{"id":"https://openalex.org/W2625522544","doi":"https://doi.org/10.1109/tnnls.2017.2709805","title":"Robust Least-Squares Support Vector Machine With Minimization of Mean and Variance of Modeling Error","display_name":"Robust Least-Squares Support Vector Machine With Minimization of Mean and Variance of Modeling Error","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2625522544","doi":"https://doi.org/10.1109/tnnls.2017.2709805","mag":"2625522544","pmid":"https://pubmed.ncbi.nlm.nih.gov/28622678"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2017.2709805","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2017.2709805","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5017573625","display_name":"Xinjiang Lu","orcid":"https://orcid.org/0000-0002-5100-1092"},"institutions":[{"id":"https://openalex.org/I4391767934","display_name":"State Key Laboratory of High Performance Complex Manufacturing","ror":"https://ror.org/04xjtqb36","country_code":null,"type":"facility","lineage":["https://openalex.org/I139660479","https://openalex.org/I4391767934"]},{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xinjiang Lu","raw_affiliation_strings":["State Key Laboratory of High Performance Complex Manufacturing, School of Mechanical & Electrical Engineering, Central South University, Hunan, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of High Performance Complex Manufacturing, School of Mechanical & Electrical Engineering, Central South University, Hunan, China","institution_ids":["https://openalex.org/I139660479","https://openalex.org/I4391767934"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100330686","display_name":"Wenbo Liu","orcid":"https://orcid.org/0000-0003-2560-0777"},"institutions":[{"id":"https://openalex.org/I4391767934","display_name":"State Key Laboratory of High Performance Complex Manufacturing","ror":"https://ror.org/04xjtqb36","country_code":null,"type":"facility","lineage":["https://openalex.org/I139660479","https://openalex.org/I4391767934"]},{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wenbo Liu","raw_affiliation_strings":["State Key Laboratory of High Performance Complex Manufacturing, School of Mechanical & Electrical Engineering, Central South University, Hunan, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of High Performance Complex Manufacturing, School of Mechanical & Electrical Engineering, Central South University, Hunan, China","institution_ids":["https://openalex.org/I139660479","https://openalex.org/I4391767934"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102267319","display_name":"Chuang Zhou","orcid":"https://orcid.org/0009-0004-0351-6739"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]},{"id":"https://openalex.org/I4391767934","display_name":"State Key Laboratory of High Performance Complex Manufacturing","ror":"https://ror.org/04xjtqb36","country_code":null,"type":"facility","lineage":["https://openalex.org/I139660479","https://openalex.org/I4391767934"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chuang Zhou","raw_affiliation_strings":["State Key Laboratory of High Performance Complex Manufacturing, School of Mechanical & Electrical Engineering, Central South University, Hunan, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of High Performance Complex Manufacturing, School of Mechanical & Electrical Engineering, Central South University, Hunan, China","institution_ids":["https://openalex.org/I139660479","https://openalex.org/I4391767934"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062776702","display_name":"Minghui Huang","orcid":"https://orcid.org/0000-0002-7087-813X"},"institutions":[{"id":"https://openalex.org/I4391767934","display_name":"State Key Laboratory of High Performance Complex Manufacturing","ror":"https://ror.org/04xjtqb36","country_code":null,"type":"facility","lineage":["https://openalex.org/I139660479","https://openalex.org/I4391767934"]},{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Minghui Huang","raw_affiliation_strings":["State Key Laboratory of High Performance Complex Manufacturing, School of Mechanical & Electrical Engineering, Central South University, Hunan, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of High Performance Complex Manufacturing, School of Mechanical & Electrical Engineering, Central South University, Hunan, China","institution_ids":["https://openalex.org/I139660479","https://openalex.org/I4391767934"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5017573625"],"corresponding_institution_ids":["https://openalex.org/I139660479","https://openalex.org/I4391767934"],"apc_list":null,"apc_paid":null,"fwci":3.5104,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.94189385,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"29","issue":"7","first_page":"1","last_page":"12"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12676","display_name":"Machine Learning and ELM","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T12676","display_name":"Machine Learning and ELM","score":0.9990000128746033,"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/T10057","display_name":"Face and Expression Recognition","score":0.9833999872207642,"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/T10876","display_name":"Fault Detection and Control Systems","score":0.9584000110626221,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/support-vector-machine","display_name":"Support vector machine","score":0.7870551347732544},{"id":"https://openalex.org/keywords/outlier","display_name":"Outlier","score":0.66073077917099},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.5503923892974854},{"id":"https://openalex.org/keywords/least-squares-support-vector-machine","display_name":"Least squares support vector machine","score":0.5492357015609741},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5189509391784668},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4895668923854828},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.48328259587287903},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.47650185227394104},{"id":"https://openalex.org/keywords/structural-risk-minimization","display_name":"Structural risk minimization","score":0.4322943687438965},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4319899082183838},{"id":"https://openalex.org/keywords/error-function","display_name":"Error function","score":0.4270777106285095},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.41663509607315063},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.4149879813194275},{"id":"https://openalex.org/keywords/gaussian-function","display_name":"Gaussian