{"id":"https://openalex.org/W2101735540","doi":"https://doi.org/10.1109/icdmw.2010.64","title":"Robust Low-Rank Subspace Segmentation with Semidefinite Guarantees","display_name":"Robust Low-Rank Subspace Segmentation with Semidefinite Guarantees","publication_year":2010,"publication_date":"2010-12-01","ids":{"openalex":"https://openalex.org/W2101735540","doi":"https://doi.org/10.1109/icdmw.2010.64","mag":"2101735540"},"language":"en","primary_location":{"id":"doi:10.1109/icdmw.2010.64","doi":"https://doi.org/10.1109/icdmw.2010.64","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icdmw.2010.64","pdf_url":null,"source":{"id":"https://openalex.org/S4393918563","display_name":"IEEE ... International Conference on Data Mining workshops","issn_l":"2375-9259","issn":["2375-9259"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["norway-1"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE International Conference on Data Mining Workshops","raw_type":"proceedings-article"},"volume":null,"type":"conference-paper","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1009.3802","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022810673","display_name":"Yuzhao Ni","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Yuzhao Ni","raw_affiliation_strings":["School of Computing, National University of Singapore, Singapore","Sch. of Comput. Nat., Univ. of Singapore, Singapore, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computing, National University of Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]},{"raw_affiliation_string":"Sch. of Comput. Nat., Univ. of Singapore, Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011253128","display_name":"Ju Sun","orcid":"https://orcid.org/0000-0002-2017-5903","observed_orcids":["https://orcid.org/0000-0002-2017-5903"]},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Ju Sun","raw_affiliation_strings":["Interactive & Digital Media Institute, National University of Singapore, Singapore","Interactive & Digital Media Inst., Nat. Univ. of Singapore, Singapore, Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Interactive & Digital Media Institute, National University of Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]},{"raw_affiliation_string":"Interactive & Digital Media Inst., Nat. Univ. of Singapore, Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100776794","display_name":"Xiao\u2013Tong Yuan","orcid":"https://orcid.org/0000-0002-7151-8806","observed_orcids":["https://orcid.org/0000-0002-7151-8806"]},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Xiaotong Yuan","raw_affiliation_strings":["Department of Electrical and Computer Engineering, National University of Singapore, Singapore","[Dept. of Electr. & Comput. Eng., Nat. Univ. of Singapore, Singapore, Singapore]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, National University of Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]},{"raw_affiliation_string":"[Dept. of Electr. & Comput. Eng., Nat. Univ. of Singapore, Singapore, Singapore]","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100381753","display_name":"Shuicheng Yan","orcid":"https://orcid.org/0000-0001-8906-3777","observed_orcids":["https://orcid.org/0000-0001-8906-3777"]},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Shuicheng Yan","raw_affiliation_strings":["Department of Electrical and Computer Engineering, National University of Singapore, Singapore","[Dept. of Electr. & Comput. Eng., Nat. Univ. of Singapore, Singapore, Singapore]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, National University of Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]},{"raw_affiliation_string":"[Dept. of Electr. & Comput. Eng., Nat. Univ. of Singapore, Singapore, Singapore]","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030078173","display_name":"Loong\u2010Fah Cheong","orcid":"https://orcid.org/0000-0001-5259-9113","observed_orcids":["https://orcid.org/0000-0001-5259-9113"]},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Loong-Fah Cheong","raw_affiliation_strings":["Department of Electrical and Computer Engineering, National University of Singapore, Singapore","[Dept. of Electr. & Comput. Eng., Nat. Univ. of Singapore, Singapore, Singapore]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, National University of Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]},{"raw_affiliation_string":"[Dept. of Electr. & Comput. Eng., Nat. Univ. of Singapore, Singapore, Singapore]","institution_ids":["https://openalex.org/I165932596"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I165932596"],"apc_list":null,"apc_paid":null,"fwci":4.3232,"has_fulltext":true,"cited_by_count":58,"citation_normalized_percentile":{"value":0.96097938,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"1179","last_page":"1188"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.7002000212669373,"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"}},"topics":[{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.7002000212669373,"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/T10637","display_name":"Advanced Clustering Algorithms Research","score":0.2671000063419342,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.01119999960064888,"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/spectral-clustering","display_name":"spectral clustering","score":0.9139999747276306},{"id":"https://openalex.org/keywords/low-rank-representation","display_name":"low-rank representation","score":0.9279999732971191},{"id":"https://openalex.org/keywords/positive-semidefinite-constraints","display_name":"positive semidefinite constraints","score":0.8840000033378601},{"id":"https://openalex.org/keywords/affinity-matrix-learning","display_name":"affinity matrix learning","score":0.8209999799728394},{"id":"https://openalex.org/keywords/sparse-reconstruction","display_name":"sparse reconstruction","score":0.9350000023841858},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"semidefinite programming","score":0.7149999737739563},{"id":"https://openalex.org/keywords/manifold-data","display_name":"manifold