{"id":"https://openalex.org/W2266965707","doi":"https://doi.org/10.1137/15m1025153","title":"Robust Low-Rank Matrix Completion by Riemannian Optimization","display_name":"Robust Low-Rank Matrix Completion by Riemannian Optimization","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2266965707","doi":"https://doi.org/10.1137/15m1025153","mag":"2266965707"},"language":"en","primary_location":{"id":"doi:10.1137/15m1025153","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1025153","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-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/A5089335913","display_name":"L\u00e9opold Cambier","orcid":"https://orcid.org/0000-0002-0147-086X"},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"L\u00e9opold Cambier","raw_affiliation_strings":["ICTEAM Institute, Universit\u00e9 catholique de Louvain, Louvain-la-Neuve, B-1348, Belgium"],"affiliations":[{"raw_affiliation_string":"ICTEAM Institute, Universit\u00e9 catholique de Louvain, Louvain-la-Neuve, B-1348, Belgium","institution_ids":["https://openalex.org/I95674353"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075495386","display_name":"Pierre-Antoine Absil","orcid":null},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"P.-A. Absil","raw_affiliation_strings":["ICTEAM Institute, Universit\u00e9 catholique de Louvain, Louvain-la-Neuve, B-1348, Belgium"],"affiliations":[{"raw_affiliation_string":"ICTEAM Institute, Universit\u00e9 catholique de Louvain, Louvain-la-Neuve, B-1348, Belgium","institution_ids":["https://openalex.org/I95674353"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5089335913"],"corresponding_institution_ids":["https://openalex.org/I95674353"],"apc_list":null,"apc_paid":null,"fwci":7.7129,"has_fulltext":false,"cited_by_count":71,"citation_normalized_percentile":{"value":0.97762297,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"38","issue":"5","first_page":"S440","last_page":"S460"},"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.994700014591217,"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"}},{"id":"https://openalex.org/T11105","display_name":"Advanced Image Processing Techniques","score":0.9945999979972839,"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/matrix-completion","display_name":"Matrix completion","score":0.9325473308563232},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7797214388847351},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.7297769784927368},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.5738946199417114},{"id":"https://openalex.org/keywords/outlier","display_name":"Outlier","score":0.5583046674728394},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5582736134529114},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5375432968139648},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5153290629386902},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4842469394207001},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47358208894729614},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.4520362615585327},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3679613471031189},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2829968333244324},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.17242726683616638},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12295219302177429},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09473365545272827}],"concepts":[{"id":"https://openalex.org/C2778459887","wikidata":"https://www.wikidata.org/wiki/Q6787865","display_name":"Matrix completion","level":3,"score":0.9325473308563232},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7797214388847351},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.7297769784927368},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.5738946199417114},{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.5583046674728394},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5582736134529114},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5375432968139648},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5153290629386902},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4842469394207001},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47358208894729614},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.4520362615585327},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3679613471031189},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2829968333244324},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.17242726683616638},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12295219302177429},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09473365545272827},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/15m1025153","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1025153","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.717.7704","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.717.7704","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://sites.uclouvain.be/absil/2015-04/RLRMC_submitted_13-06-15.pdf","raw_type":"text"},{"id":"pmh:oai:dial.uclouvain.be:boreal:172843","is_oa":false,"landing_page_url":"http://hdl.handle.net/2078.1/172843","pdf_url":null,"source":{"id":"https://openalex.org/S4306401902","display_name":"Digital Access to Libraries (Universit\u00e9 catholique de Louvain (UCL), l'Universit\u00e9 de Namur (UNamur) and the Universit\u00e9 Saint-Louis (USL-B))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I95674353","host_organization_name":"UCLouvain","host_organization_lineage":["https://openalex.org/I95674353"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Scientific Computing, Vol. 38, no. 5, p. S440-S460 (2016)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4706192905","display_name":null,"funder_award_id":"PDR T.0173.13","funder_id":"https://openalex.org/F4320321390","funder_display_name":"Fonds De La Recherche Scientifique - FNRS"}],"funders":[{"id":"https://openalex.org/F4320321390","display_name":"Fonds De La Recherche Scientifique - FNRS","ror":"https://ror.org/03q83t159"},{"id":"https://openalex.org/F4320321454","display_name":"Belgian Federal Science Policy Office","ror":"https://ror.org/01fapfv42"},{"id":"https://openalex.org/F4320321584","display_name":"F\u00e9d\u00e9ration Wallonie-Bruxelles","ror":"https://ror.org/04q01pf08"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W195665135","https://openalex.org/W1557324374","https://openalex.org/W1590407118","https://openalex.org/W1613169971","https://openalex.org/W1804110266","https://openalex.org/W1919155910","https://openalex.org/W1972710290","https://openalex.org/W1974042113","https://openalex.org/W2012929908","https://openalex.org/W2014237985","https://openalex.org/W2020781868","https://openalex.org/W2047071281","https://openalex.org/W2058078260","https://openalex.org/W2071494625","https://openalex.org/W2096642693","https://openalex.org/W2101191125","https://openalex.org/W2104359797","https://openalex.org/W2126407450","https://openalex.org/W2145179194","https://openalex.org/W2145962650","https://openalex.org/W2158121106","https://openalex.org/W2167623372","https://openalex.org/W2341535507","https://openalex.org/W2408452220","https://openalex.org/W2611328865","https://openalex.org/W2962834831","https://openalex.org/W2962909343","https://openalex.org/W2963831709","https://openalex.org/W3138835833"],"related_works":["https://openalex.org/W2964006653","https://openalex.org/W2788826952","https://openalex.org/W4302315572","https://openalex.org/W2084983808","https://openalex.org/W2325477568","https://openalex.org/W1991825408","https://openalex.org/W4318564253","https://openalex.org/W1969698720","https://openalex.org/W1507830821","https://openalex.org/W2963965423"],"abstract_inverted_index":{"Low-rank":[0],"matrix":[1,13,40,43],"completion":[2,44],"is":[3],"the":[4,35,49,63,67,77,83,86,93,103,107,120,123,127],"problem":[5,36],"where":[6,45],"one":[7],"tries":[8],"to":[9,32,74],"recover":[10],"a":[11,18,29,46],"low-rank":[12,39,78],"from":[14],"noisy":[15],"observations":[16],"of":[17,20,37,48,65,89,92,106],"subset":[19],"its":[21,99],"entries.":[22],"In":[23],"this":[24],"paper,":[25],"we":[26,97],"propose":[27],"RMC,":[28],"new":[30],"method":[31,60,125],"deal":[33,75],"with":[34,76],"robust":[38],"completion,":[41],"i.e.,":[42],"fraction":[47],"observed":[50],"entries":[51],"are":[52],"corrupted":[53],"by":[54,101],"non-Gaussian":[55],"noise,":[56],"typically":[57],"outliers.":[58],"The":[59],"relies":[61],"on":[62,115,122,126],"idea":[64],"smoothing":[66],"$\\ell_1$":[68,94],"norm":[69],"and":[70,96,118],"using":[71],"Riemannian":[72],"optimization":[73],"constraint.":[79],"We":[80,110],"first":[81],"state":[82],"algorithm":[84],"as":[85],"successive":[87],"minimization":[88],"smooth":[90],"approximations":[91],"norm,":[95],"analyze":[98],"convergence":[100],"showing":[102],"strict":[104],"decrease":[105],"objective":[108],"function.":[109],"then":[111],"perform":[112],"numerical":[113],"experiments":[114],"synthetic":[116],"data":[117],"demonstrate":[119],"effectiveness":[121],"proposed":[124],"Netflix":[128],"dataset.":[129]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}