function","score":0.41040918231010437},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36162495613098145},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.33242785930633545},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2981218993663788},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.250459760427475},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.11303237080574036}],"concepts":[{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.7870551347732544},{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.66073077917099},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.5503923892974854},{"id":"https://openalex.org/C145828037","wikidata":"https://www.wikidata.org/wiki/Q17086219","display_name":"Least squares support vector machine","level":3,"score":0.5492357015609741},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5189509391784668},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4895668923854828},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.48328259587287903},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.47650185227394104},{"id":"https://openalex.org/C154507838","wikidata":"https://www.wikidata.org/wiki/Q7625053","display_name":"Structural risk minimization","level":3,"score":0.4322943687438965},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4319899082183838},{"id":"https://openalex.org/C202286095","wikidata":"https://www.wikidata.org/wiki/Q579262","display_name":"Error function","level":2,"score":0.4270777106285095},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.41663509607315063},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.4149879813194275},{"id":"https://openalex.org/C7218915","wikidata":"https://www.wikidata.org/wiki/Q1054475","display_name":"Gaussian function","level":3,"score":0.41040918231010437},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36162495613098145},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33242785930633545},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2981218993663788},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.250459760427475},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.11303237080574036},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","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},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2017.2709805","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2017.2709805","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:28622678","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/28622678","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8","score":0.4099999964237213}],"awards":[{"id":"https://openalex.org/G1348281123","display_name":null,"funder_award_id":"51675539","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W220234023","https://openalex.org/W755941632","https://openalex.org/W1540358749","https://openalex.org/W1680392829","https://openalex.org/W1972809999","https://openalex.org/W1978996791","https://openalex.org/W1985819320","https://openalex.org/W1989358763","https://openalex.org/W1990381576","https://openalex.org/W1998730337","https://openalex.org/W2005569959","https://openalex.org/W2015725852","https://openalex.org/W2017084531","https://openalex.org/W2019821804","https://openalex.org/W2060462435","https://openalex.org/W2062112423","https://openalex.org/W2064593130","https://openalex.org/W2064769840","https://openalex.org/W2067563600","https://openalex.org/W2085894327","https://openalex.org/W2090572164","https://openalex.org/W2101674911","https://openalex.org/W2107376597","https://openalex.org/W2110417041","https://openalex.org/W2112733735","https://openalex.org/W2124161253","https://openalex.org/W2125858817","https://openalex.org/W2132208889","https://openalex.org/W2151388232","https://openalex.org/W2172442941","https://openalex.org/W2222043790","https://openalex.org/W2324720792","https://openalex.org/W2360116519","https://openalex.org/W2617851845","https://openalex.org/W2752885492","https://openalex.org/W3003405055","https://openalex.org/W3120740533","https://openalex.org/W3142318058","https://openalex.org/W4242691841","https://openalex.org/W4301501800","https://openalex.org/W6622374868","https://openalex.org/W6632355836","https://openalex.org/W6637386731","https://openalex.org/W6639489664","https://openalex.org/W6677063653"],"related_works":["https://openalex.org/W2348987257","https://openalex.org/W1963674083","https://openalex.org/W2140039100","https://openalex.org/W2357762447","https://openalex.org/W2371052470","https://openalex.org/W2374792899","https://openalex.org/W2364409237","https://openalex.org/W2386661643","https://openalex.org/W2370845081","https://openalex.org/W1968036192"],"abstract_inverted_index":{"The":[0,73,221],"least-squares":[1],"support":[2],"vector":[3],"machine":[4],"(LS-SVM)":[5],"is":[6,49,52,71,156,171,213,228],"a":[7,18,45,61,76,82,120,195,199,204,208],"popular":[8],"data-driven":[9],"modeling":[10,60,89,108,129,137,149],"method":[11,48,146,170],"and":[12,51,99,131,155,160,203,212,233],"has":[13,25],"been":[14],"successfully":[15],"applied":[16],"to":[17,40,54,110,126,139,165,176,198,207],"wide":[19],"range":[20],"of":[21,75,84,87,96,106,135,223],"applications.":[22],"However,":[23],"it":[24,100],"some":[26],"disadvantages,":[27],"including":[28],"being":[29,38],"ineffective":[30],"at":[31],"handling":[32],"non-Gaussian":[33,69],"noise":[34,70],"as":[35,37,91,93],"well":[36,92],"sensitive":[39],"outliers.":[41],"In":[42,141],"this":[43],"paper,":[44],"robust":[46,162,184,216,226],"LS-SVM":[47,193,227],"proposed":[50,145,183,192,225],"shown":[53],"have":[55],"more":[56,161,215],"reliable":[57],"performance":[58],"when":[59],"nonlinear":[62],"system":[63],"under":[64],"conditions":[65],"where":[66],"Gaussian":[67],"or":[68],"present.":[72],"construction":[74],"new":[77],"objective":[78],"function":[79],"allows":[80],"for":[81,181],"reduction":[83],"the":[85,88,94,104,107,115,128,133,136,144,148,178,182,191,218,224],"mean":[86,105,134],"error":[90,109,130,138,150],"minimization":[95],"its":[97],"variance,":[98],"does":[101],"not":[102],"constrain":[103],"zero.":[111,140],"This":[112],"differs":[113],"from":[114],"traditional":[116,219],"LS-SVM,":[117],"which":[118],"uses":[119],"worst-case":[121],"scenario":[122],"approach":[123],"in":[124,163,174],"order":[125,175],"minimize":[127],"constrains":[132],"doing":[142],"so,":[143],"takes":[147],"distribution":[151],"information":[152],"into":[153],"consideration":[154],"thus":[157,214],"less":[158],"conservative":[159],"regards":[164],"random":[166],"noise.":[167],"A":[168],"solving":[169],"then":[172],"developed":[173],"determine":[177],"optimal":[179],"parameters":[180],"LS-SVM.":[185,220],"An":[186],"additional":[187],"analysis":[188],"indicates":[189],"that":[190],"gives":[194],"smaller":[196],"weight":[197,206],"large-error":[200],"training":[201,210],"sample":[202],"larger":[205],"small-error":[209],"sample,":[211],"than":[217],"effectiveness":[222],"demonstrated":[229],"using":[230],"both":[231],"artificial":[232],"real":[234],"life":[235],"cases.":[236]},"counts_by_year":[{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":7}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}