{"id":"https://openalex.org/W2766053647","doi":"https://doi.org/10.1109/tip.2017.2764262","title":"Implicit Block Diagonal Low-Rank Representation","display_name":"Implicit Block Diagonal Low-Rank Representation","publication_year":2017,"publication_date":"2017-10-18","ids":{"openalex":"https://openalex.org/W2766053647","doi":"https://doi.org/10.1109/tip.2017.2764262","mag":"2766053647","pmid":"https://pubmed.ncbi.nlm.nih.gov/29053462"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2017.2764262","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2017.2764262","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"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 Image Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5048069849","display_name":"Xingyu Xie","orcid":"https://orcid.org/0000-0002-8756-5981"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xingyu Xie","raw_affiliation_strings":["College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101604533","display_name":"Xianglin Guo","orcid":"https://orcid.org/0000-0002-8517-715X"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xianglin Guo","raw_affiliation_strings":["College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China","institution_ids":["https://openalex.org/I9842412"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019542310","display_name":"Guangcan Liu","orcid":"https://orcid.org/0000-0002-9428-4387"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guangcan Liu","raw_affiliation_strings":["B-DAT Laboratory, Nanjing University of Information Science and Technology, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"B-DAT Laboratory, Nanjing University of Information Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I200845125"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100384655","display_name":"Jun Wang","orcid":"https://orcid.org/0000-0001-9223-2615"},"institutions":[{"id":"https://openalex.org/I9842412","display_name":"Nanjing University of Aeronautics and Astronautics","ror":"https://ror.org/01scyh794","country_code":"CN","type":"education","lineage":["https://openalex.org/I9842412"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Wang","raw_affiliation_strings":["College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China"],"affiliations":[{"raw_affiliation_string":"College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China","institution_ids":["https://openalex.org/I9842412"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5048069849"],"corresponding_institution_ids":["https://openalex.org/I9842412"],"apc_list":null,"apc_paid":null,"fwci":7.1607,"has_fulltext":false,"cited_by_count":90,"citation_normalized_percentile":{"value":0.98024037,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"27","issue":"1","first_page":"477","last_page":"489"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9994999766349792,"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":0.9994999766349792,"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/T10057","display_name":"Face and Expression Recognition","score":0.9983000159263611,"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/T10689","display_name":"Remote-Sensing Image Classification","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"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/kernelization","display_name":"Kernelization","score":0.6567644476890564},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.5611920356750488},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.560476541519165},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5365967750549316},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.520012617111206},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.49890851974487305},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.48409950733184814},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46595603227615356},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45787569880485535},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.4476831257343292},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.4183552861213684},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.4152211546897888},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.32268399000167847},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3169565796852112},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.20440426468849182},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.14048853516578674},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.11913758516311646}],"concepts":[{"id":"https://openalex.org/C207225210","wikidata":"https://www.wikidata.org/wiki/Q1759539","display_name":"Kernelization","level":3,"score":0.6567644476890564},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.5611920356750488},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.560476541519165},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5365967750549316},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.520012617111206},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.49890851974487305},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.48409950733184814},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46595603227615356},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45787569880485535},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.4476831257343292},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.4183552861213684},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.4152211546897888},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32268399000167847},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3169565796852112},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.20440426468849182},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.14048853516578674},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.11913758516311646},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tip.2017.2764262","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2017.2764262","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"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 