{"id":"https://openalex.org/W3213475720","doi":"https://doi.org/10.1109/tit.2022.3223230","title":"Unique Sparse Decomposition of Low Rank Matrices","display_name":"Unique Sparse Decomposition of Low Rank Matrices","publication_year":2022,"publication_date":"2022-11-17","ids":{"openalex":"https://openalex.org/W3213475720","doi":"https://doi.org/10.1109/tit.2022.3223230","mag":"3213475720"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2022.3223230","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3223230","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","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/A5090184480","display_name":"Dian Jin","orcid":"https://orcid.org/0000-0001-7782-8824"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Dian Jin","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Rutgers University, New Brunswick, Piscataway, NJ, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Rutgers University, New Brunswick, Piscataway, NJ, USA","institution_ids":["https://openalex.org/I102322142"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050333855","display_name":"Xin Bing","orcid":"https://orcid.org/0000-0001-7462-9360"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Xin Bing","raw_affiliation_strings":["Department of Statistical Sciences, University of Toronto, Toronto, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Statistical Sciences, University of Toronto, Toronto, Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100667140","display_name":"Yuqian Zhang","orcid":"https://orcid.org/0000-0001-6080-9125"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yuqian Zhang","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Rutgers University, New Brunswick, Piscataway, NJ, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Rutgers University, New Brunswick, Piscataway, NJ, USA","institution_ids":["https://openalex.org/I102322142"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5090184480"],"corresponding_institution_ids":["https://openalex.org/I102322142"],"apc_list":null,"apc_paid":null,"fwci":0.6502,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.5840132,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"69","issue":"4","first_page":"2452","last_page":"2484"},"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9930999875068665,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7123570442199707},{"id":"https://openalex.org/keywords/sparse-approximation","display_name":"Sparse approximation","score":0.6407005786895752},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6073832511901855},{"id":"https://openalex.org/keywords/initialization","display_name":"Initialization","score":0.5980808734893799},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5936580300331116},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5929819941520691},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.5861430168151855},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.5707554221153259},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5090448260307312},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.5010714530944824},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.45422011613845825},{"id":"https://openalex.org/keywords/permutation-matrix","display_name":"Permutation matrix","score":0.4444265365600586},{"id":"https://openalex.org/keywords/matrix-completion","display_name":"Matrix completion","score":0.4382859766483307},{"id":"https://openalex.org/keywords/unit-sphere","display_name":"Unit sphere","score":0.4330664277076721},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3636890649795532},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33322516083717346},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20777425169944763},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08840584754943848}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7123570442199707},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.6407005786895752},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6073832511901855},{"id":"https://openalex.org/C114466953","wikidata":"https://www.wikidata.org/wiki/Q6034165","display_name":"Initialization","level":2,"score":0.5980808734893799},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5936580300331116},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5929819941520691},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.5861430168151855},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5707554221153259},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5090448260307312},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.5010714530944824},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.45422011613845825},{"id":"https://openalex.org/C84140500","wikidata":"https://www.wikidata.org/wiki/Q851512","display_name":"Permutation matrix","level":3,"score":0.4444265365600586},{"id":"https://openalex.org/C2778459887","wikidata":"https://www.wikidata.org/wiki/Q6787865","display_name":"Matrix