{"id":"https://openalex.org/W2785436244","doi":"https://doi.org/10.1109/tsp.2018.2885494","title":"Matrix Completion With Deterministic Pattern: A Geometric Perspective","display_name":"Matrix Completion With Deterministic Pattern: A Geometric Perspective","publication_year":2018,"publication_date":"2018-12-11","ids":{"openalex":"https://openalex.org/W2785436244","doi":"https://doi.org/10.1109/tsp.2018.2885494","mag":"2785436244"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2018.2885494","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2018.2885494","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1802.00047","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025917676","display_name":"Alexander Shapiro","orcid":"https://orcid.org/0000-0002-4776-0053"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Alexander Shapiro","raw_affiliation_strings":["H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, USA"],"affiliations":[{"raw_affiliation_string":"H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103006471","display_name":"Yao Xie","orcid":"https://orcid.org/0000-0002-1410-3639"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yao Xie","raw_affiliation_strings":["H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, USA"],"affiliations":[{"raw_affiliation_string":"H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100421978","display_name":"Rui Zhang","orcid":"https://orcid.org/0000-0001-9418-0863"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rui Zhang","raw_affiliation_strings":["H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, USA"],"affiliations":[{"raw_affiliation_string":"H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5025917676"],"corresponding_institution_ids":["https://openalex.org/I130701444"],"apc_list":null,"apc_paid":null,"fwci":3.5383,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.92986237,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"67","issue":"4","first_page":"1088","last_page":"1103"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9990000128746033,"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":0.9990000128746033,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9866999983787537,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9692000150680542,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/uniqueness","display_name":"Uniqueness","score":0.7246920466423035},{"id":"https://openalex.org/keywords/matrix-completion","display_name":"Matrix completion","score":0.6831350326538086},{"id":"https://openalex.org/keywords/perspective","display_name":"Perspective (graphical)","score":0.6443033218383789},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.629212498664856},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.6005125641822815},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.596672534942627},{"id":"https://openalex.org/keywords/verifiable-secret-sharing","display_name":"Verifiable secret sharing","score":0.5787381529808044},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5019161701202393},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.42542269825935364},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4048541486263275},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40206947922706604},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3493747115135193},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16514074802398682},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.12184816598892212},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09806743264198303}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7246920466423035},{"id":"https://openalex.org/C2778459887","wikidata":"https://www.wikidata.org/wiki/Q6787865","display_name":"Matrix completion","level":3,"score":0.6831350326538086},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.6443033218383789},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.629212498664856},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.6005125641822815},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.596672534942627},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.5787381529808044},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5019161701202393},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.42542269825935364},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4048541486263275},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40206947922706604},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3493747115135193},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16514074802398682},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12184816598892212},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09806743264198303},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tsp.2018.2885494","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2018.2885494","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1802.00047","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1802.00047","pdf_url":"https://arxiv.org/pdf/1802.00047","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1802.00047","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1802.00047","pdf_url":"https://arxiv.org/pdf/1802.00047","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3526341773","display_name":null,"funder_award_id":"1633196","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3572953870","display_name":null,"funder_award_id":"CCF-1442635","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4477870991","display_name":null,"funder_award_id":"DMS-1830210","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7860735129","display_name":null,"funder_award_id":"SNL 