{"id":"https://openalex.org/W3202074398","doi":"https://doi.org/10.1109/ssci50451.2021.9660146","title":"Optimal N-ary ECOC Matrices for Ensemble Classification","display_name":"Optimal N-ary ECOC Matrices for Ensemble Classification","publication_year":2021,"publication_date":"2021-12-05","ids":{"openalex":"https://openalex.org/W3202074398","doi":"https://doi.org/10.1109/ssci50451.2021.9660146","mag":"3202074398"},"language":"en","primary_location":{"id":"doi:10.1109/ssci50451.2021.9660146","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ssci50451.2021.9660146","pdf_url":null,"source":{"id":"https://openalex.org/S4363604921","display_name":"2021 IEEE Symposium Series on Computational Intelligence (SSCI)","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":"2021 IEEE Symposium Series on Computational Intelligence (SSCI)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2110.02161","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018025457","display_name":"Hi\u00ea\u00fa D. Nguy\u00ea\u00f1","orcid":"https://orcid.org/0000-0002-2319-3955"},"institutions":[{"id":"https://openalex.org/I44265643","display_name":"Rowan University","ror":"https://ror.org/049v69k10","country_code":"US","type":"education","lineage":["https://openalex.org/I44265643"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hieu D. Nguyen","raw_affiliation_strings":["Rowan University, Glassboro, NJ","Rowan University#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rowan University, Glassboro, NJ","institution_ids":["https://openalex.org/I44265643"]},{"raw_affiliation_string":"Rowan University#TAB#","institution_ids":["https://openalex.org/I44265643"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008156718","display_name":"Lucas J. Lavalva","orcid":null},"institutions":[{"id":"https://openalex.org/I44265643","display_name":"Rowan University","ror":"https://ror.org/049v69k10","country_code":"US","type":"education","lineage":["https://openalex.org/I44265643"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lucas J. LaValva","raw_affiliation_strings":["Rowan University, Glassboro, NJ","Rowan University#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rowan University, Glassboro, NJ","institution_ids":["https://openalex.org/I44265643"]},{"raw_affiliation_string":"Rowan University#TAB#","institution_ids":["https://openalex.org/I44265643"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049730546","display_name":"Shen-Shyang Ho","orcid":"https://orcid.org/0000-0002-0353-7159"},"institutions":[{"id":"https://openalex.org/I44265643","display_name":"Rowan University","ror":"https://ror.org/049v69k10","country_code":"US","type":"education","lineage":["https://openalex.org/I44265643"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shen-Shyang Hot","raw_affiliation_strings":["Rowan University, Glassboro, NJ","Rowan University#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rowan University, Glassboro, NJ","institution_ids":["https://openalex.org/I44265643"]},{"raw_affiliation_string":"Rowan University#TAB#","institution_ids":["https://openalex.org/I44265643"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059008266","display_name":"Mohammed Sarosh Khan","orcid":"https://orcid.org/0000-0002-2416-4304"},"institutions":[{"id":"https://openalex.org/I44265643","display_name":"Rowan University","ror":"https://ror.org/049v69k10","country_code":"US","type":"education","lineage":["https://openalex.org/I44265643"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mohammed Sarosh Khan","raw_affiliation_strings":["Rowan University, Glassboro, NJ","Rowan University#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rowan University, Glassboro, NJ","institution_ids":["https://openalex.org/I44265643"]},{"raw_affiliation_string":"Rowan University#TAB#","institution_ids":["https://openalex.org/I44265643"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076848170","display_name":"Nicholas Kaegi","orcid":null},"institutions":[{"id":"https://openalex.org/I44265643","display_name":"Rowan University","ror":"https://ror.org/049v69k10","country_code":"US","type":"education","lineage":["https://openalex.org/I44265643"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nicholas Kaegi","raw_affiliation_strings":["Rowan University, Glassboro, NJ","Rowan University#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Rowan University, Glassboro, NJ","institution_ids":["https://openalex.org/I44265643"]},{"raw_affiliation_string":"Rowan University#TAB#","institution_ids":["https://openalex.org/I44265643"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I44265643"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11410738,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10057","display_name":"Face and Expression Recognition","score":0.9984999895095825,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.986299991607666,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.8187534809112549},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6996447443962097},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5981959700584412},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5653692483901978},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.563449501991272},{"id":"https://openalex.org/keywords/row","display_name":"Row","score":0.5356326699256897},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.5245989561080933},{"id":"https://openalex.org/keywords/hamming-graph","display_name":"Hamming graph","score":0.5100269913673401},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.49968910217285156},{"id":"https://openalex.org/keywords/hamming-weight","display_name":"Hamming weight","score":0.4877408444881439},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.47797080874443054},{"id":"https://openalex.org/keywords/prime-power","display_name":"Prime power","score":0.45875999331474304},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.4415208697319031},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4385881721973419},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4270172715187073},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4168761670589447},{"id":"https://openalex.org/keywords/hamming-bound","display_name":"Hamming