{"id":"https://openalex.org/W2963069169","doi":"https://doi.org/10.1109/tgrs.2016.2535298","title":"Biobjective Nonnegative Matrix Factorization: Linear Versus Kernel-Based Models","display_name":"Biobjective Nonnegative Matrix Factorization: Linear Versus Kernel-Based Models","publication_year":2016,"publication_date":"2016-04-07","ids":{"openalex":"https://openalex.org/W2963069169","doi":"https://doi.org/10.1109/tgrs.2016.2535298","mag":"2963069169"},"language":"en","primary_location":{"id":"doi:10.1109/tgrs.2016.2535298","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tgrs.2016.2535298","pdf_url":null,"source":{"id":"https://openalex.org/S111326731","display_name":"IEEE Transactions on Geoscience and Remote Sensing","issn_l":"0196-2892","issn":["0196-2892","1558-0644"],"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 Geoscience and Remote Sensing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-01965048","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049872589","display_name":"Fei Zhu","orcid":"https://orcid.org/0000-0002-8113-3707"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I140494188","display_name":"Universit\u00e9 de Technologie de Troyes","ror":"https://ror.org/01qhqcj41","country_code":"FR","type":"education","lineage":["https://openalex.org/I140494188"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Fei Zhu","raw_affiliation_strings":["Institut Charles Delaunay (CNRS), Universit\u00e9 de Technologie de Troyes, Troyes, France","LM2S - Laboratoire Mod\u00e9lisation et S\u00fbret\u00e9 des Syst\u00e8mes (UTT - 12, rue Marie Curie - BP 2060 - 10010 TROYES CEDEX - France)"],"affiliations":[{"raw_affiliation_string":"Institut Charles Delaunay (CNRS), Universit\u00e9 de Technologie de Troyes, Troyes, France","institution_ids":["https://openalex.org/I140494188","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"LM2S - Laboratoire Mod\u00e9lisation et S\u00fbret\u00e9 des Syst\u00e8mes (UTT - 12, rue Marie Curie - BP 2060 - 10010 TROYES CEDEX - France)","institution_ids":["https://openalex.org/I140494188"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074267243","display_name":"Paul Honein\u00e9","orcid":"https://orcid.org/0000-0002-3042-183X"},"institutions":[{"id":"https://openalex.org/I140494188","display_name":"Universit\u00e9 de Technologie de Troyes","ror":"https://ror.org/01qhqcj41","country_code":"FR","type":"education","lineage":["https://openalex.org/I140494188"]},{"id":"https://openalex.org/I62396329","display_name":"Universit\u00e9 de Rouen Normandie","ror":"https://ror.org/03nhjew95","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I62396329"]},{"id":"https://openalex.org/I4210108118","display_name":"Laboratoire d'Informatique, du Traitement de l'Information et des Syst\u00e8mes","ror":"https://ror.org/01f1vfy95","country_code":"FR","type":"facility","lineage":["https://openalex.org/I141576021","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4210105918","https://openalex.org/I4210108118","https://openalex.org/I62396329","https://openalex.org/I88814501"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Paul Honeine","raw_affiliation_strings":["Laboratoire d'Informatique, du Traitement de l'Information et des Systemes (LITIS), Universit\u00e9 de Rouen, Saint-Etienne-du-Rouvray, France","LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Syst\u00e8mes (Avenue de l'Universit\u00e9 76800 Saint-\u00c9tienne-du-Rouvray - France)","LM2S - Laboratoire Mod\u00e9lisation et S\u00fbret\u00e9 des Syst\u00e8mes (UTT - 12, rue Marie Curie - BP 2060 - 10010 TROYES CEDEX - France)"],"affiliations":[{"raw_affiliation_string":"Laboratoire d'Informatique, du Traitement de l'Information et des Systemes (LITIS), Universit\u00e9 de Rouen, Saint-Etienne-du-Rouvray, France","institution_ids":["https://openalex.org/I62396329","https://openalex.org/I4210108118"]},{"raw_affiliation_string":"LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Syst\u00e8mes (Avenue de l'Universit\u00e9 76800 Saint-\u00c9tienne-du-Rouvray - France)","institution_ids":["https://openalex.org/I4210108118"]},{"raw_affiliation_string":"LM2S - Laboratoire Mod\u00e9lisation et S\u00fbret\u00e9 des Syst\u00e8mes (UTT - 12, rue Marie Curie - BP 2060 - 10010 TROYES CEDEX - France)","institution_ids":["https://openalex.org/I140494188"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5049872589"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I140494188"],"apc_list":null,"apc_paid":null,"fwci":4.8443,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.95699604,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"54","issue":"7","first_page":"4012","last_page":"4022"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10689","display_name":"Remote-Sensing Image Classification","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T10689","display_name":"Remote-Sensing Image Classification","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T11659","display_name":"Advanced Image Fusion Techniques","score":0.9941999912261963,"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"}},{"id":"https://openalex.org/T11019","display_name":"Image Enhancement Techniques","score":0.9866999983787537,"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":0.8571326732635498},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6972067952156067},{"id":"https://openalex.org/keywords/hyperspectral-imaging","display_name":"Hyperspectral imaging","score":0.625672459602356},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.5380465984344482},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.5335555076599121},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.5208407044410706},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.501605749130249},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49093249440193176},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.4846689999103546},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4605589807033539},{"id":"https://openalex.org/keywords/feature-extraction","display_name":"Feature extraction","score":0.4552059471607208},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.42099589109420776},{"id":"https://openalex.org/keywords/pareto-principle","display_name":"Pareto principle","score":0.4184451103210449},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.41699647903442383},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35218656063079834},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07865488529205322}],"concepts":[{"id":"https://openalex.org/C152671427","wikidata":"https://www.wikidata.org/wiki/Q10843505","display_name":"Non-negative matrix factorization","level":4,"score":0.8571326732635498},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6972067952156067},{"id":"https://openalex.org/C159078339","wikidata":"https://www.wikidata.org/wiki/Q959005","display_name":"Hyperspectral imaging","level":2,"score":0.625672459602356},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.5380465984344482},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.5335555076599121},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.5208407044410706},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.501605749130249},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49093249440193176},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.4846689999103546},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4605589807033539},{"id":"https://openalex.org/C52622490","wikidata":"https://www.wikidata.org/wiki/Q1026626","display_name":"Feature extraction","level":2,"score":0.4552059471607208},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.42099589109420776},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.4184451103210449},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.41699647903442383},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35218656063079834},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07865488529205322},{"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/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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tgrs.2016.2535298","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tgrs.2016.2535298","pdf_url":null,"source":{"id":"https://openalex.org/S111326731","display_name":"IEEE Transactions on Geoscience and Remote Sensing","issn_l":"0196-2892","issn":["0196-2892","1558-0644"],"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 Geoscience and Remote Sensing","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01965048v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01965048","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Geoscience and Remote Sensing, 2016, 54 (7), pp.4012 - 4022. ⟨10.1109/TGRS.2016.2535298⟩","raw_type":"Journal articles"},{"id":"pmh:oai:HAL:hal-02304274v1","is_oa":false,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-02304274","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 