{"id":"https://openalex.org/W3127651001","doi":"https://doi.org/10.1109/tsp.2021.3055000","title":"Supervised Learning and Canonical Decomposition of Multivariate Functions","display_name":"Supervised Learning and Canonical Decomposition of Multivariate Functions","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3127651001","doi":"https://doi.org/10.1109/tsp.2021.3055000","mag":"3127651001"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2021.3055000","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2021.3055000","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"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/A5077063387","display_name":"Nikos Kargas","orcid":"https://orcid.org/0000-0002-3798-2875"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nikos Kargas","raw_affiliation_strings":["Department of ECE, University of Minnesota, Minneapolis, MN, USA"],"raw_orcid":"https://orcid.org/0000-0002-3798-2875","affiliations":[{"raw_affiliation_string":"Department of ECE, University of Minnesota, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050186120","display_name":"Nicholas D. Sidiropoulos","orcid":"https://orcid.org/0000-0002-3385-7911"},"institutions":[{"id":"https://openalex.org/I51556381","display_name":"University of Virginia","ror":"https://ror.org/0153tk833","country_code":"US","type":"education","lineage":["https://openalex.org/I51556381"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nicholas D. Sidiropoulos","raw_affiliation_strings":["Department of ECE, University of Virginia, Charlottesville, VA, USA"],"raw_orcid":"https://orcid.org/0000-0002-3385-7911","affiliations":[{"raw_affiliation_string":"Department of ECE, University of Virginia, Charlottesville, VA, USA","institution_ids":["https://openalex.org/I51556381"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7879,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.84316038,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"69","issue":null,"first_page":"1097","last_page":"1107"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9998999834060669,"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":0.9998999834060669,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9057000279426575,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.6831295490264893},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.6205214262008667},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5435450077056885},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.530913233757019},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.4911358058452606},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.47565338015556335},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.44754257798194885},{"id":"https://openalex.org/keywords/canonical-correlation","display_name":"Canonical correlation","score":0.4428724944591522},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4281059205532074},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4269089996814728},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.41758018732070923},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41659173369407654},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40513888001441956},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3522004783153534},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3296663165092468},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.30689936876296997},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.17556610703468323},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10705843567848206}],"concepts":[{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.6831295490264893},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.6205214262008667},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5435450077056885},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.530913233757019},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.4911358058452606},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.47565338015556335},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.44754257798194885},{"id":"https://openalex.org/C153874254","wikidata":"https://www.wikidata.org/wiki/Q115542","display_name":"Canonical correlation","level":2,"score":0.4428724944591522},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4281059205532074},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4269089996814728},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.41758018732070923},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41659173369407654},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40513888001441956},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3522004783153534},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3296663165092468},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.30689936876296997},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.17556610703468323},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10705843567848206},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tsp.2021.3055000","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2021.3055000","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W1575364304","https://openalex.org/W1722514995","https://openalex.org/W1798945469","https://openalex.org/W1963826206","https://openalex.org/W1970195563","https://openalex.org/W1993482030","https://openalex.org/W2033154334","https://openalex.org/W2038920431","https://openalex.org/W2050968963","https://openalex.org/W2055470928","https://openalex.org/W2088993232","https://openalex.org/W2101234009","https://openalex.org/W2102937240","https://openalex.org/W2103392911","https://openalex.org/W2121739212","https://openalex.org/W2137983211","https://openalex.org/W2295739661","https://openalex.org/W2432356473","https://openalex.org/W2469230926","https://openalex.org/W2470457291","https://openalex.org/W2505972586","https://openalex.org/W2528907418","https://openalex.org/W2557086248","https://openalex.org/W2588556635","https://openalex.org/W2621722328","https://openalex.org/W2752217370","https://openalex.org/W2774921216","https://openalex.org/W2787894218","https://openalex.org/W2798766386","https://openalex.org/W2902132336","https://openalex.org/W2914578694","https://openalex.org/W2963048316","https://openalex.org/W2963432357","https://openalex.org/W2963450615","https://openalex.org/W2964003140","https://openalex.org/W2964290417","https://openalex.org/W2997064993","https://openalex.org/W3099444291","https://openalex.org/W3120740533","https://openalex.org/W3146803896","https://openalex.org/W4250739957","https://openalex.org/W4293869761","https://openalex.org/W4295910374","https://openalex.org/W4298155380","https://openalex.org/W4299655675","https://openalex.org/W6634371209","https://openalex.org/W6638060716","https://openalex.org/W6675354045","https://openalex.org/W6679667936","https://openalex.org/W6718112784","https://openalex.org/W6720612731","https://openalex.org/W6724478308","https://openalex.org/W6730089078","https://openalex.org/W6743676628","https://openalex.org/W6745442365","https://openalex.org/W6751747387"],"related_works":["https://openalex.org/W1565185441","https://openalex.org/W1968846550","https://openalex.org/W302711736","https://openalex.org/W2313359725","https://openalex.org/W2375550484","https://openalex.org/W2619932150","https://openalex.org/W3134705486","https://openalex.org/W2013124714","https://openalex.org/W2121524531","https://openalex.org/W2444009674"],"abstract_inverted_index":{"Learning":[0],"a":[1,24,52,58,68,75,108],"function":[2,56,102,122],"from":[3,32],"input":[4],"and":[5,40,66,113,151,157],"output":[6],"data":[7],"pairs":[8],"is":[9,91,123],"one":[10],"of":[11,26,37,60,79],"the":[12,27,80,120,127],"most":[13],"fundamental":[14],"tasks":[15],"in":[16],"machine":[17],"learning.":[18,49],"In":[19,84],"this":[20],"work,":[21,88],"we":[22],"propose":[23,67],"generalization":[25],"Canonical":[28],"Polyadic":[29],"Decomposition":[30],"(CPD)":[31],"tensors":[33],"to":[34,47,86,141,143],"multivariate":[35,55,101,159],"functions":[36],"continuous":[38],"variables,":[39],"show":[41],"how":[42],"it":[43,95,117,140],"can":[44,96,104],"be":[45,105],"applied":[46],"supervised":[48],"We":[50,146],"approximate":[51],"compactly":[53,99],"supported":[54,100],"using":[57],"tensor":[59,70],"truncated":[61],"multidimensional":[62,110],"Fourier":[63,81,111],"series":[64],"coefficients":[65,82],"hidden":[69],"factorization":[71],"formulation":[72],"for":[73],"learning":[74],"low-rank":[76],"CPD":[77],"model":[78,97,133],"tensor.":[83],"contrast":[85],"prior":[87],"our":[89,132],"method":[90],"quite":[92],"general":[93],"as":[94],"any":[98],"that":[103,119],"well-approximated":[106],"by":[107,126],"finite":[109],"series,":[112],"under":[114],"certain":[115],"conditions":[116],"guarantees":[118],"unknown":[121],"uniquely":[124],"characterized":[125],"given":[128],"input-output":[129],"data.":[130],"Furthermore,":[131],"naturally":[134],"allows":[135],"stochastic":[136],"gradient":[137],"updates":[138],"allowing":[139],"scale":[142],"larger":[144],"datasets.":[145],"develop":[147],"two":[148],"optimization":[149],"algorithms":[150],"demonstrate":[152],"promising":[153],"results":[154],"on":[155],"synthetic":[156],"real":[158],"regression":[160],"tasks.":[161]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
