{"id":"https://openalex.org/W2023358798","doi":"https://doi.org/10.14311/nnw.2011.21.022","title":"ROBUST PCA METHODS FOR COMPLETE AND MISSING DATA","display_name":"ROBUST PCA METHODS FOR COMPLETE AND MISSING DATA","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2023358798","doi":"https://doi.org/10.14311/nnw.2011.21.022","mag":"2023358798"},"language":"en","primary_location":{"id":"doi:10.14311/nnw.2011.21.022","doi":"https://doi.org/10.14311/nnw.2011.21.022","is_oa":false,"landing_page_url":"https://doi.org/10.14311/nnw.2011.21.022","pdf_url":null,"source":{"id":"https://openalex.org/S206406316","display_name":"Neural Network World","issn_l":"1210-0552","issn":["1210-0552","2336-4335"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310314184","host_organization_name":"Czech Technical University in Prague","host_organization_lineage":["https://openalex.org/P4310314184"],"host_organization_lineage_names":["Czech Technical University in Prague"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Network World","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5085358291","display_name":"Juha Karhunen","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Juha Karhunen","raw_affiliation_strings":["Helsinki University of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Helsinki University of Technology","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5085358291"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0047,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.76509115,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"21","issue":"5","first_page":"357","last_page":"392"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.8476999998092651,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11871","display_name":"Advanced Statistical Methods and Models","score":0.8476999998092651,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T13141","display_name":"Statistical Methods and Applications","score":0.0357000008225441,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10057","display_name":"Face and Expression Recognition","score":0.031300000846385956,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/robust-pca","display_name":"robust principal component analysis","score":0.9950000047683716},{"id":"https://openalex.org/keywords/missing-data","display_name":"missing data","score":0.9589999914169312},{"id":"https://openalex.org/keywords/outliers","display_name":"outliers","score":0.7829999923706055},{"id":"https://openalex.org/keywords/eigenvector-estimation","display_name":"eigenvector estimation","score":0.7639999985694885},{"id":"https://openalex.org/keywords/subspace-estimation","display_name":"subspace estimation","score":0.8690000176429749},{"id":"https://openalex.org/keywords/robust-estimation","display_name":"robust estimation","score":0.5879999995231628},{"id":"https://openalex.org/keywords/long-tailed-distributions","display_name":"long-tailed distributions","score":0.7039999961853027},{"id":"https://openalex.org/keywords/nonlinear-models","display_name":"nonlinear models","score":0.5080000162124634},{"id":"https://openalex.org/keywords/data-preprocessing","display_name":"data preprocessing","score":0.4880000054836273}],"concepts":[{"id":"https://openalex.org/C9357733","wikidata":"https://www.wikidata.org/wiki/Q6878417","display_name":"Missing data","level":2,"score":0.5945264101028442},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5222685933113098},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.4843250513076782},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.48276057839393616},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3214406669139862},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.19095143675804138}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.14311/nnw.2011.21.022","doi":"https://doi.org/10.14311/nnw.2011.21.022","is_oa":false,"landing_page_url":"https://doi.org/10.14311/nnw.2011.21.022","pdf_url":null,"source":{"id":"https://openalex.org/S206406316","display_name":"Neural Network World","issn_l":"1210-0552","issn":["1210-0552","2336-4335"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310314184","host_organization_name":"Czech Technical University in Prague","host_organization_lineage":["https://openalex.org/P4310314184"],"host_organization_lineage_names":["Czech Technical University in Prague"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Network World","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.723.6052","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.723.6052","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://users.ics.aalto.fi/juha/papers/BW_NNW_RobustPCA.