{"id":"https://openalex.org/W2541308381","doi":"https://doi.org/10.1109/tit.2018.2879912","title":"A Theoretical Analysis of Noisy Sparse Subspace Clustering on Dimensionality-Reduced Data","display_name":"A Theoretical Analysis of Noisy Sparse Subspace Clustering on Dimensionality-Reduced Data","publication_year":2018,"publication_date":"2018-11-06","ids":{"openalex":"https://openalex.org/W2541308381","doi":"https://doi.org/10.1109/tit.2018.2879912","mag":"2541308381"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2018.2879912","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2879912","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/A5100424577","display_name":"Yining Wang","orcid":"https://orcid.org/0000-0001-9410-0392"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yining Wang","raw_affiliation_strings":["Machine Learning Department, Carnegie Mellon University, Pittsburgh, PA, USA"],"raw_orcid":"https://orcid.org/0000-0001-9410-0392","affiliations":[{"raw_affiliation_string":"Machine Learning Department, Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100394392","display_name":"Yu-Xiang Wang","orcid":"https://orcid.org/0000-0002-6403-212X"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yu-Xiang Wang","raw_affiliation_strings":["Machine Learning Department, Carnegie Mellon University, Pittsburgh, PA, USA"],"raw_orcid":"https://orcid.org/0000-0002-6403-212X","affiliations":[{"raw_affiliation_string":"Machine Learning Department, Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100758181","display_name":"Aarti Singh","orcid":"https://orcid.org/0000-0002-8278-3672"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Aarti Singh","raw_affiliation_strings":["Machine Learning Department, Carnegie Mellon University, Pittsburgh, PA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Machine Learning Department, Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.378,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.85706391,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"65","issue":"2","first_page":"685","last_page":"706"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9984999895095825,"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":0.9984999895095825,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9973999857902527,"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/T10326","display_name":"Indoor and Outdoor Localization Technologies","score":0.9846000075340271,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/subspace-topology","display_name":"Subspace topology","score":0.7845277190208435},{"id":"https://openalex.org/keywords/random-projection","display_name":"Random projection","score":0.7382489442825317},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.7198740839958191},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.7097722887992859},{"id":"https://openalex.org/keywords/data-point","display_name":"Data point","score":0.6458343863487244},{"id":"https://openalex.org/keywords/clustering-high-dimensional-data","display_name":"Clustering high-dimensional data","score":0.5928937792778015},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.5826958417892456},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.5683910250663757},{"id":"https://openalex.org/keywords/random-subspace-method","display_name":"Random subspace method","score":0.5488654971122742},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5069694519042969},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.48664435744285583},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.44742918014526367},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4156283140182495},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.40742480754852295},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3908940255641937}],"concepts":[{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.7845277190208435},{"id":"https://openalex.org/C2777036070","wikidata":"https://www.wikidata.org/wiki/Q18393452","display_name":"Random projection","level":2,"score":0.7382489442825317},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.7198740839958191},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.7097722887992859},{"id":"https://openalex.org/C21080849","wikidata":"https://www.wikidata.org/wiki/Q13611879","display_name":"Data point","level":2,"score":0.6458343863487244},{"id":"https://openalex.org/C184509293","wikidata":"https://www.wikidata.org/wiki/Q5136711","display_name":"Clustering high-dimensional data","level":3,"score":0.5928937792778015},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5826958417892456},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.5683910250663757},{"id":"https://openalex.org/C106135958","wikidata":"https://www.wikidata.org/wiki/Q7291993","display_name":"Random subspace method","level":3,"score":0.5488654971122742},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5069694519042969},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.48664435744285583},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.44742918014526367},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4156283140182495},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.40742480754852295},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3908940255641937},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2018.2879912","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2879912","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":[{"display_name":"Partnerships for the