completion","level":3,"score":0.4382859766483307},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.4330664277076721},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3636890649795532},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33322516083717346},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20777425169944763},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08840584754943848},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2022.3223230","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3223230","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W143004564","https://openalex.org/W1517295252","https://openalex.org/W1540764732","https://openalex.org/W1603765807","https://openalex.org/W1762709062","https://openalex.org/W1975900269","https://openalex.org/W2006544565","https://openalex.org/W2009941369","https://openalex.org/W2019502123","https://openalex.org/W2026622206","https://openalex.org/W2039665200","https://openalex.org/W2044809283","https://openalex.org/W2089385570","https://openalex.org/W2096686680","https://openalex.org/W2096900708","https://openalex.org/W2097417531","https://openalex.org/W2116840760","https://openalex.org/W2122825543","https://openalex.org/W2123649031","https://openalex.org/W2145962650","https://openalex.org/W2174781702","https://openalex.org/W2294798173","https://openalex.org/W2407000478","https://openalex.org/W2514234490","https://openalex.org/W2601846890","https://openalex.org/W2745949522","https://openalex.org/W2962959718","https://openalex.org/W2963589422","https://openalex.org/W2965497096","https://openalex.org/W2972345688","https://openalex.org/W2998108430","https://openalex.org/W3008537012","https://openalex.org/W3008904489","https://openalex.org/W3014542904","https://openalex.org/W3015546988","https://openalex.org/W3018018008","https://openalex.org/W3042661192","https://openalex.org/W3049025113","https://openalex.org/W3085197375","https://openalex.org/W3094331929","https://openalex.org/W3103457637","https://openalex.org/W3105677939","https://openalex.org/W3153711428","https://openalex.org/W4231510805","https://openalex.org/W4237723258","https://openalex.org/W6639619044","https://openalex.org/W6675907514","https://openalex.org/W6675992869","https://openalex.org/W6679042499","https://openalex.org/W6680770193","https://openalex.org/W6714134332","https://openalex.org/W6734280532","https://openalex.org/W6751757243","https://openalex.org/W6771777522","https://openalex.org/W6773236401","https://openalex.org/W6780388124"],"related_works":["https://openalex.org/W2091883426","https://openalex.org/W2174948646","https://openalex.org/W3173235360","https://openalex.org/W4294691692","https://openalex.org/W2024017047","https://openalex.org/W4318256793","https://openalex.org/W2789229307","https://openalex.org/W2594370889","https://openalex.org/W2390720471","https://openalex.org/W2051410394"],"abstract_inverted_index":{"The":[0],"problem":[1,19,29,149],"of":[2,9,30,35,123],"finding":[3],"a":[4,10,15,32,36,53,146,182],"unique":[5,33],"low":[6,37,119],"dimensional":[7],"decomposition":[8,34,122],"given":[11],"matrix":[12,39,73,101],"has":[13,84],"been":[14],"fundamental":[16],"and":[17,99,177],"recurrent":[18],"in":[20],"many":[21],"areas.":[22],"In":[23],"this":[24,118],"paper,":[25],"we":[26,57],"study":[27],"the":[28,72,100,152,174],"seeking":[31],"rank":[38],"<inline-formula":[40,59,74,89,102,124],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[41,60,75,90,103,125,167,204],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[42,61,76,91,104,126],"<tex-math":[43,62,77,92,105,127],"notation=\"LaTeX\">$\\boldsymbol":[44,63,78,106,128],"Y\\in":[45],"\\mathbb":[46,80,108],"R":[47],"^{p\\times":[48],"n}$":[49,110],"</tex-math></inline-formula>":[50,70,83,97,111,130],"that":[51,117,164],"admits":[52],"sparse":[54,121],"representation.":[55],"Specifically,":[56],"consider":[58],"Y=":[64],"\\boldsymbol":[65,67],"A":[66],"X":[68],"$":[69],"where":[71],"A\\in":[79],"R^{p\\times":[81],"r}$":[82],"full":[85],"column":[86],"rank,":[87,120],"with":[88,187],"notation=\"LaTeX\">$r":[93],"&lt;":[94],"\\min":[95],"\\{n,p\\}$":[96],",":[98],"X\\in":[107],"R^{r\\times":[109],"is":[112,171],"element-wise":[113],"sparse.":[114],"We":[115],"prove":[116],"Y$":[129],"can":[131,178],"be":[132,179],"uniquely":[133],"identified,":[134],"up":[135],"to":[136,173],"some":[137],"intrinsic":[138],"signed":[139],"permutation.":[140],"Our":[141,155,193],"approach":[142],"relies":[143],"on":[144],"solving":[145],"nonconvex":[147,160],"optimization":[148,161],"constrained":[150],"over":[151],"unit":[153],"sphere.":[154],"geometric":[156],"analysis":[157],"for":[158],"its":[159],"landscape":[162],"shows":[163],"any":[165,188],"<italic":[166],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">strict</i>":[168],"local":[169],"solution":[170],"close":[172],"ground":[175],"truth,":[176],"recovered":[180],"by":[181,198],"simple":[183],"data-driven":[184],"initialization":[185],"followed":[186],"second":[189],"order":[190],"descent":[191],"algorithm.":[192],"theoretical":[194],"findings":[195],"are":[196],"corroborated":[197],"numerical":[199],"experiments.":[200],"<xref":[201],"ref-type=\"fn\"":[202],"rid=\"fn1\"":[203],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</xref>":[205]},"counts_by_year":[{"year":2025,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