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":73,"referenced_works":["https://openalex.org/W1489793438","https://openalex.org/W1494131642","https://openalex.org/W1513013675","https://openalex.org/W1527786297","https://openalex.org/W1538983967","https://openalex.org/W1540362944","https://openalex.org/W1548802052","https://openalex.org/W1550657683","https://openalex.org/W1590686163","https://openalex.org/W1663973292","https://openalex.org/W1878870224","https://openalex.org/W1920010643","https://openalex.org/W1973178306","https://openalex.org/W1980373236","https://openalex.org/W1984121966","https://openalex.org/W1995721042","https://openalex.org/W2002011878","https://openalex.org/W2004406940","https://openalex.org/W2032196190","https://openalex.org/W2044465660","https://openalex.org/W2044758663","https://openalex.org/W2044822299","https://openalex.org/W2053090063","https://openalex.org/W2056217087","https://openalex.org/W2056885940","https://openalex.org/W2059432853","https://openalex.org/W2064468293","https://openalex.org/W2074033194","https://openalex.org/W2078626246","https://openalex.org/W2079454091","https://openalex.org/W2079991732","https://openalex.org/W2086136644","https://openalex.org/W2088943692","https://openalex.org/W2091675249","https://openalex.org/W2093865719","https://openalex.org/W2094265461","https://openalex.org/W2098477891","https://openalex.org/W2098884960","https://openalex.org/W2107785802","https://openalex.org/W2108395474","https://openalex.org/W2114038444","https://openalex.org/W2117404342","https://openalex.org/W2118034806","https://openalex.org/W2118128687","https://openalex.org/W2126906809","https://openalex.org/W2130269771","https://openalex.org/W2131329059","https://openalex.org/W2133515443","https://openalex.org/W2134816084","https://openalex.org/W2143560894","https://openalex.org/W2145268734","https://openalex.org/W2146610201","https://openalex.org/W2148842444","https://openalex.org/W2149149727","https://openalex.org/W2151673022","https://openalex.org/W2155482699","https://openalex.org/W2155981932","https://openalex.org/W2168321118","https://openalex.org/W2169064301","https://openalex.org/W2170108436","https://openalex.org/W2172249709","https://openalex.org/W2263726068","https://openalex.org/W2287814884","https://openalex.org/W2290669837","https://openalex.org/W2314513482","https://openalex.org/W2333645279","https://openalex.org/W2500095286","https://openalex.org/W2609412092","https://openalex.org/W2896671805","https://openalex.org/W2997337171","https://openalex.org/W3099514962","https://openalex.org/W4300806635","https://openalex.org/W4388297464"],"related_works":["https://openalex.org/W2053295697","https://openalex.org/W2169908081","https://openalex.org/W3008253579","https://openalex.org/W1648965208","https://openalex.org/W4313122090","https://openalex.org/W1878870224","https://openalex.org/W2523664717","https://openalex.org/W2774937756","https://openalex.org/W4409197000","https://openalex.org/W7097197966"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper,":[3],"we":[4,152],"consider":[5],"and":[6,38,50,100],"introduce":[7,113],"methods":[8,115,136,155],"for":[9,34,53,116,172],"robust":[10,114],"principal":[11],"component":[12],"analysis":[13],"(PCA),":[14],"including":[15],"also":[16],"cases":[17,167],"where":[18],"there":[19],"are":[20,93,146],"missing":[21,160],"values":[22],"in":[23,97,148,165],"the":[24,44,48,78,98,106,120,125,149],"data.":[25,150],"PCA":[26,71,110,121,126,143],"is":[27,41,51,57],"a":[28],"widely":[29],"applied":[30,59],"standard":[31,142],"statistical":[32],"method":[33],"data":[35,49,61,99,158],"preprocessing,":[36],"compression,":[37],"analysis.":[39],"It":[40],"based":[42],"on":[43],"second-order":[45],"statistics":[46],"of":[47,68,77,84,118],"optimal":[52],"Gaussian":[54],"data,":[55],"but":[56],"often":[58,138],"to":[60,95,156],"sets":[62],"having":[63],"unknown":[64],"or":[65,82,124],"other":[66],"types":[67],"probability":[69],"distributions.":[70],"can":[72],"be":[73],"derived":[74],"from":[75],"minimization":[76],"mean-square":[79],"representation":[80],"error":[81],"maximization":[83],"variances":[85],"under":[86],"orthonormality":[87],"constraints.":[88],"However,":[89],"these":[90],"quadratic":[91],"criteria":[92],"sensitive":[94],"outliers":[96,145],"long-tailed":[101],"distributions,":[102],"which":[103],"may":[104],"degrade":[105],"results":[107,132,140],"given":[108],"by":[109,129],"badly.":[111],"We":[112],"estimation":[117],"both":[119],"eigenvectors":[122],"directly":[123],"subspace":[127],"spanned":[128],"them.":[130],"Experimental":[131],"show":[133],"that":[134],"our":[135,154],"provide":[137],"better":[139],"than":[141],"when":[144],"present":[147],"Furthermore,":[151],"extend":[153],"incomplete":[157],"with":[159],"values.":[161],"The":[162],"problems":[163],"arising":[164],"such":[166],"have":[168],"several":[169],"features":[170],"typical":[171],"nonlinear":[173],"models.":[174],"1":[175]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}
