{"id":"https://openalex.org/W2576338689","doi":"https://doi.org/10.1109/tnnls.2017.2648038","title":"A Fast Algorithm of Convex Hull Vertices Selection for Online Classification","display_name":"A Fast Algorithm of Convex Hull Vertices Selection for Online Classification","publication_year":2017,"publication_date":"2017-01-20","ids":{"openalex":"https://openalex.org/W2576338689","doi":"https://doi.org/10.1109/tnnls.2017.2648038","mag":"2576338689","pmid":"https://pubmed.ncbi.nlm.nih.gov/28113351"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2017.2648038","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2017.2648038","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/A5021998285","display_name":"Shuguang Ding","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shuguang Ding","raw_affiliation_strings":["Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049695170","display_name":"Xiangli Nie","orcid":"https://orcid.org/0000-0001-5208-4670"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210094879","display_name":"Shandong Institute of Automation","ror":"https://ror.org/00qdtba35","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210094879","https://openalex.org/I4210142748"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiangli Nie","raw_affiliation_strings":["State Key Laboratory of Management Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0001-5208-4670","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Management Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210094879"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026688050","display_name":"Hong Qiao","orcid":"https://orcid.org/0000-0001-6384-3687"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210094879","display_name":"Shandong Institute of Automation","ror":"https://ror.org/00qdtba35","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210094879","https://openalex.org/I4210142748"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hong Qiao","raw_affiliation_strings":["State Key Laboratory of Management Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China","University of Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Management Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210094879"]},{"raw_affiliation_string":"University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100335192","display_name":"Bo Zhang","orcid":"https://orcid.org/0000-0001-7355-0941"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bo Zhang","raw_affiliation_strings":["LSEC and Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0001-7355-0941","affiliations":[{"raw_affiliation_string":"LSEC and Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8317,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.8937382,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"29","issue":"4","first_page":"792","last_page":"806"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9966999888420105,"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":0.9966999888420105,"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12761","display_name":"Data Stream Mining Techniques","score":0.9958000183105469,"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/convex-hull","display_name":"Convex hull","score":0.8129621744155884},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5676480531692505},{"id":"https://openalex.org/keywords/output-sensitive-algorithm","display_name":"Output-sensitive algorithm","score":0.5654990673065186},{"id":"https://openalex.org/keywords/outlier","display_name":"Outlier","score":0.554258406162262},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.5471240282058716},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.48555466532707214},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4426718056201935},{"id":"https://openalex.org/keywords/convex-polytope","display_name":"Convex polytope","score":0.44177743792533875},{"id":"https://openalex.org/keywords/orthogonal-convex-hull","display_name":"Orthogonal convex hull","score":0.4382352828979492},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.41541242599487305},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.41506534814834595},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.38344377279281616},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3537307381629944},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.2968903183937073},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29489371180534363},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.292235404253006},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1914636194705963},{"id":"https://openalex.org/keywords/convex-body","display_name":"Convex body","score":0.11486321687698364}],"concepts":[{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.8129621744155884},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5676480531692505},{"id":"https://openalex.org/C39132409","wikidata":"https://www.wikidata.org/wiki/Q7112860","display_name":"Output-sensitive algorithm","level":5,"score":0.5654990673065186},{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.554258406162262},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.5471240282058716},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.48555466532707214},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4426718056201935},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.44177743792533875},{"id":"https://openalex.org/C64051489","wikidata":"https://www.wikidata.org/wiki/Q7104528","display_name":"Orthogonal