{"id":"https://openalex.org/W4320494699","doi":"https://doi.org/10.3390/a16020104","title":"Quadratic Multilinear Discriminant Analysis for Tensorial Data Classification","display_name":"Quadratic Multilinear Discriminant Analysis for Tensorial Data Classification","publication_year":2023,"publication_date":"2023-02-11","ids":{"openalex":"https://openalex.org/W4320494699","doi":"https://doi.org/10.3390/a16020104"},"language":"en","primary_location":{"id":"doi:10.3390/a16020104","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a16020104","pdf_url":"https://www.mdpi.com/1999-4893/16/2/104/pdf?version=1677036229","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"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":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/16/2/104/pdf?version=1677036229","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005152415","display_name":"Cristian Minoccheri","orcid":"https://orcid.org/0000-0001-5910-1066"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Cristian Minoccheri","raw_affiliation_strings":["Department of Computational Medicine and Bioinformatics, University of Michigan, Ann Arbor, MI 48109, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computational Medicine and Bioinformatics, University of Michigan, Ann Arbor, MI 48109, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031022775","display_name":"Olivia Alge","orcid":"https://orcid.org/0000-0002-1029-6664"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Olivia Alge","raw_affiliation_strings":["Department of Computational Medicine and Bioinformatics, University of Michigan, Ann Arbor, MI 48109, USA"],"raw_orcid":"https://orcid.org/0000-0002-1029-6664","affiliations":[{"raw_affiliation_string":"Department of Computational Medicine and Bioinformatics, University of Michigan, Ann Arbor, MI 48109, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031330604","display_name":"Jonathan Gryak","orcid":"https://orcid.org/0000-0002-5125-7741"},"institutions":[{"id":"https://openalex.org/I111455621","display_name":"Queens College, CUNY","ror":"https://ror.org/03v8adn41","country_code":"US","type":"education","lineage":["https://openalex.org/I111455621"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jonathan Gryak","raw_affiliation_strings":["Computer Science Department, Queen\u2019s College, CUNY, New York, NY 11367, USA","Computer Science Department, Queen's College, CUNY, New York, NY 11367, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Department, Queen\u2019s College, CUNY, New York, NY 11367, USA","institution_ids":["https://openalex.org/I111455621"]},{"raw_affiliation_string":"Computer Science Department, Queen's College, CUNY, New York, NY 11367, USA","institution_ids":["https://openalex.org/I111455621"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067697464","display_name":"Kayvan Najarian","orcid":"https://orcid.org/0000-0003-4485-6612"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kayvan Najarian","raw_affiliation_strings":["Department of Computational Medicine and Bioinformatics, University of Michigan, Ann Arbor, MI 48109, USA","Emergency Medicine, University of Michigan, Ann Arbor, MI 48109, USA","Michigan Center for Integrative Research in Critical Care (MCIRCC), University of Michigan, Ann Arbor, MI 48109, USA","Michigan Institute for Data Science (MIDAS), University of Michigan, Ann Arbor, MI 48109, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computational Medicine and Bioinformatics, University of Michigan, Ann Arbor, MI 48109, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Emergency Medicine, University of Michigan, Ann Arbor, MI 48109, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Michigan Center for Integrative Research in Critical Care (MCIRCC), University of Michigan, Ann Arbor, MI 48109, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Michigan Institute for Data Science (MIDAS), University of Michigan, Ann Arbor, MI 48109, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062636643","display_name":"Harm Derksen","orcid":"https://orcid.org/0000-0002-8292-8173"},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Harm Derksen","raw_affiliation_strings":["Mathematics Department, Northeastern University, Boston, MA 02115, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, Northeastern University, Boston, MA 02115, USA","institution_ids":["https://openalex.org/I12912129"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5005152415"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":0.3202,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.39808917,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"16","issue":"2","first_page":"104","last_page":"104"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11447","display_name":"Blind