{"id":"https://openalex.org/W4404760634","doi":"https://doi.org/10.3390/sym16121585","title":"Decomposition and Symmetric Kernel Deep Neural Network Fuzzy Support Vector Machine","display_name":"Decomposition and Symmetric Kernel Deep Neural Network Fuzzy Support Vector Machine","publication_year":2024,"publication_date":"2024-11-27","ids":{"openalex":"https://openalex.org/W4404760634","doi":"https://doi.org/10.3390/sym16121585"},"language":"en","primary_location":{"id":"doi:10.3390/sym16121585","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16121585","pdf_url":"https://www.mdpi.com/2073-8994/16/12/1585/pdf?version=1732704204","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/16/12/1585/pdf?version=1732704204","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026538116","display_name":"Karim El Moutaouakil","orcid":"https://orcid.org/0000-0003-3922-5592"},"institutions":[{"id":"https://openalex.org/I81605866","display_name":"Sidi Mohamed Ben Abdellah University","ror":"https://ror.org/04efg9a07","country_code":"MA","type":"education","lineage":["https://openalex.org/I81605866"]}],"countries":["MA"],"is_corresponding":true,"raw_author_name":"Karim El Moutaouakil","raw_affiliation_strings":["Laboratory of Engineering Science, Polydisciplinary Faculty of Taza, Sidi Mohamed Ben Abdellah of Fez, Taza P.O. Box 1223, Morocco"],"raw_orcid":"https://orcid.org/0000-0003-3922-5592","affiliations":[{"raw_affiliation_string":"Laboratory of Engineering Science, Polydisciplinary Faculty of Taza, Sidi Mohamed Ben Abdellah of Fez, Taza P.O. Box 1223, Morocco","institution_ids":["https://openalex.org/I81605866"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030031168","display_name":"Mohammed Roudani","orcid":null},"institutions":[{"id":"https://openalex.org/I81605866","display_name":"Sidi Mohamed Ben Abdellah University","ror":"https://ror.org/04efg9a07","country_code":"MA","type":"education","lineage":["https://openalex.org/I81605866"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Mohammed Roudani","raw_affiliation_strings":["Laboratory of Engineering Science, Polydisciplinary Faculty of Taza, Sidi Mohamed Ben Abdellah of Fez, Taza P.O. Box 1223, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory of Engineering Science, Polydisciplinary Faculty of Taza, Sidi Mohamed Ben Abdellah of Fez, Taza P.O. Box 1223, Morocco","institution_ids":["https://openalex.org/I81605866"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5097633417","display_name":"Azedine Ouhmid","orcid":null},"institutions":[{"id":"https://openalex.org/I81605866","display_name":"Sidi Mohamed Ben Abdellah University","ror":"https://ror.org/04efg9a07","country_code":"MA","type":"education","lineage":["https://openalex.org/I81605866"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Azedine Ouhmid","raw_affiliation_strings":["Laboratory of Engineering Science, Polydisciplinary Faculty of Taza, Sidi Mohamed Ben Abdellah of Fez, Taza P.O. Box 1223, Morocco"],"raw_orcid":"https://orcid.org/0009-0001-1457-9565","affiliations":[{"raw_affiliation_string":"Laboratory of Engineering Science, Polydisciplinary Faculty of Taza, Sidi Mohamed Ben Abdellah of Fez, Taza P.O. Box 1223, Morocco","institution_ids":["https://openalex.org/I81605866"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026194474","display_name":"Anton Zhilenkov","orcid":"https://orcid.org/0000-0003-1555-1318"},"institutions":[{"id":"https://openalex.org/I4210141538","display_name":"State Marine Technical University of St. Petersburg","ror":"https://ror.org/03spdpm68","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210141538"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Anton Zhilenkov","raw_affiliation_strings":["Department of Cyber-Physical Systems, St. Petersburg State Marine Technical University, Saint Petersburg 190121, Russia"],"raw_orcid":"https://orcid.org/0000-0003-1555-1318","affiliations":[{"raw_affiliation_string":"Department of Cyber-Physical Systems, St. Petersburg State Marine Technical University, Saint Petersburg 190121, Russia","institution_ids":["https://openalex.org/I4210141538"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068858971","display_name":"Saleh