data","score":0.4320000112056732}],"concepts":[{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5839850306510925},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.5812060832977295},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5769109725952148},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.522476315498352},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5137041807174683},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5119212865829468},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.48351410031318665},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45868706703186035},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.44471243023872375},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.4123212397098541},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3968486189842224},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35119718313217163},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3203672170639038},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.22718709707260132},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.15889891982078552},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.09454208612442017},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/icdmw.2010.64","doi":"https://doi.org/10.1109/icdmw.2010.64","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icdmw.2010.64","pdf_url":null,"source":{"id":"https://openalex.org/S4393918563","display_name":"IEEE ... International Conference on Data Mining workshops","issn_l":"2375-9259","issn":["2375-9259"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["norway-1"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2010 IEEE International Conference on Data Mining Workshops","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1009.3802","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1009.3802","pdf_url":"https://arxiv.org/pdf/1009.3802","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.767.7717","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.767.7717","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1009.3802.pdf","raw_type":"text"},{"id":"pmh:oai:scholarbank.nus.edu.sg:10635/43314","doi":null,"is_oa":false,"landing_page_url":"http://scholarbank.nus.edu.sg/handle/10635/43314","pdf_url":null,"source":{"id":"https://openalex.org/S7407052290","display_name":"National University of Singapore","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scopus","raw_type":"Conference Paper"},{"id":"doi:10.48550/arxiv.1009.3802","doi":"https://doi.org/10.48550/arxiv.1009.3802","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1009.3802","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1009.3802","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1009.3802","pdf_url":"https://arxiv.org/pdf/1009.3802","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320698","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49"},{"id":"https://openalex.org/F4320320749","display_name":"Media Development Authority - Singapore","ror":"https://ror.org/00hhhdj49"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2101735540.pdf","grobid_xml":"https://content.openalex.org/works/W2101735540.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W79405465","https://openalex.org/W83404773","https://openalex.org/W658559791","https://openalex.org/W1573318337","https://openalex.org/W1736339626","https://openalex.org/W1904464160","https://openalex.org/W1950520880","https://openalex.org/W1986007546","https://openalex.org/W2003217181","https://openalex.org/W2003361735","https://openalex.org/W2023722580","https://openalex.org/W2052311585","https://openalex.org/W2085261163","https://openalex.org/W2103972604","https://openalex.org/W2118154608","https://openalex.org/W2118550318","https://openalex.org/W2121947440","https://openalex.org/W2124608575","https://openalex.org/W2129131372","https://openalex.org/W2132914434","https://openalex.org/W2135046866","https://openalex.org/W2145962650","https://openalex.org/W2149863017","https://openalex.org/W2339666411","https://openalex.org/W2611328865","https://openalex.org/W2798909945","https://openalex.org/W2799061466","https://openalex.org/W2950565951","https://openalex.org/W3102105495","https://openalex.org/W4230946174","https://openalex.org/W6677554766","https://openalex.org/W6929385289","https://openalex.org/W7014191107"],"related_works":["https://openalex.org/W188881548","https://openalex.org/W3101387085","https://openalex.org/W3026594100","https://openalex.org/W2572974391","https://openalex.org/W2785583244","https://openalex.org/W7103656307","https://openalex.org/W2500665848","https://openalex.org/W2950565951","https://openalex.org/W2144902590","https://openalex.org/W2309767227"],"abstract_inverted_index":{"Recently":[0],"there":[1,62,85],"is":[2,86,156,188],"a":[3],"line":[4],"of":[5,38,74,134,194],"research":[6],"work":[7],"proposing":[8],"to":[9,14,102,148,158,173,192],"employ":[10],"Spectral":[11],"Clustering":[12],"(SC)":[13],"segment":[15],"(group)":[16],"high-dimensional":[17],"structural":[18],"data":[19,214],"such":[20],"as":[21],"those":[22],"(approximately)":[23],"lying":[24],"on":[25,209],"subspaces":[26],"or":[27,118],"low-dimensional":[28],"manifolds.":[29],"By":[30],"learning":[31,111],"the":[32,36,49,60,71,75,94,104,159,183],"affinity":[33,77,95],"matrix":[34,78],"in":[35,43,51,82,128,151],"form":[37],"sparse":[39],"reconstruction,":[40],"techniques":[41],"proposed":[42,161],"this":[44],"vein":[45],"often":[46,87],"considerably":[47],"boost":[48],"performance":[50],"subspace":[52],"settings":[53],"where":[54],"traditional":[55],"SC":[56,97],"can":[57,125],"fail.":[58],"Despite":[59],"success,":[61],"are":[63],"fundamental":[64],"problems":[65],"that":[66,92,122,138,193],"have":[67],"been":[68],"left":[69],"unsolved:":[70],"spectrum":[72],"property":[73],"learned":[76],"cannot":[79],"be":[80,126],"gauged":[81],"advance,":[83],"and":[84,120,166,170,176,204,212],"one":[88],"ugly":[89],"symmetrization":[90],"step":[91],"post-processes":[93],"for":[96],"input.":[98],"Hence":[99],"we":[100],"advocate":[101],"enforce":[103],"symmetric":[105],"positive":[106],"semidefinite":[107],"constraint":[108],"explicitly":[109],"during":[110],"(Low-Rank":[112],"Representation":[113,163],"with":[114],"Positive":[115],"SemiDefinite":[116],"constraint,":[117],"LRR-PSD),":[119],"show":[121,149],"factually":[123],"it":[124],"solved":[127],"an":[129],"exquisite":[130],"scheme":[131,206],"efficiently":[132],"instead":[133],"general-purpose":[135],"SDP":[136],"solvers":[137],"usually":[139],"scale":[140],"up":[141],"poorly.":[142],"We":[143,199],"provide":[144],"rigorous":[145],"mathematical":[146],"derivations":[147],"that,":[150],"its":[152],"canonical":[153],"form,":[154],"LRR-PSD":[155,175],"equivalent":[157],"recently":[160],"Low-Rank":[162],"(LRR)":[164],"scheme,":[165],"hence":[167],"offer":[168],"theoretic":[169,202],"practical":[171],"insights":[172],"both":[174,210],"LRR,":[177,195],"inviting":[178],"future":[179],"research.":[180],"As":[181],"per":[182],"computational":[184],"cost,":[185],"our":[186,201],"proposal":[187],"at":[189],"most":[190],"comparable":[191],"if":[196],"not":[197],"less.":[198],"validate":[200],"analysis":[203],"optimization":[205],"by":[207],"experiments":[208],"synthetic":[211],"real":[213],"sets.":[215]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":8}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}