{"id":"https://openalex.org/W2141874187","doi":"https://doi.org/10.1109/cvpr.2009.5206584","title":"Nonlinear Nonnegative Component Analysis","display_name":"Nonlinear Nonnegative Component Analysis","publication_year":2009,"publication_date":"2009-06-01","ids":{"openalex":"https://openalex.org/W2141874187","doi":"https://doi.org/10.1109/cvpr.2009.5206584","mag":"2141874187"},"language":"en","primary_location":{"id":"doi:10.1109/cvpr.2009.5206584","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2009.5206584","pdf_url":null,"source":{"id":"https://openalex.org/S4363607795","display_name":"2009 IEEE Conference on Computer Vision and Pattern Recognition","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"2009 IEEE Conference on Computer Vision and Pattern Recognition","raw_type":"proceedings-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/A5080553022","display_name":"Stefanos Zafeiriou","orcid":"https://orcid.org/0000-0002-5222-1740"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Stefanos Zafeiriou","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Imperial College London, UK","Dept. of Electr. & Electron. Eng., Imperial Coll., London, London, UK"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Imperial College London, UK","institution_ids":["https://openalex.org/I47508984"]},{"raw_affiliation_string":"Dept. of Electr. & Electron. Eng., Imperial Coll., London, London, UK","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103426811","display_name":"Maria Petrou","orcid":null},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Maria Petrou","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Imperial College London, UK","Dept. of Electr. & Electron. Eng., Imperial Coll., London, London, UK"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Imperial College London, UK","institution_ids":["https://openalex.org/I47508984"]},{"raw_affiliation_string":"Dept. of Electr. & Electron. Eng., Imperial Coll., London, London, UK","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5080553022"],"corresponding_institution_ids":["https://openalex.org/I47508984"],"apc_list":null,"apc_paid":null,"fwci":1.9746,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.86924939,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"3","issue":null,"first_page":"2860","last_page":"2865"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9973000288009644,"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"}},"topics":[{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9973000288009644,"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/T10057","display_name":"Face and Expression Recognition","score":0.9947999715805054,"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/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9631999731063843,"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/non-negative-matrix-factorization","display_name":"Non-negative matrix factorization","score":0.8373941779136658},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6773868799209595},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.519719123840332},{"id":"https://openalex.org/keywords/stationary-point","display_name":"Stationary point","score":0.5032455325126648},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.5030390620231628},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5005888938903809},{"id":"https://openalex.org/keywords/independent-component-analysis","display_name":"Independent component analysis","score":0.4532041847705841},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.44823333621025085},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4370593726634979},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4361041486263275},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.4325193166732788},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4009110629558563},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38765162229537964},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36682450771331787},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.11916503310203552},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10162132978439331}],"concepts":[{"id":"https://openalex.org/C152671427","wikidata":"https://www.wikidata.org/wiki/Q10843505","display_name":"Non-negative matrix factorization","level":4,"score":0.8373941779136658},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6773868799209595},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.519719123840332},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.5032455325126648},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.5030390620231628},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5005888938903809},{"id":"https://openalex.org/C51432778","wikidata":"https://www.wikidata.org/wiki/Q1259145","display_name":"Independent component analysis","level":2,"score":0.4532041847705841},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.44823333621025085},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4370593726634979},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4361041486263275},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.4325193166732788},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4009110629558563},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38765162229537964},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36682450771331787},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.11916503310203552},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10162132978439331},{"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/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cvpr.2009.5206584","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2009.5206584","pdf_url":null,"source":{"id":"https://openalex.org/S4363607795","display_name":"2009 IEEE Conference on Computer Vision and Pattern Recognition","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"2009 IEEE Conference on Computer Vision and Pattern Recognition","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.708.4937","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.708.4937","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ibug.doc.ic.ac.uk/media/uploads/documents/cvpr_2009.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.46000000834465027,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1506222585","https://openalex.org/W1524182137","https://openalex.org/W1527240141","https://openalex.org/W1548802052","https://openalex.org/W1571599052","https://openalex.org/W1902027874","https://openalex.org/W1984259551","https://openalex.org/W2029900646","https://openalex.org/W2096698399","https://openalex.org/W2106115875","https://openalex.org/W2110096996","https://openalex.org/W2133396101","https://openalex.org/W2148207152","https://openalex.org/W2149292383","https://openalex.org/W2162137382","https://openalex.org/W2468714721","https://openalex.org/W2624213918","https://openalex.org/W3119651796","https://openalex.org/W4205778870","https://openalex.org/W4285719527","https://openalex.org/W6634941687"],"related_works":["https://openalex.org/W4390394189","https://openalex.org/W2037504162","https://openalex.org/W2539013788","https://openalex.org/W2792706544","https://openalex.org/W1568451138","https://openalex.org/W2156699640","https://openalex.org/W2045265907","https://openalex.org/W2972997031","https://openalex.org/W34555840","https://openalex.org/W2146544734"],"abstract_inverted_index":{"In":[0,70],"this":[1],"paper":[2],"general":[3,48],"solutions":[4],"for":[5,10,109],"nonlinear":[6,55],"nonnegative":[7,56],"component":[8,57],"analysis":[9,58],"data":[11],"representation":[12],"and":[13,30,129],"recognition":[14,132],"are":[15],"proposed.":[16],"That":[17],"is,":[18],"motivated":[19],"by":[20],"a":[21,41,47,54,96],"combination":[22],"of":[23,92,99,113,123],"the":[24,61,71,82,89,93,100,110,121,124],"Nonnegative":[25,66],"Matrix":[26,67],"Factorization":[27,68],"(NMF)":[28],"algorithm":[29,39],"kernel":[31],"theory,":[32],"which":[33],"has":[34],"lead":[35],"to":[36],"an":[37],"NMF":[38],"in":[40,127],"polynomial":[42],"feature":[43],"space,":[44],"we":[45,104],"propose":[46,105],"framework":[49],"where":[50],"one":[51],"can":[52,77],"build":[53],"using":[59],"kernels,":[60],"so-called":[62],"projected":[63],"gradient":[64],"Kernel":[65],"(PGKNMF).":[69],"proposed":[72,125],"approach,":[73],"arbitrary":[74],"positive":[75],"kernels":[76],"be":[78],"adopted":[79],"while":[80],"at":[81],"same":[83],"time":[84],"it":[85],"is":[86,95],"ensured":[87],"that":[88],"limit":[90],"point":[91,98,107],"procedure":[94],"stationary":[97],"optimization":[101],"problem.":[102],"Moreover,":[103],"fixed":[106],"algorithms":[108],"special":[111],"case":[112],"Radial":[114],"Basis":[115],"Function":[116],"(RBF)":[117],"kernels.":[118],"We":[119],"demonstrate":[120],"power":[122],"methods":[126],"face":[128],"facial":[130],"expression":[131],"applications.":[133]},"counts_by_year":[{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