Mobayen","orcid":"https://orcid.org/0000-0002-5676-1875"},"institutions":[{"id":"https://openalex.org/I75357094","display_name":"National Yunlin University of Science and Technology","ror":"https://ror.org/04qkq2m54","country_code":"TW","type":"education","lineage":["https://openalex.org/I75357094"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Saleh Mobayen","raw_affiliation_strings":["Graduate School of Intelligent Data Science, National Yunlin University of Science and Technology, Douliou, Yunlin 640301, Taiwan"],"raw_orcid":"https://orcid.org/0000-0002-5676-1875","affiliations":[{"raw_affiliation_string":"Graduate School of Intelligent Data Science, National Yunlin University of Science and Technology, Douliou, Yunlin 640301, Taiwan","institution_ids":["https://openalex.org/I75357094"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5026538116","https://openalex.org/A5068858971"],"corresponding_institution_ids":["https://openalex.org/I75357094","https://openalex.org/I81605866"],"apc_list":{"value":2400,"currency":"CHF","value_usd":2728},"apc_paid":{"value":2400,"currency":"CHF","value_usd":2728},"fwci":0.4576,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.6097886,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"16","issue":"12","first_page":"1585","last_page":"1585"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9988999962806702,"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":0.9988999962806702,"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/T12676","display_name":"Machine Learning and ELM","score":0.9986000061035156,"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/T10320","display_name":"Neural Networks and Applications","score":0.9973000288009644,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6754437685012817},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.6385282874107361},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.5987311005592346},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5786230564117432},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5192082524299622},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5068252682685852},{"id":"https://openalex.org/keywords/outlier","display_name":"Outlier","score":0.5064331293106079},{"id":"https://openalex.org/keywords/autoencoder","display_name":"Autoencoder","score":0.41678690910339355},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3675970137119293},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.25117027759552}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6754437685012817},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.6385282874107361},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.5987311005592346},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5786230564117432},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5192082524299622},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5068252682685852},{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.5064331293106079},{"id":"https://openalex.org/C101738243","wikidata":"https://www.wikidata.org/wiki/Q786435","display_name":"Autoencoder","level":3,"score":0.41678690910339355},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3675970137119293},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25117027759552},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym16121585","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16121585","pdf_url":"https://www.mdpi.com/2073-8994/16/12/1585/pdf?version=1732704204","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:f3f1d949f9ec44e5b4f03def582dffa9","is_oa":false,"landing_page_url":"https://doaj.org/article/f3f1d949f9ec44e5b4f03def582dffa9","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 16, Iss 12, p 1585 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym16121585","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16121585","pdf_url":"https://www.mdpi.com/2073-8994/16/12/1585/pdf?version=1732704204","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5038617067","display_name":null,"funder_award_id":"075\u201015\u20102022\u2010312","funder_id":"https://openalex.org/F4320327494","funder_display_name":"Ministry of Science and