goals","id":"https://metadata.un.org/sdg/17","score":0.44999998807907104}],"awards":[{"id":"https://openalex.org/G6113881652","display_name":null,"funder_award_id":"CAREER IIS-1252412","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6537933445","display_name":null,"funder_award_id":"YIP FA9550-14-1-0285","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G6656405873","display_name":null,"funder_award_id":"BCS-0941518","funder_id":"https://openalex.org/F4320337387","funder_display_name":"Division of Computing and Communication Foundations"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337387","display_name":"Division of Computing and Communication Foundations","ror":"https://ror.org/01mng8331"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":76,"referenced_works":["https://openalex.org/W120847089","https://openalex.org/W590711263","https://openalex.org/W1493892051","https://openalex.org/W1529624360","https://openalex.org/W1533128638","https://openalex.org/W1535505269","https://openalex.org/W1560153690","https://openalex.org/W1577111082","https://openalex.org/W1602085912","https://openalex.org/W1606778734","https://openalex.org/W1669104078","https://openalex.org/W1873763122","https://openalex.org/W1878405293","https://openalex.org/W1950520880","https://openalex.org/W1993962865","https://openalex.org/W1997201895","https://openalex.org/W2025391886","https://openalex.org/W2027595342","https://openalex.org/W2072719872","https://openalex.org/W2093813380","https://openalex.org/W2100282471","https://openalex.org/W2101043704","https://openalex.org/W2102628473","https://openalex.org/W2102823806","https://openalex.org/W2107411554","https://openalex.org/W2118154608","https://openalex.org/W2120872934","https://openalex.org/W2121947440","https://openalex.org/W2132014503","https://openalex.org/W2132788060","https://openalex.org/W2139054653","https://openalex.org/W2144902590","https://openalex.org/W2151683004","https://openalex.org/W2152461258","https://openalex.org/W2164931791","https://openalex.org/W2165874743","https://openalex.org/W2165916500","https://openalex.org/W2168973828","https://openalex.org/W2177347332","https://openalex.org/W2187667697","https://openalex.org/W2229238337","https://openalex.org/W2294644361","https://openalex.org/W2478460150","https://openalex.org/W2561426102","https://openalex.org/W2613579343","https://openalex.org/W2615383372","https://openalex.org/W2911978475","https://openalex.org/W2949910245","https://openalex.org/W2963496380","https://openalex.org/W2963654369","https://openalex.org/W2963753660","https://openalex.org/W2963768921","https://openalex.org/W2964193132","https://openalex.org/W3004752963","https://openalex.org/W3010434925","https://openalex.org/W3099880660","https://openalex.org/W3101056443","https://openalex.org/W3102566946","https://openalex.org/W4205228770","https://openalex.org/W4250657332","https://openalex.org/W6638071513","https://openalex.org/W6638909838","https://openalex.org/W6639246211","https://openalex.org/W6639294948","https://openalex.org/W6640861363","https://openalex.org/W6675526904","https://openalex.org/W6677959539","https://openalex.org/W6679768017","https://openalex.org/W6679903135","https://openalex.org/W6681275918","https://openalex.org/W6682143360","https://openalex.org/W6684578312","https://openalex.org/W6686567431","https://openalex.org/W6686589845","https://openalex.org/W6704231826","https://openalex.org/W6758947373"],"related_works":["https://openalex.org/W2054290985","https://openalex.org/W2952300832","https://openalex.org/W4302328041","https://openalex.org/W2963753660","https://openalex.org/W2541308381","https://openalex.org/W2087831740","https://openalex.org/W2349719765","https://openalex.org/W2221849156","https://openalex.org/W4321101942","https://openalex.org/W2964193132"],"abstract_inverted_index":{"Subspace":[0],"clustering":[1,64,69],"is":[2,41],"the":[3,33,45,57,85,147],"problem":[4],"of":[5,13,35,47,60,76,109,146],"partitioning":[6],"unlabeled":[7],"data":[8,17,36,96],"points":[9,18,37,97],"into":[10,123],"a":[11,25,61,106,124,134],"number":[12],"clusters":[14],"so":[15],"that":[16,121],"within":[19,98],"one":[20],"cluster":[21],"lie":[22],"approximately":[23],"on":[24,78],"low-dimensional":[26],"linear":[27],"subspace.":[28],"In":[29,52],"many":[30],"practical":[31],"scenarios,":[32],"dimensionality":[34,110],"to":[38,44,84,133],"be":[39],"clustered":[40],"compressed":[42],"due":[43],"constraints":[46],"measurement,":[48],"computation,":[49],"or":[50],"privacy.":[51],"this":[53],"paper,":[54],"we":[55,129],"study":[56],"theoretical":[58],"properties":[59],"popular":[62],"subspace":[63,68,100,125],"algorithm":[65,138],"named":[66],"sparse":[67],"(SSC)":[70],"and":[71,95,104,119,139,143],"establish":[72],"formal":[73],"success":[74],"conditions":[75],"SSC":[77,137],"dimensionality-reduced":[79],"data.":[80],"Our":[81],"analysis":[82,132],"applies":[83],"most":[86],"general":[87],"fully":[88],"deterministic":[89],"model,":[90],"where":[91],"both":[92,141],"underlying":[93],"subspaces":[94],"each":[99],"are":[101],"deterministically":[102],"positioned,":[103],"also":[105],"wide":[107],"range":[108],"reduction":[111],"techniques":[112],"(e.g.,":[113],"Gaussian":[114],"random":[115],"projection,":[116],"uniform":[117],"subsampling,":[118],"sketching)":[120],"fall":[122],"embedding":[126],"framework.":[127],"Finally,":[128],"apply":[130],"our":[131],"differentially":[135],"private":[136],"established":[140],"privacy":[142],"utility":[144],"guarantees":[145],"proposed":[148],"method.":[149]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}