Source Separation Techniques","score":0.9983000159263611,"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"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9764999747276306,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/multilinear-map","display_name":"Multilinear map","score":0.9303716421127319},{"id":"https://openalex.org/keywords/linear-discriminant-analysis","display_name":"Linear discriminant analysis","score":0.6811729669570923},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.6574826240539551},{"id":"https://openalex.org/keywords/discriminant","display_name":"Discriminant","score":0.5846626162528992},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5685849189758301},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4949793219566345},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.4790705144405365},{"id":"https://openalex.org/keywords/leverage","display_name":"Leverage (statistics)","score":0.46895092725753784},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.45139288902282715},{"id":"https://openalex.org/keywords/mahalanobis-distance","display_name":"Mahalanobis distance","score":0.4446841776371002},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43858981132507324},{"id":"https://openalex.org/keywords/quadratic-classifier","display_name":"Quadratic classifier","score":0.43154090642929077},{"id":"https://openalex.org/keywords/classifier","display_name":"Classifier (UML)","score":0.3832627534866333},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3687386214733124}],"concepts":[{"id":"https://openalex.org/C84392682","wikidata":"https://www.wikidata.org/wiki/Q1952404","display_name":"Multilinear map","level":2,"score":0.9303716421127319},{"id":"https://openalex.org/C69738355","wikidata":"https://www.wikidata.org/wiki/Q1228929","display_name":"Linear discriminant analysis","level":2,"score":0.6811729669570923},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.6574826240539551},{"id":"https://openalex.org/C78397625","wikidata":"https://www.wikidata.org/wiki/Q192487","display_name":"Discriminant","level":2,"score":0.5846626162528992},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5685849189758301},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4949793219566345},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.4790705144405365},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.46895092725753784},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.45139288902282715},{"id":"https://openalex.org/C1921717","wikidata":"https://www.wikidata.org/wiki/Q1334846","display_name":"Mahalanobis distance","level":2,"score":0.4446841776371002},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43858981132507324},{"id":"https://openalex.org/C52620605","wikidata":"https://www.wikidata.org/wiki/Q7268357","display_name":"Quadratic classifier","level":3,"score":0.43154090642929077},{"id":"https://openalex.org/C95623464","wikidata":"https://www.wikidata.org/wiki/Q1096149","display_name":"Classifier (UML)","level":2,"score":0.3832627534866333},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3687386214733124},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a16020104","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a16020104","pdf_url":"https://www.mdpi.com/1999-4893/16/2/104/pdf?version=1677036229","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"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":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:6bca1068951840d0ae9b3963f3c35402","is_oa":true,"landing_page_url":"https://doaj.org/article/6bca1068951840d0ae9b3963f3c35402","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 16, Iss 2, p 104 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1999-4893/16/2/104/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/a16020104","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/a16020104","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a16020104","pdf_url":"https://www.mdpi.com/1999-4893/16/2/104/pdf?version=1677036229","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"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":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7099999785423279,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G1027035476","display_name":null,"funder_award_id":"T32GM070449","funder_id":"https://openalex.org/F4320337354","funder_display_name":"National Institute of General Medical Sciences"},{"id":"https://openalex.org/G4699534745","display_name":null,"funder_award_id":"T32GM070449","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G580482727","display_name":null,"funder_award_id":"T32 GM070449","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G594532277","display_name":"BIGDATA: F: Algorithms for Tensor-Based Modeling of Large Scale Structured Data","funder_award_id":"1837985","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"},{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"},{"id":"https://openalex.org/F4320337354","display_name":"National Institute of General Medical Sciences","ror":"https://ror.org/04q48ey07"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4320494699.pdf","grobid_xml":"https://content.openalex.org/works/W4320494699.