014150709","funder_id":"https://openalex.org/F4320332180","funder_display_name":"Defense Advanced Research Projects Agency"},{"id":"https://openalex.org/G8104471843","display_name":null,"funder_award_id":"CMMI-1538746","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G855777396","display_name":null,"funder_award_id":"CCF-1650913","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W1621556183","https://openalex.org/W1748168094","https://openalex.org/W1884359871","https://openalex.org/W1968135884","https://openalex.org/W1968398095","https://openalex.org/W1968843188","https://openalex.org/W2000157792","https://openalex.org/W2005102197","https://openalex.org/W2050230608","https://openalex.org/W2055433312","https://openalex.org/W2056453713","https://openalex.org/W2089905787","https://openalex.org/W2103972604","https://openalex.org/W2118550318","https://openalex.org/W2119058682","https://openalex.org/W2120872934","https://openalex.org/W2133999891","https://openalex.org/W2134332047","https://openalex.org/W2137392412","https://openalex.org/W2144730813","https://openalex.org/W2145040771","https://openalex.org/W2146130798","https://openalex.org/W2166163936","https://openalex.org/W2167077875","https://openalex.org/W2171046470","https://openalex.org/W2268674159","https://openalex.org/W2406385802","https://openalex.org/W2517080291","https://openalex.org/W2566608758","https://openalex.org/W2611328865","https://openalex.org/W2766863567","https://openalex.org/W2768927505","https://openalex.org/W2772646190","https://openalex.org/W2774750933","https://openalex.org/W2792374469","https://openalex.org/W2810923269","https://openalex.org/W2963476323","https://openalex.org/W2964072480","https://openalex.org/W3003365835","https://openalex.org/W3010434925","https://openalex.org/W3098346713","https://openalex.org/W3099447760","https://openalex.org/W3100283647","https://openalex.org/W3104501706","https://openalex.org/W3105489725","https://openalex.org/W3124617746","https://openalex.org/W3145128584","https://openalex.org/W4236242434","https://openalex.org/W4246219036","https://openalex.org/W4247661411","https://openalex.org/W4294373705","https://openalex.org/W6637766136","https://openalex.org/W6677959539","https://openalex.org/W6682042988","https://openalex.org/W6736425207","https://openalex.org/W6740257388","https://openalex.org/W6745725969"],"related_works":["https://openalex.org/W2952489973","https://openalex.org/W4300776969","https://openalex.org/W2106005123","https://openalex.org/W2788210652","https://openalex.org/W2266965707","https://openalex.org/W2972830027","https://openalex.org/W4387323768","https://openalex.org/W2084983808","https://openalex.org/W3144354057","https://openalex.org/W3213035342"],"abstract_inverted_index":{"We":[0,45,60,107],"consider":[1],"the":[2,20,34,39,47,70,74,92,103,111,130,146],"matrix":[3,35,42,80],"completion":[4,36,81],"problem":[5],"with":[6],"a":[7,50,57,101,123],"deterministic":[8],"pattern":[9],"of":[10,53,77,94,145],"observed":[11,134],"entries.":[12,135],"In":[13],"this":[14,87],"setting,":[15],"we":[16,68,97,137],"aim":[17],"to":[18,33,128],"answer":[19,46],"question:":[21],"Under":[22],"what":[23],"conditions":[24],"will":[25],"there":[26],"be":[27],"(at":[28],"least":[29],"locally)":[30],"unique":[31],"solution":[32],"problem,":[37],"i.e.,":[38],"underlying":[40],"true":[41],"is":[43,89,105],"identifiable?":[44],"question":[48],"from":[49,133],"certain":[51],"point":[52],"view":[54],"and":[55,96,120],"outline":[56],"geometric":[58],"perspective.":[59],"give":[61],"an":[62],"algebraically":[63],"verifiable":[64],"sufficient":[65],"condition,":[66,72],"which":[67],"call":[69],"well-posedness":[71],"for":[73,91],"local":[75],"uniqueness":[76],"minimum":[78],"rank":[79,132],"(MRMC)":[82],"solutions.":[83],"It":[84],"appears":[85],"that":[86,110],"condition":[88,104],"basic":[90],"analysis":[93],"MRMC,":[95],"show":[98],"that,":[99],"in":[100],"sense,":[102],"generic.":[106],"also":[108],"argue":[109],"low-rank":[112],"approximation":[113],"approaches":[114],"are":[115],"more":[116],"stable":[117],"than":[118],"MRMC":[119],"further":[121],"propose":[122],"sequential":[124],"statistical":[125],"testing":[126],"procedure":[127],"determine":[129],"\u201ctrue\u201d":[131],"Finally,":[136],"provide":[138],"numerical":[139],"examples":[140],"aimed":[141],"at":[142],"verifying":[143],"validity":[144],"presented":[147],"theory.":[148]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