Image Processing","raw_type":"journal-article"},{"id":"pmid:29053462","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/29053462","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on image processing : a publication of the IEEE Signal Processing Society","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G367232148","display_name":null,"funder_award_id":"61502238","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5043828642","display_name":null,"funder_award_id":"61402224","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5873875152","display_name":null,"funder_award_id":"BK2014833","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G6007836921","display_name":null,"funder_award_id":"NE2016004","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G8641035702","display_name":null,"funder_award_id":"BK20160040","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G8830730299","display_name":null,"funder_award_id":"61622305","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8884467456","display_name":null,"funder_award_id":"NE2014402","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320308380","display_name":"Yale University","ror":"https://ror.org/03v76x132"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W79405465","https://openalex.org/W360528349","https://openalex.org/W1496571393","https://openalex.org/W1607012965","https://openalex.org/W1976632974","https://openalex.org/W1997201895","https://openalex.org/W1998627394","https://openalex.org/W2002329661","https://openalex.org/W2003217181","https://openalex.org/W2015904350","https://openalex.org/W2017441234","https://openalex.org/W2048023990","https://openalex.org/W2078853581","https://openalex.org/W2094465594","https://openalex.org/W2097308346","https://openalex.org/W2100549954","https://openalex.org/W2100556411","https://openalex.org/W2103560185","https://openalex.org/W2103972604","https://openalex.org/W2106115875","https://openalex.org/W2117539524","https://openalex.org/W2118154608","https://openalex.org/W2121947440","https://openalex.org/W2123921160","https://openalex.org/W2132914434","https://openalex.org/W2139054653","https://openalex.org/W2154202969","https://openalex.org/W2165874743","https://openalex.org/W2167732364","https://openalex.org/W2183341477","https://openalex.org/W2184634347","https://openalex.org/W2239853929","https://openalex.org/W2271221198","https://openalex.org/W2271263562","https://openalex.org/W2294644361","https://openalex.org/W2344260814","https://openalex.org/W2410894298","https://openalex.org/W2463532177","https://openalex.org/W2509542487","https://openalex.org/W2532206188","https://openalex.org/W2951085447","https://openalex.org/W2963165461","https://openalex.org/W2963840432","https://openalex.org/W3102566946","https://openalex.org/W3105835503","https://openalex.org/W3118608800","https://openalex.org/W4250657332","https://openalex.org/W4254313632","https://openalex.org/W6603183647","https://openalex.org/W6629607343","https://openalex.org/W6675164516","https://openalex.org/W6684578312","https://openalex.org/W6686534882","https://openalex.org/W6725689142","https://openalex.org/W6747568791","https://openalex.org/W6787972765"],"related_works":["https://openalex.org/W2470197230","https://openalex.org/W1991452943","https://openalex.org/W2110827730","https://openalex.org/W1999989727","https://openalex.org/W1647998871","https://openalex.org/W2151383796","https://openalex.org/W2381535510","https://openalex.org/W1518235162","https://openalex.org/W2164814160","https://openalex.org/W2095257757"],"abstract_inverted_index":{"While":[0],"current":[1],"block":[2,26,66,88,100],"diagonal":[3,27,67,89,101],"constrained":[4],"subspace":[5],"clustering":[6],"methods":[7],"are":[8],"performed":[9],"explicitly":[10],"on":[11,154],"the":[12,25,30,40,58,63,95,104,115,131,146,161],"original":[13],"data":[14,42,158],"space,":[15],"in":[16,44,62,77,117],"practice,":[17],"it":[18,50],"is":[19,46,51],"often":[20],"more":[21],"desirable":[22],"to":[23,55],"embed":[24],"prior":[28,102],"into":[29,103],"reproducing":[31],"kernel":[32],"Hilbert":[33],"feature":[34,97],"space":[35],"by":[36,93,122],"kernelization":[37,61],"techniques,":[38],"as":[39],"underlying":[41],"structure":[43],"reality":[45],"usually":[47],"nonlinear.":[48],"However,":[49],"still":[52],"unknown":[53],"how":[54],"carry":[56],"out":[57],"embedding":[59],"and":[60,99,130,156],"models":[64],"with":[65],"constraints.":[68],"In":[69],"this":[70,78],"paper,":[71],"we":[72,81,112,140],"shall":[73],"take":[74],"a":[75,83,126,134],"step":[76],"direction.":[79],"First,":[80],"establish":[82],"novel":[84],"model":[85,116],"termed":[86],"implicit":[87,96],"low-rank":[90,106],"representation":[91,98,107,129],"(IBDLR),":[92],"incorporating":[94],"prevalent":[105],"method.":[108],"Second,":[109],"mostly":[110],"important,":[111],"show":[113],"that":[114],"IBDLR":[118,165],"could":[119],"be":[120],"kernelized":[121],"making":[123],"use":[124],"of":[125,133,148,163],"smoothed":[127],"dual":[128],"specifics":[132],"proximal":[135],"gradient-based":[136],"optimization":[137,150],"algorithm.":[138,151],"Finally,":[139],"provide":[141],"some":[142],"theoretical":[143],"analyses":[144],"for":[145],"convergence":[147],"our":[149,164],"Comprehensive":[152],"experiments":[153],"synthetic":[155],"real-world":[157],"sets":[159],"demonstrate":[160],"superiorities":[162],"over":[166],"state-of-the-art":[167],"methods.":[168]},"counts_by_year":[{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":14},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":14},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":5}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