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W1538092215","https://openalex.org/W1548929633","https://openalex.org/W1595198506","https://openalex.org/W1963616901","https://openalex.org/W1967675002","https://openalex.org/W1980666386","https://openalex.org/W1983467829","https://openalex.org/W1988001416","https://openalex.org/W1997038974","https://openalex.org/W2024165284","https://openalex.org/W2042901969","https://openalex.org/W2056974237","https://openalex.org/W2068222852","https://openalex.org/W2079705627","https://openalex.org/W2106221905","https://openalex.org/W2130689294","https://openalex.org/W2162800060","https://openalex.org/W2162894628","https://openalex.org/W2167623372","https://openalex.org/W2410423566","https://openalex.org/W2469230926","https://openalex.org/W2495557304","https://openalex.org/W2612640872","https://openalex.org/W2805323765","https://openalex.org/W2889151206","https://openalex.org/W3011253069","https://openalex.org/W3013951206","https://openalex.org/W4205293427","https://openalex.org/W6665720480","https://openalex.org/W6679505136","https://openalex.org/W6684641359"],"related_works":["https://openalex.org/W2113454941","https://openalex.org/W2951122819","https://openalex.org/W4288315282","https://openalex.org/W2350751952","https://openalex.org/W2362114017","https://openalex.org/W1999647744","https://openalex.org/W4285246984","https://openalex.org/W2075660794","https://openalex.org/W1984080040","https://openalex.org/W2366124773"],"abstract_inverted_index":{"Over":[0],"the":[1,19,37,44,61,69,86,92,158,170,184,191,219],"past":[2],"decades,":[3],"there":[4],"has":[5],"been":[6],"an":[7,163,176],"increase":[8],"of":[9,23,28,39,74,110,155,165,178,189],"attention":[10],"to":[11,16,43,72,84,91,96,122,137,157,183,210],"adapting":[12],"machine":[13],"learning":[14],"methods":[15],"fully":[17],"exploit":[18],"higher":[20],"order":[21],"structure":[22],"tensorial":[24],"data.":[25],"One":[26],"problem":[27],"great":[29],"interest":[30],"is":[31,57,68,199],"tensor":[32],"classification,":[33],"and":[34,66,95,133,208,215],"in":[35,205],"particular":[36],"extension":[38,71],"linear":[40],"discriminant":[41,54,76],"analysis":[42,55],"multilinear":[45,53],"setting.":[46],"We":[47,102,118],"propose":[48],"a":[49,98,108,187],"novel":[50],"method":[51,106,136,145,173,194],"for":[52],"that":[56],"radically":[58],"different":[59,201],"from":[60],"ones":[62],"considered":[63],"so":[64],"far,":[65],"it":[67],"first":[70],"tensors":[73,129],"quadratic":[75],"analysis.":[77],"Our":[78,160,197],"proposed":[79,115],"approach":[80,161,198],"uses":[81],"invariant":[82],"theory":[83],"extend":[85],"nearest":[87],"Mahalanobis":[88],"distance":[89],"classifier":[90],"higher-order":[93],"setting,":[94],"formulate":[97],"well-behaved":[99],"optimization":[100],"problem.":[101],"extensively":[103],"test":[104],"our":[105,135,144],"on":[107,167,218],"variety":[109],"synthetic":[111],"data,":[112],"outperforming":[113],"previously":[114],"MDA":[116,148],"techniques.":[117],"also":[119],"show":[120],"how":[121],"leverage":[123],"multi-lead":[124],"ECG":[125],"data":[126],"by":[127],"constructing":[128],"via":[130],"taut":[131],"string,":[132],"use":[134],"classify":[138],"healthy":[139],"signals":[140,185],"versus":[141],"unhealthy":[142],"ones;":[143],"outperforms":[146],"state-of-the-art":[147],"methods,":[149],"especially":[150],"after":[151,180],"adding":[152,181],"significant":[153],"levels":[154],"noise":[156,182],"signals.":[159],"reached":[162,174,195],"AUC":[164,177],"0.95(0.03)":[166],"clean":[168],"signals\u2014where":[169],"second":[171,192],"best":[172,193],"0.91(0.03)\u2014and":[175],"0.89(0.03)":[179],"(with":[186],"signal-to-noise-ratio":[188],"\u221230)\u2014where":[190],"0.85(0.05).":[196],"fundamentally":[200],"than":[202],"previous":[203],"work":[204],"this":[206],"direction,":[207],"proves":[209],"be":[211],"faster,":[212],"more":[213,216],"stable,":[214],"accurate":[217],"tests":[220],"we":[221],"performed.":[222]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