Higher Education of the Russian Federation"},{"id":"https://openalex.org/G597338630","display_name":null,"funder_award_id":"075-15-2022","funder_id":"https://openalex.org/F4320327494","funder_display_name":"Ministry of Science and Higher Education of the Russian Federation"},{"id":"https://openalex.org/G6444257319","display_name":null,"funder_award_id":"075-15-","funder_id":"https://openalex.org/F4320327494","funder_display_name":"Ministry of Science and Higher Education of the Russian Federation"}],"funders":[{"id":"https://openalex.org/F4320327494","display_name":"Ministry of Science and Higher Education of the Russian Federation","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4404760634.pdf","grobid_xml":"https://content.openalex.org/works/W4404760634.grobid-xml"},"referenced_works_count":116,"referenced_works":["https://openalex.org/W14071851","https://openalex.org/W62823307","https://openalex.org/W81972919","https://openalex.org/W184023059","https://openalex.org/W955312132","https://openalex.org/W1004918569","https://openalex.org/W1492690922","https://openalex.org/W1502922572","https://openalex.org/W1512098439","https://openalex.org/W1513015544","https://openalex.org/W1546961578","https://openalex.org/W1560724230","https://openalex.org/W1590323350","https://openalex.org/W1938690017","https://openalex.org/W1967849786","https://openalex.org/W1970940244","https://openalex.org/W1984707692","https://openalex.org/W1986702797","https://openalex.org/W1993793464","https://openalex.org/W1994807229","https://openalex.org/W1997254627","https://openalex.org/W2007534217","https://openalex.org/W2012834844","https://openalex.org/W2013502943","https://openalex.org/W2015311866","https://openalex.org/W2017588182","https://openalex.org/W2031823405","https://openalex.org/W2041406732","https://openalex.org/W2044571869","https://openalex.org/W2049287639","https://openalex.org/W2051812123","https://openalex.org/W2056928653","https://openalex.org/W2071563913","https://openalex.org/W2079129965","https://openalex.org/W2081621367","https://openalex.org/W2082988498","https://openalex.org/W2083673985","https://openalex.org/W2084136177","https://openalex.org/W2084809122","https://openalex.org/W2090089568","https://openalex.org/W2092466978","https://openalex.org/W2092483655","https://openalex.org/W2095981367","https://openalex.org/W2098505831","https://openalex.org/W2098770944","https://openalex.org/W2101335668","https://openalex.org/W2102451151","https://openalex.org/W2105464873","https://openalex.org/W2109033859","https://openalex.org/W2114598124","https://openalex.org/W2118670840","https://openalex.org/W2121033924","https://openalex.org/W2121215298","https://openalex.org/W2122922389","https://openalex.org/W2123012927","https://openalex.org/W2132005946","https://openalex.org/W2133772980","https://openalex.org/W2136130862","https://openalex.org/W2138882494","https://openalex.org/W2138963285","https://openalex.org/W2140069289","https://openalex.org/W2144655069","https://openalex.org/W2144752499","https://openalex.org/W2144859853","https://openalex.org/W2145295623","https://openalex.org/W2150772522","https://openalex.org/W2154420049","https://openalex.org/W2154913025","https://openalex.org/W2158653102","https://openalex.org/W2164535072","https://openalex.org/W2164641162","https://openalex.org/W2165644552","https://openalex.org/W2166473218","https://openalex.org/W2169495281","https://openalex.org/W2170860445","https://openalex.org/W2172000360","https://openalex.org/W2263203561","https://openalex.org/W2282723360","https://openalex.org/W2343106965","https://openalex.org/W2343897292","https://openalex.org/W2345218921","https://openalex.org/W2402218985","https://openalex.org/W2544442470","https://openalex.org/W2891005478","https://openalex.org/W2905148377","https://openalex.org/W3003413895","https://openalex.org/W3133841704","https://openalex.org/W3183920302","https://openalex.org/W3188170485","https://openalex.org/W3208144970","https://openalex.org/W4205471456","https://openalex.org/W4239510810","https://openalex.org/W4244952642","https://openalex.org/W4246066915","https://openalex.org/W4250589301","https://openalex.org/W4256146887","https://openalex.org/W4283