bound","score":0.41447824239730835},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.2086820900440216},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19365498423576355},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.16100433468818665},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.1259639859199524}],"concepts":[{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.8187534809112549},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6996447443962097},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5981959700584412},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5653692483901978},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.563449501991272},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.5356326699256897},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.5245989561080933},{"id":"https://openalex.org/C29696283","wikidata":"https://www.wikidata.org/wiki/Q369440","display_name":"Hamming graph","level":5,"score":0.5100269913673401},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.49968910217285156},{"id":"https://openalex.org/C63361517","wikidata":"https://www.wikidata.org/wiki/Q5645805","display_name":"Hamming weight","level":5,"score":0.4877408444881439},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.47797080874443054},{"id":"https://openalex.org/C174072685","wikidata":"https://www.wikidata.org/wiki/Q1667469","display_name":"Prime power","level":3,"score":0.45875999331474304},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4415208697319031},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4385881721973419},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4270172715187073},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4168761670589447},{"id":"https://openalex.org/C166530166","wikidata":"https://www.wikidata.org/wiki/Q1970635","display_name":"Hamming bound","level":5,"score":0.41447824239730835},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.2086820900440216},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19365498423576355},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.16100433468818665},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.1259639859199524},{"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/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/ssci50451.2021.9660146","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ssci50451.2021.9660146","pdf_url":null,"source":{"id":"https://openalex.org/S4363604921","display_name":"2021 IEEE Symposium Series on Computational Intelligence (SSCI)","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":"2021 IEEE Symposium Series on Computational Intelligence (SSCI)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2110.02161","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2110.02161","pdf_url":"https://arxiv.org/pdf/2110.02161","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:3202074398","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2110.02161","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2110.02161","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2110.02161","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2110.02161","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2110.02161","pdf_url":"https://arxiv.org/pdf/2110.02161","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1975532204","display_name":null,"funder_award_id":"DMS-1722563","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3202074398.pdf","grobid_xml":"https://content.openalex.org/works/W3202074398.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1676820704","https://openalex.org/W1966045914","https://openalex.org/W2005051678","https://openalex.org/W2008426763","https://openalex.org/W2101276256","https://openalex.org/W2123506034","https://openalex.org/W2128715378","https://openalex.org/W2133436028","https://openalex.org/W2144562310","https://openalex.org/W2917837129","https://openalex.org/W2979541246","https://openalex.org/W6635310694"],"related_works":["https://openalex.org/W3099510449","https://openalex.org/W2083441951","https://openalex.org/W2166485816","https://openalex.org/W2744903301","https://openalex.org/W1972828245","https://openalex.org/W2112033542","https://openalex.org/W2186830145","https://openalex.org/W2046447920","https://openalex.org/W2038367370","https://openalex.org/W2205243458","https://openalex.org/W2183449570","https://openalex.org/W2599729588","https://openalex.org/W2951671515","https://openalex.org/W2743327613","https://openalex.org/W2974276993","https://openalex.org/W2752958946","https://openalex.org/W2010444367","https://openalex.org/W2848800498","https://openalex.org/W2076838219","https://openalex.org/W2275724313"],"abstract_inverted_index":{"A":[0],"new":[1],"recursive":[2],"construction":[3,24,39],"of":[4,51,62,116,125],"<tex":[5,33,42,48,80,106,117,139,156],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[6,34,43,49,81,107,118,140,157],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$N$</tex>":[7,35,44,82,108],"-ary":[8,83],"error-correcting":[9],"output":[10],"code":[11],"(ECOC)":[12],"matrices":[13,47,78,164],"for":[14,25,69,79,155],"ensemble":[15],"classification":[16,85],"methods":[17],"is":[18,102,109,142,149],"presented,":[19],"generalizing":[20],"the":[21,114,123,132,146],"classic":[22],"doubling":[23],"binary":[26],"Hadamard":[27],"matrices.":[28,100],"Given":[29],"any":[30,60],"prime":[31],"integer":[32],",":[36],"this":[37],"deterministic":[38,76],"generates":[40],"base-":[41],"symmetric":[45],"square":[46],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">$M$</tex>":[50,119,141,158],"prime-power":[52],"dimension":[53,115],"having":[54],"optimal":[55],"minimum":[56,135,168],"Hamming":[57,136,169],"distance":[58,137,153,170],"between":[59],"two":[61],"its":[63],"rows":[64],"and":[65,88],"columns.":[66],"Experimental":[67],"results":[68],"six":[70],"datasets":[71],"demonstrate":[72],"that":[73,113,161],"using":[74,96],"these":[75,162],"coding":[77,99],"ECOC":[84],"yields":[86],"comparable":[87],"in":[89,127,134,171],"many":[90],"cases":[91],"higher":[92,167],"accuracy":[93],"compared":[94],"to":[95,144,173],"randomly":[97,174],"generated":[98,175],"This":[101,148],"particular":[103],"true":[104],"when":[105,138],"adaptively":[110],"chosen":[111],"so":[112],"matches":[120],"closely":[121],"with":[122],"number":[124],"classes":[126],"a":[128,152],"dataset,":[129],"which":[130,159],"reduces":[131],"loss":[133],"truncated":[143],"fit":[145],"dataset.":[147],"verified":[150],"through":[151],"formula":[154],"shows":[160],"adaptive":[163],"have":[165],"significantly":[166],"comparison":[172],"ones.":[176]},"counts_by_year":[],"updated_date":"2026-07-01T08:55:40.977307","created_date":"2025-10-10T00:00:00"}