{"id":"https://openalex.org/W2058078260","doi":"https://doi.org/10.1137/110845768","title":"Low-Rank Matrix Completion by Riemannian Optimization","display_name":"Low-Rank Matrix Completion by Riemannian Optimization","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2058078260","doi":"https://doi.org/10.1137/110845768","mag":"2058078260"},"language":"en","primary_location":{"id":"doi:10.1137/110845768","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110845768","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/189619","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039297086","display_name":"Bart Vandereycken","orcid":"https://orcid.org/0000-0002-6501-816X"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Bart Vandereycken","raw_affiliation_strings":["\u00c9cole Polytechnique, F\u00e9d\u00e9rale de Lausanne#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c9cole Polytechnique, F\u00e9d\u00e9rale de Lausanne#TAB#","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5039297086"],"corresponding_institution_ids":["https://openalex.org/I5124864"],"apc_list":null,"apc_paid":null,"fwci":38.0935,"has_fulltext":false,"cited_by_count":520,"citation_normalized_percentile":{"value":0.99926472,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"23","issue":"2","first_page":"1214","last_page":"1236"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9865999817848206,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11105","display_name":"Advanced Image Processing Techniques","score":0.9861999750137329,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7941359281539917},{"id":"https://openalex.org/keywords/matrix-completion","display_name":"Matrix completion","score":0.7576679587364197},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.6059867143630981},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5620518326759338},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5335507988929749},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.5200781226158142},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.49282315373420715},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4402427077293396},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3772050142288208},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23036369681358337},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.22979995608329773}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7941359281539917},{"id":"https://openalex.org/C2778459887","wikidata":"https://www.wikidata.org/wiki/Q6787865","display_name":"Matrix completion","level":3,"score":0.7576679587364197},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.6059867143630981},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5620518326759338},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5335507988929749},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.5200781226158142},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49282315373420715},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4402427077293396},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3772050142288208},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23036369681358337},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.22979995608329773},{"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/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","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/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","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/C25023664","wikidata":"https://www.wikidata.org/wiki/Q1575637","display_name":"Hankel matrix","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/110845768","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110845768","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.414.1140","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.414.1140","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.sam.math.ethz.ch/~kressner/pub/MatrixCompletionManifold.pdf","raw_type":"text"},{"id":"pmh:oai:infoscience.epfl.ch:189619","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/189619","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:189619","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/189619","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":61,"referenced_works":["https://openalex.org/W191817552","https://openalex.org/W1557324374","https://openalex.org/W1573301526","https://openalex.org/W1679203207","https://openalex.org/W1730255663","https://openalex.org/W1736339626","https://openalex.org/W1804110266","https://openalex.org/W1910710798","https://openalex.org/W1923779967","https://openalex.org/W1964200011","https://