{"id":"https://openalex.org/W3135747855","doi":"https://doi.org/10.1109/msp.2020.3046233","title":"On Characteristic Rank for Matrix and Tensor Completion [Lecture Notes]","display_name":"On Characteristic Rank for Matrix and Tensor Completion [Lecture Notes]","publication_year":2021,"publication_date":"2021-02-26","ids":{"openalex":"https://openalex.org/W3135747855","doi":"https://doi.org/10.1109/msp.2020.3046233","mag":"3135747855"},"language":"en","primary_location":{"id":"doi:10.1109/msp.2020.3046233","is_oa":false,"landing_page_url":"https://doi.org/10.1109/msp.2020.3046233","pdf_url":null,"source":{"id":"https://openalex.org/S120977877","display_name":"IEEE Signal Processing Magazine","issn_l":"1053-5888","issn":["1053-5888","1558-0792"],"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 Signal Processing Magazine","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/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 School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA"],"affiliations":[{"raw_affiliation_string":"H. Milton Stewart School of School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047736740","display_name":"Yao Xie","orcid":"https://orcid.org/0000-0001-6777-2951"},"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 School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA"],"affiliations":[{"raw_affiliation_string":"H. Milton Stewart School of School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102969380","display_name":"Rui Zhang","orcid":"https://orcid.org/0000-0002-4975-5135"},"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 School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia, USA"],"affiliations":[{"raw_affiliation_string":"H. Milton Stewart School of School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia, 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":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04474002,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"38","issue":"2","first_page":"125","last_page":"129"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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":0.9951000213623047,"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"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9944000244140625,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/identifiability","display_name":"Identifiability","score":0.7653680443763733},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.7550545334815979},{"id":"https://openalex.org/keywords/matrix-completion","display_name":"Matrix completion","score":0.6799987554550171},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6619736552238464},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5735501050949097},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.5503305196762085},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5374598503112793},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5317835807800293},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4849283993244171},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.46081727743148804},{"id":"https://openalex.org/keywords/signal","display_name":"SIGNAL (programming language)","score":0.441506028175354},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.43021538853645325},{"id":"https://openalex.org/keywords/matrix-algebra","display_name":"Matrix algebra","score":0.424991250038147},{"id":"https://openalex.org/keywords/low-rank-approximation","display_name":"Low-rank approximation","score":0.424460232257843},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3958510160446167},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37515905499458313},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36704736948013306},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3203188478946686},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2479228675365448},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.13837692141532898},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.12798696756362915},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07987898588180542},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.07315951585769653},{"id":"https://openalex.org/keywords/digital-signal-processing","display_name":"Digital signal processing","score":0.0714971125125885}],"concepts":[{"id":"https://openalex.org/C122770356","wikidata":"https://www.wikidata.org/wiki/Q1656753","display_name":"Identifiability","level":2,"score":0.7653680443763733},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.7550545334815979},{"id":"https://openalex.org/C2778459887","wikidata":"https://www.wikidata.org/wiki/Q6787865","display_name":"Matrix completion","level":3,"score":0.6799987554550171},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6619736552238464},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5735501050949097},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.5503305196762085},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5374598503112793},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5317835807800293},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4849283993244171},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46081727743148804},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.441506028175354},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.43021538853645325},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.424991250038147},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.424460232257843},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3958510160446167},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37515905499458313},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36704736948013306},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3203188478946686},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2479228675365448},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.13837692141532898},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12798696756362915},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07987898588180542},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.07315951585769653},{"id":"https://openalex.org/C84462506","wikidata":"https://www.wikidata.org/wiki/Q173142","display_name":"Digital signal processing","level":2,"score":0.0714971125125885},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"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/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"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/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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/msp.2020.3046233","is_oa":false,"landing_page_url":"https://doi.org/10.1109/msp.2020.3046233","pdf_url":null,"source":{"id":"https://openalex.org/S120977877","display_name":"IEEE Signal Processing Magazine","issn_l":"1053-5888","issn":["1053-5888","1558-0792"],"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 Signal Processing Magazine","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2285217686","display_name":null,"funder_award_id":"1938106","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G5084972002","display_name":null,"funder_award_id":"1830210","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G6120277484","display_name":null,"funder_award_id":"1650913","funder_id":"https://openalex.org/F4320337387","funder_display_name":"Division of Computing and Communication Foundations"},{"id":"https://openalex.org/G6127310570","display_name":null,"funder_award_id":"2015787","funder_id":"https://openalex.org/F4320337391","funder_display_name":"Division of Civil, Mechanical and Manufacturing Innovation"}],"funders":[{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"},{"id":"https://openalex.org/F4320337387","display_name":"Division of Computing and Communication Foundations","ror":"https://ror.org/01mng8331"},{"id":"https://openalex.org/F4320337391","display_name":"Division of Civil, Mechanical and Manufacturing Innovation","ror":"https://ror.org/028yd4c30"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1974672421","https://openalex.org/W1989811026","https://openalex.org/W2024165284","https://openalex.org/W2055433312","https://openalex.org/W2097415784","https://openalex.org/W2134332047","https://openalex.org/W2469230926","https://openalex.org/W2785436244","https://openalex.org/W2972719005","https://openalex.org/W3088046644","https://openalex.org/W4301621763","https://openalex.org/W6768217511","https://openalex.org/W6783495111"],"related_works":["https://openalex.org/W2952489973","https://openalex.org/W2106005123","https://openalex.org/W4300776969","https://openalex.org/W2266965707","https://openalex.org/W2108753466","https://openalex.org/W2084983808","https://openalex.org/W2906317811","https://openalex.org/W4318564253","https://openalex.org/W2402491700","https://openalex.org/W2808067721"],"abstract_inverted_index":{"In":[0],"this":[1,35],"lecture":[2],"note,":[3],"we":[4],"discuss":[5],"a":[6,17],"fundamental":[7],"concept,":[8],"referred":[9],"to":[10,64],"as":[11],"the":[12,22,49,66],"characteristic":[13],"rank,":[14],"that":[15],"suggests":[16],"general":[18],"framework":[19,36],"for":[20],"characterizing":[21],"basic":[23,46],"properties":[24],"of":[25,51],"various":[26],"low-dimensional":[27],"models":[28],"used":[29],"in":[30],"signal":[31],"processing.":[32],"We":[33,58],"illustrate":[34,65],"through":[37],"two":[38],"examples-matrix":[39],"and":[40,53],"three-way":[41],"tensor":[42],"completion":[43],"problems-and":[44],"consider":[45,59],"properties,":[47],"including":[48],"identifiability":[50],"matrices":[52],"tensors,":[54],"given":[55],"partial":[56],"observations.":[57],"cases":[60],"without":[61],"observation":[62],"noise":[63],"principle.":[67]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