0196-2892","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01965048v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01965048","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Geoscience and Remote Sensing, 2016, 54 (7), pp.4012 - 4022. ⟨10.1109/TGRS.2016.2535298⟩","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W88153722","https://openalex.org/W1506222585","https://openalex.org/W1573690241","https://openalex.org/W1595498733","https://openalex.org/W1963659868","https://openalex.org/W2005818237","https://openalex.org/W2011315899","https://openalex.org/W2019149505","https://openalex.org/W2019274094","https://openalex.org/W2024022568","https://openalex.org/W2041115669","https://openalex.org/W2042626896","https://openalex.org/W2054892132","https://openalex.org/W2058192020","https://openalex.org/W2059465815","https://openalex.org/W2060629443","https://openalex.org/W2060675355","https://openalex.org/W2064219748","https://openalex.org/W2064690543","https://openalex.org/W2070424424","https://openalex.org/W2073650477","https://openalex.org/W2075241504","https://openalex.org/W2078222544","https://openalex.org/W2085147830","https://openalex.org/W2101431131","https://openalex.org/W2101837437","https://openalex.org/W2106334424","https://openalex.org/W2109533493","https://openalex.org/W2110096996","https://openalex.org/W2113976600","https://openalex.org/W2114486983","https://openalex.org/W2118718620","https://openalex.org/W2124172487","https://openalex.org/W2125678373","https://openalex.org/W2127062304","https://openalex.org/W2129391118","https://openalex.org/W2130855892","https://openalex.org/W2132538571","https://openalex.org/W2135029798","https://openalex.org/W2142584058","https://openalex.org/W2144492104","https://openalex.org/W2149292383","https://openalex.org/W2157321686","https://openalex.org/W2168103112","https://openalex.org/W2169466597","https://openalex.org/W2324815542","https://openalex.org/W2541576858","https://openalex.org/W2571268788","https://openalex.org/W2766547421","https://openalex.org/W3122463936","https://openalex.org/W3143596294","https://openalex.org/W4234074216","https://openalex.org/W6634188236","https://openalex.org/W6665292313","https://openalex.org/W6677759377","https://openalex.org/W6680012447","https://openalex.org/W6745716280"],"related_works":["https://openalex.org/W4308269461","https://openalex.org/W4281395053","https://openalex.org/W2020769413","https://openalex.org/W2985420097","https://openalex.org/W2127243424","https://openalex.org/W4390394189","https://openalex.org/W2037504162","https://openalex.org/W2539013788","https://openalex.org/W2792706544","https://openalex.org/W1568451138"],"abstract_inverted_index":{"Nonnegative":[0],"matrix":[1],"factorization":[2],"(NMF)":[3],"is":[4,108],"a":[5,33,55,59,96],"powerful":[6],"class":[7],"of":[8,81,88,98,124],"feature":[9,71],"extraction":[10],"techniques":[11,28],"that":[12],"has":[13],"been":[14,30],"successfully":[15],"applied":[16],"in":[17,21,37,67],"many":[18],"fields,":[19],"particularly":[20,58],"signal":[22],"and":[23,70,110,117],"image":[24],"processing.":[25],"Current":[26],"NMF":[27,53,94,128],"have":[29],"limited":[31],"to":[32,50],"single-objective":[34],"optimization":[35],"problem,":[36,57],"either":[38],"its":[39],"linear":[40],"or":[41],"nonlinear":[42],"kernel-based":[43],"formulation.":[44],"In":[45],"this":[46],"paper,":[47],"we":[48],"propose":[49],"revisit":[51],"the":[52,63,79,82,86,91,104,122,125,131],"as":[54],"multiobjective":[56,89],"biobjective":[60,93,127],"one,":[61],"where":[62],"objective":[64],"functions":[65],"defined":[66],"both":[68],"input":[69],"spaces":[72],"are":[73],"taken":[74],"into":[75],"account.":[76],"By":[77],"taking":[78],"advantage":[80],"sum-weighted":[83],"method":[84],"from":[85],"literature":[87],"optimization,":[90],"proposed":[92,126],"determines":[95],"set":[97],"nondominated,":[99],"Pareto":[100,106],"optimal,":[101],"solutions.":[102],"Moreover,":[103],"corresponding":[105],"front":[107],"approximated":[109],"studied.":[111],"Experimental":[112],"results":[113],"on":[114],"unmixing":[115],"synthetic":[116],"real":[118],"hyperspectral":[119],"images":[120],"confirm":[121],"efficiency":[123],"compared":[129],"with":[130],"state-of-the-art":[132],"methods.":[133]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2019-07-30T00:00:00"}