie Chi","orcid":"https://orcid.org/0000-0002-6766-5459"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yuejie Chi","raw_affiliation_strings":["Carnegie Mellon University,Department of Electrical and Computer Engineering","Department of Electrical and Computer Engineering, Carnegie Mellon University"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University,Department of Electrical and Computer Engineering","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5074490643"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":0.7759,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.71312618,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"2019","issue":null,"first_page":"721","last_page":"725"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11778","display_name":"Electrical and Bioimpedance Tomography","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.677725076675415},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.6655192375183105},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5725972056388855},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5489799976348877},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.5350970029830933},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5307497978210449},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49399930238723755},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.48762407898902893},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.4475001394748688},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4396188259124756},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.4326995611190796},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4251159429550171},{"id":"https://openalex.org/keywords/matrix-completion","display_name":"Matrix completion","score":0.4184448719024658},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37150174379348755},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.18106937408447266},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1370987594127655},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08804771304130554},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.0833011269569397}],"concepts":[{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.677725076675415},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6655192375183105},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5725972056388855},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5489799976348877},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.5350970029830933},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5307497978210449},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49399930238723755},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.48762407898902893},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.4475001394748688},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4396188259124756},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.4326995611190796},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4251159429550171},{"id":"https://openalex.org/C2778459887","wikidata":"https://www.wikidata.org/wiki/Q6787865","display_name":"Matrix completion","level":3,"score":0.4184448719024658},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37150174379348755},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.18106937408447266},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1370987594127655},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08804771304130554},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0833011269569397},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/ieeeconf44664.2019.9048714","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ieeeconf44664.2019.9048714","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 53rd Asilomar Conference on Signals, Systems, and Computers","raw_type":"proceedings-article"},{"id":"mag:3081350733","is_oa":false,"landing_page_url":"https://jglobal.jst.go.jp/en/detail?JGLOBAL_ID=202002217680513109","pdf_url":null,"source":{"id":"https://openalex.org/S4306512817","display_name":"IEEE Conference Proceedings","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"IEEE Conference Proceedings","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":61,"referenced_works":["https://openalex.org/W1189174436","https://openalex.org/W1884015253","https://openalex.org/W1884359871","https://openalex.org/W2000157792","https://openalex.org/W2047071281","https://openalex.org/W2064771273","https://openalex.org/W2106005123","https://openalex.org/W2111297856","https://openalex.org/W2116680824","https://openalex.org/W2118550318","https://openalex.org/W2120872934","https://openalex.org/W2134332047","https://openalex.org/W2143075842","https://openalex.org/W2144730813","https://openalex.org/W2166163936","https://openalex.org/W2268674159","https://openalex.org/W2399402693","https://openalex.org/W2403076655","https://openalex.org/W2474090883","https://openalex.org/W2586353914","https://openalex.org/W2592246480","https://openalex.org/W2604130501","https://openalex.org/W2611328865","https://openalex.org/W2757463546","https://openalex.org/W2768927505","https://openalex.org/W2810541051","https://openalex.org/W2918965983","https://openalex.org/W2962714108","https://openalex.org/W2963099043","https://openalex.org/W2963449128","https://openalex.org/W2963622172","https://openalex.org/W2963685382","https://openalex.org/W2963731874","https://openalex.org/W2964065413","https://openalex.org/W2964146881","https://openalex.org/W2964156132","https://openalex.org/W2964220724","https://openalex.org/W2964256664","https://openalex.org/W2964309963","https://openalex.org/W2969215180","https://openalex.org/W3010434925","https://openalex.org/W3104501706","https://openalex.org/W3106271742","https://openalex.org/W6627707193","https://openalex.org/W6639384702","https://openalex.org/W6676665419","https://openalex.org/W6677255997","https://openalex.org/W6677959539","https://openalex.org/W6712153814","https://openalex.org/W6712787327","https://openalex.org/W6713161955","https://openalex.org/W6717522514","https://openalex.org/W6720643467","https://openalex.org/W6735923916","https://openalex.org/W6744267322","https://openalex.org/W6745725969","https://openalex.org/W6748269070","https://openalex.org/W6749925554","https://openalex.org/W6751100130","https://openalex.org/W6752571064","https://openalex.org/W6767371102"],"related_works":["https://openalex.org/W2952489973","https://openalex.org/W4300776969","https://openalex.org/W2106005123","https://openalex.org/W3103289951","https://openalex.org/W2266965707","https://openalex.org/W4387323768","https://openalex.org/W2084983808","https://openalex.org/W2906317811","https://openalex.org/W4318564253","https://openalex.org/W2994409951"],"abstract_inverted_index":{"Low-rank":[0],"matrix":[1,19,54,82,91],"estimation":[2],"plays":[3],"a":[4,47,89,93,146],"central":[5],"role":[6],"in":[7,57,124],"many":[8],"applications":[9],"across":[10],"science":[11],"and":[12,32,160],"engineering.":[13],"Recently,":[14],"nonconvex":[15],"formulations":[16],"based":[17,140],"on":[18,45,141],"factorization":[20],"are":[21,40],"provably":[22],"solved":[23],"by":[24],"simple":[25],"gradient":[26,110],"descent":[27,111],"algorithms":[28],"with":[29],"strong":[30],"computational":[31],"statistical":[33],"guarantees.":[34],"However,":[35],"when":[36,67],"the":[37,52,65,70,81,102,106,115,122,126,132,135,143,154],"low-rank":[38,90],"matrices":[39],"asymmetric,":[41],"existing":[42],"approaches":[43],"rely":[44],"adding":[46],"regularization":[48],"term":[49],"to":[50,87,157],"balance":[51],"two":[53],"factors":[55,127],"which":[56,85],"practice":[58],"can":[59],"be":[60,162],"removed":[61],"safely":[62],"without":[63,114],"hurting":[64],"performance":[66],"initialized":[68],"via":[69],"spectral":[71],"method.":[72],"In":[73],"this":[74,78],"paper,":[75],"we":[76],"justify":[77],"theoretically":[79],"for":[80,153],"sensing":[83],"problem,":[84],"aims":[86],"recover":[88],"from":[92],"small":[94],"number":[95],"of":[96,117,121,134,145,163],"linear":[97],"measurements.":[98],"As":[99],"long":[100],"as":[101],"measurement":[103],"ensemble":[104],"satisfies":[105],"restricted":[107],"isometry":[108],"property,":[109],"converges":[112],"linearly":[113],"need":[116],"explicitly":[118],"promoting":[119],"balancedness":[120],"factors;":[123],"fact,":[125],"stay":[128],"balanced":[129],"automatically":[130],"throughout":[131],"execution":[133],"algorithm.":[136],"Our":[137],"analysis":[138],"is":[139],"analyzing":[142],"evolution":[144],"new":[147],"distance":[148],"metric":[149],"that":[150],"directly":[151],"accounts":[152],"ambiguity":[155],"due":[156],"invertible":[158],"transforms,":[159],"might":[161],"independent":[164],"interest.":[165]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}