convex hull","level":5,"score":0.4382352828979492},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.41541242599487305},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.41506534814834595},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.38344377279281616},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3537307381629944},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.2968903183937073},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29489371180534363},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.292235404253006},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1914636194705963},{"id":"https://openalex.org/C134912446","wikidata":"https://www.wikidata.org/wiki/Q5166516","display_name":"Convex body","level":4,"score":0.11486321687698364},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2017.2648038","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2017.2648038","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:28113351","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/28113351","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":[],"awards":[{"id":"https://openalex.org/G465819471","display_name":null,"funder_award_id":"61379093","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4681919330","display_name":null,"funder_award_id":"61602483","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5652064144","display_name":null,"funder_award_id":"61210009","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":38,"referenced_works":["https://openalex.org/W26816478","https://openalex.org/W1480376833","https://openalex.org/W1494289067","https://openalex.org/W1621799579","https://openalex.org/W1622263187","https://openalex.org/W1628991974","https://openalex.org/W1965788850","https://openalex.org/W1979711143","https://openalex.org/W1984500730","https://openalex.org/W1994720006","https://openalex.org/W2022400045","https://openalex.org/W2040870580","https://openalex.org/W2049351696","https://openalex.org/W2054291723","https://openalex.org/W2076346323","https://openalex.org/W2091350393","https://openalex.org/W2097382951","https://openalex.org/W2114453181","https://openalex.org/W2118075434","https://openalex.org/W2125993116","https://openalex.org/W2135106139","https://openalex.org/W2141097525","https://openalex.org/W2142978586","https://openalex.org/W2150621701","https://openalex.org/W2152793312","https://openalex.org/W2153631847","https://openalex.org/W2153635508","https://openalex.org/W2156909104","https://openalex.org/W2158978974","https://openalex.org/W2296714235","https://openalex.org/W2534230712","https://openalex.org/W3119651796","https://openalex.org/W3120740533","https://openalex.org/W4249572517","https://openalex.org/W4301501800","https://openalex.org/W6601080436","https://openalex.org/W6680272842","https://openalex.org/W6697324915"],"related_works":["https://openalex.org/W2375652826","https://openalex.org/W2300145982","https://openalex.org/W2363904277","https://openalex.org/W2048874717","https://openalex.org/W2580512045","https://openalex.org/W2365830408","https://openalex.org/W2058179942","https://openalex.org/W2358001426","https://openalex.org/W2128601753","https://openalex.org/W1569666406"],"abstract_inverted_index":{"Reducing":[0],"samples":[1],"through":[2],"convex":[3,50,56,81,106,184],"hull":[4,51,57,82,107,185],"vertices":[5,186],"selection":[6],"(CHVS)":[7],"within":[8],"each":[9],"class":[10],"is":[11,37,83,99,108,132,139,158,169],"an":[12,101,115],"important":[13],"and":[14,59,79,135,188,198,205],"effective":[15],"method":[16],"for":[17,172],"online":[18],"classification":[19],"problems,":[20],"since":[21],"the":[22,29,33,49,55,60,65,68,74,96,128,136,143,146,155,173,176,182,190,203,208],"classifier":[23],"can":[24],"be":[25,111],"trained":[26],"rapidly":[27],"with":[28,90,162],"selected":[30,112,187],"samples.":[31,125,192],"However,":[32],"process":[34],"of":[35,62,72,104,130,207],"CHVS":[36],"NP-hard.":[38],"In":[39,64,126],"this":[40],"paper,":[41],"we":[42],"propose":[43],"a":[44,77,80,86,91,150],"fast":[45],"algorithm":[46,138],"to":[47,110,121,160],"select":[48],"vertices,":[52],"based":[53,180],"on":[54,181,195],"decomposition":[58],"property":[61],"projection.":[63],"proposed":[66,137,209],"algorithm,":[67],"quadratic":[69],"minimization":[70],"problem":[71,89],"computing":[73],"distance":[75],"between":[76,175],"point":[78],"converted":[84],"into":[85],"linear":[87],"equation":[88],"low":[92],"computational":[93],"complexity.":[94],"When":[95],"data":[97,200],"dimension":[98,151],"high,":[100],"approximate,":[102],"instead":[103],"exact,":[105],"allowed":[109],"by":[113,141],"setting":[114],"appropriate":[116],"termination":[117],"condition":[118],"in":[119,145],"order":[120],"delete":[122],"more":[123],"nonimportant":[124],"addition,":[127],"impact":[129],"outliers":[131,144],"also":[133],"considered,":[134],"improved":[140],"deleting":[142],"initial":[147],"procedure.":[148],"Furthermore,":[149],"convention":[152],"technique":[153],"via":[154],"kernel":[156],"trick":[157],"used":[159],"deal":[161],"nonlinearly":[163],"separable":[164],"problems.":[165],"An":[166],"upper":[167],"bound":[168],"theoretically":[170],"proved":[171],"difference":[174],"support":[177],"vector":[178],"machines":[179],"approximate":[183],"all":[189],"training":[191],"Experimental":[193],"results":[194],"both":[196],"synthetic":[197],"real":[199],"sets":[201],"show":[202],"effectiveness":[204],"validity":[206],"algorithm.":[210]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}