openalex.org/W1966810449","https://openalex.org/W1981745143","https://openalex.org/W1995650916","https://openalex.org/W1997321933","https://openalex.org/W1998367754","https://openalex.org/W2000157792","https://openalex.org/W2001801912","https://openalex.org/W2007437396","https://openalex.org/W2010100052","https://openalex.org/W2011359124","https://openalex.org/W2018089423","https://openalex.org/W2028324955","https://openalex.org/W2037253724","https://openalex.org/W2045512849","https://openalex.org/W2047071281","https://openalex.org/W2056405837","https://openalex.org/W2057531168","https://openalex.org/W2058209380","https://openalex.org/W2060204507","https://openalex.org/W2060854861","https://openalex.org/W2064404969","https://openalex.org/W2079361630","https://openalex.org/W2098760944","https://openalex.org/W2103972604","https://openalex.org/W2107220907","https://openalex.org/W2110662303","https://openalex.org/W2117198760","https://openalex.org/W2118550318","https://openalex.org/W2121667911","https://openalex.org/W2125947724","https://openalex.org/W2134332047","https://openalex.org/W2138505091","https://openalex.org/W2143075842","https://openalex.org/W2144730813","https://openalex.org/W2145179194","https://openalex.org/W2152279941","https://openalex.org/W2158923808","https://openalex.org/W2160634266","https://openalex.org/W2169125102","https://openalex.org/W2179686847","https://openalex.org/W2285512060","https://openalex.org/W2339666411","https://openalex.org/W2341535507","https://openalex.org/W2611328865","https://openalex.org/W2616032753","https://openalex.org/W2798766386","https://openalex.org/W2798909945","https://openalex.org/W2951312833","https://openalex.org/W2962834831","https://openalex.org/W3029645440","https://openalex.org/W3031689935"],"related_works":["https://openalex.org/W2952489973","https://openalex.org/W4300776969","https://openalex.org/W2108753466","https://openalex.org/W4375953589","https://openalex.org/W2736398265","https://openalex.org/W2012929908","https://openalex.org/W2054519467","https://openalex.org/W2055706496","https://openalex.org/W1712752320","https://openalex.org/W2373299583"],"abstract_inverted_index":{"The":[0,44,140],"matrix":[1,11,26,79],"completion":[2,27],"problem":[3],"consists":[4],"of":[5,17,41,49,58,89,118,122],"finding":[6],"or":[7],"approximating":[8],"a":[9,14,22,83,119],"low-rank":[10,78],"based":[12],"on":[13,33,61],"few":[15],"samples":[16],"this":[18,77],"matrix.":[19],"We":[20,63],"propose":[21],"new":[23],"algorithm":[24,45,124],"for":[25,134,150],"that":[28,128,144],"minimizes":[29],"the":[30,34,38,56,66,87,110,126,129,138,157],"least-square":[31],"distance":[32],"sampling":[35],"set":[36],"over":[37,76],"Riemannian":[39],"manifold":[40],"fixed-rank":[42],"matrices.":[43,90],"is":[46],"an":[47],"adaptation":[48],"classical":[50],"nonlinear":[51],"conjugate":[52,111],"gradients,":[53],"developed":[54],"within":[55],"framework":[57],"retraction-based":[59],"optimization":[60,75],"manifolds.":[62],"describe":[64,94],"all":[65],"necessary":[67,72],"objects":[68],"from":[69],"differential":[70],"geometry":[71],"to":[73],"perform":[74],"manifold,":[80],"seen":[81],"as":[82,101],"submanifold":[84],"embedded":[85],"in":[86],"space":[88],"In":[91],"particular,":[92],"we":[93,115],"how":[95,104],"metric":[96],"projection":[97],"can":[98],"be":[99],"used":[100],"retraction":[102],"and":[103,153],"vector":[105],"transport":[106],"lets":[107],"us":[108],"obtain":[109],"search":[112],"directions.":[113],"Finally,":[114],"prove":[116],"convergence":[117],"regularized":[120],"version":[121],"our":[123,145],"under":[125],"assumption":[127],"restricted":[130],"isometry":[131],"property":[132],"holds":[133],"incoherent":[135],"matrices":[136],"throughout":[137],"iterations.":[139],"numerical":[141],"experiments":[142],"indicate":[143],"approach":[146],"scales":[147],"very":[148],"well":[149],"large-scale":[151],"problems":[152],"compares":[154],"favorably":[155],"with":[156],"state-of-the-art,":[158],"while":[159],"outperforming":[160],"most":[161],"existing":[162],"solvers.":[163]},"counts_by_year":[{"year":2026,"cited_by_count":14},{"year":2025,"cited_by_count":34},{"year":2024,"cited_by_count":43},{"year":2023,"cited_by_count":31},{"year":2022,"cited_by_count":35},{"year":2021,"cited_by_count":58},{"year":2020,"cited_by_count":53},{"year":2019,"cited_by_count":51},{"year":2018,"cited_by_count":48},{"year":2017,"cited_by_count":37},{"year":2016,"cited_by_count":40},{"year":2015,"cited_by_count":31},{"year":2014,"cited_by_count":17},{"year":2013,"cited_by_count":20},{"year":2012,"cited_by_count":5}],"updated_date":"2026-06-16T09:24:06.705377","created_date":"2025-10-10T00:00:00"}