788823","https://openalex.org/W4319589330","https://openalex.org/W4366589772","https://openalex.org/W4391805143","https://openalex.org/W4403159155","https://openalex.org/W6600569696","https://openalex.org/W6602553625","https://openalex.org/W6604538516","https://openalex.org/W6629804754","https://openalex.org/W6634442568","https://openalex.org/W6640409437","https://openalex.org/W6641446668","https://openalex.org/W6653629126","https://openalex.org/W6658434593","https://openalex.org/W6670478616","https://openalex.org/W6678059867","https://openalex.org/W6679374065","https://openalex.org/W6680751671","https://openalex.org/W6681414149","https://openalex.org/W6682443497"],"related_works":["https://openalex.org/W3013693939","https://openalex.org/W2566616303","https://openalex.org/W2159052453","https://openalex.org/W3131327266","https://openalex.org/W2734887215","https://openalex.org/W2803255133","https://openalex.org/W4297051394","https://openalex.org/W2752972570","https://openalex.org/W4386815338","https://openalex.org/W2145836866"],"abstract_inverted_index":{"Algorithms":[0],"involving":[1,161],"kernel":[2,33,210],"functions,":[3],"such":[4],"as":[5],"support":[6,113],"vector":[7],"machine":[8],"(SVM),":[9],"have":[10],"attracted":[11],"huge":[12],"attention":[13],"within":[14],"the":[15,30,70,81,84,99,104,112,120,127,137,149,167,171,183,187,208,232,246,249],"artificial":[16],"learning":[17],"communities.":[18],"The":[19,92],"performance":[20,247],"of":[21,32,41,77,83,170,186,196,234,248],"these":[22],"algorithms":[23],"is":[24,95,200],"greatly":[25],"influenced":[26],"by":[27],"outliers":[28],"and":[29,67,115,123,156,212,222,225,239,255],"choice":[31],"functions.":[34],"This":[35],"paper":[36],"introduces":[37],"a":[38,75,178],"new":[39],"version":[40],"SVM":[42,49],"named":[43],"Deep":[44],"Decomposition":[45],"Neural":[46],"Network":[47],"Fuzzy":[48],"(DDNN-FSVM).":[50],"To":[51,110,130,147],"this":[52],"end,":[53],"we":[54,118,135,152],"consider":[55],"an":[56],"auto-encoder":[57],"(AE)":[58],"deep":[59],"neural":[60],"network":[61],"with":[62],"three":[63,141,172],"layers:":[64],"input,":[65],"hidden,":[66],"output.":[68],"Unusually,":[69],"AE\u2019s":[71],"hidden":[72],"layer":[73],"comprises":[74],"number":[76],"neurons":[78],"greater":[79],"than":[80],"dimension":[82],"input":[85],"samples,":[86],"which":[87],"guarantees":[88],"linear":[89],"data":[90],"separation.":[91],"encoder":[93],"operator":[94],"then":[96],"introduced":[97],"into":[98,140],"FSVM\u2019s":[100],"dual":[101],"to":[102,107,193,202,228],"map":[103],"training":[105],"samples":[106],"high-dimension":[108],"spaces.":[109],"learn":[111,131],"vectors":[114],"autoencoder":[116],"parameters,":[117],"introduce":[119],"loss":[121],"function":[122,211],"regularization":[124],"terms":[125],"in":[126,175],"FSVM":[128,251],"dual.":[129],"from":[132],"large-scale":[133,162],"data,":[134],"decompose":[136],"resulting":[138,150],"model":[139],"small-dimensional":[142],"submodels":[143,173],"using":[144],"Lagrangian":[145],"decomposition.":[146],"solve":[148],"problems,":[151],"use":[153,195],"SMO,":[154],"ISDA,":[155],"SCG":[157],"for":[158,182],"optimization":[159],"problems":[160],"data.":[163],"We":[164,215],"demonstrate":[165],"that":[166],"optimal":[168,184],"values":[169],"solved":[174],"parallel":[176],"provide":[177],"good":[179],"lower":[180],"bound":[181],"value":[185],"initial":[188],"model.":[189],"In":[190],"addition,":[191],"thanks":[192],"its":[194],"fuzzy":[197],"weights,":[198],"DDNN-FSVM":[199,205,217,243],"resistant":[201],"outliers.":[203],"Moreover,":[204],"simultaneously":[206],"learns":[207],"appropriate":[209],"separation":[213],"path.":[214],"tested":[216],"on":[218,231,245],"several":[219,257],"well-known":[220,229,258],"digital":[221],"image":[223],"datasets":[224,254],"compared":[226],"it":[227],"classifiers":[230],"basis":[233],"accuracy,":[235],"precision,":[236],"f-measure,":[237],"g-means,":[238],"recall.":[240],"On":[241],"average,":[242],"improved":[244],"classic":[250],"across":[252],"all":[253],"outperformed":[256],"classifiers.":[259]},"counts_by_year":[{"year":2025,"cited_by_count":3}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}