{"id":"https://openalex.org/W3043975730","doi":"https://doi.org/10.1109/tsp.2020.3010719","title":"A Second-Order Method for Fitting the Canonical Polyadic Decomposition With Non-Least-Squares Cost","display_name":"A Second-Order Method for Fitting the Canonical Polyadic Decomposition With Non-Least-Squares Cost","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3043975730","doi":"https://doi.org/10.1109/tsp.2020.3010719","mag":"3043975730"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2020.3010719","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2020.3010719","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":true,"oa_status":"green","oa_url":"https://lirias.kuleuven.be/handle/123456789/658272","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049123030","display_name":"Michiel Vandecappelle","orcid":"https://orcid.org/0000-0001-6231-5313"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Michiel Vandecappelle","raw_affiliation_strings":["Department of Electrical Engineering ESAT/ STADIUS, KU Leuven, Leuven, Belgium","Kulak, Group Science, Engineering and Technology, KU Leuven, Kortrijk, Belgium"],"raw_orcid":"https://orcid.org/0000-0001-6231-5313","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering ESAT/ STADIUS, KU Leuven, Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Kulak, Group Science, Engineering and Technology, KU Leuven, Kortrijk, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003192020","display_name":"Nico Vervliet","orcid":"https://orcid.org/0000-0003-3006-4155"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Nico Vervliet","raw_affiliation_strings":["Department of Electrical Engineering ESAT/ STADIUS, KU Leuven, Leuven, Belgium","Kulak, Group Science, Engineering and Technology, KU Leuven, Kortrijk, Belgium"],"raw_orcid":"https://orcid.org/0000-0003-3006-4155","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering ESAT/ STADIUS, KU Leuven, Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Kulak, Group Science, Engineering and Technology, KU Leuven, Kortrijk, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009006026","display_name":"Lieven De Lathauwer","orcid":"https://orcid.org/0000-0001-5562-5014"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Lieven De Lathauwer","raw_affiliation_strings":["Department of Electrical Engineering ESAT/ STADIUS, KU Leuven, Leuven, Belgium","Kulak, Group Science, Engineering and Technology, KU Leuven, Kortrijk, Belgium"],"raw_orcid":"https://orcid.org/0000-0001-5562-5014","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering ESAT/ STADIUS, KU Leuven, Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]},{"raw_affiliation_string":"Kulak, Group Science, Engineering and Technology, KU Leuven, Kortrijk, Belgium","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5049123030"],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":null,"apc_paid":null,"fwci":1.9757,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.87176326,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"68","issue":null,"first_page":"4454","last_page":"4465"},"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9908999800682068,"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":0.9842000007629395,"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/hessian-matrix","display_name":"Hessian matrix","score":0.8684751987457275},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6299035549163818},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5948091745376587},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.538926362991333},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.5302203297615051},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.45877230167388916},{"id":"https://openalex.org/keywords/qr-decomposition","display_name":"QR decomposition","score":0.4416287839412689},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4028545618057251},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.19755271077156067},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09497851133346558}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.8684751987457275},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6299035549163818},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5948091745376587},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.538926362991333},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.5302203297615051},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.45877230167388916},{"id":"https://openalex.org/C188060507","wikidata":"https://www.wikidata.org/wiki/Q653242","display_name":"QR decomposition","level":3,"score":0.4416287839412689},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4028545618057251},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.19755271077156067},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09497851133346558},{"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/tsp.2020.3010719","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2020.3010719","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"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/658272","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/658272","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Ieee Transactions On Signal Processing, vol. 68, (4454-4465)","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/658272","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/658272","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Ieee Transactions On Signal Processing, vol. 68, (4454-4465)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2787453302","display_name":null,"funder_award_id":"30468160","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321390","display_name":"Fonds De La Recherche Scientifique - FNRS","ror":"https://ror.org/03q83t159"},{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"},{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W210719916","https://openalex.org/W1590929617","https://openalex.org/W1974785908","https://openalex.org/W1980849288","https://openalex.org/W1983458887","https://openalex.org/W1985242206","https://openalex.org/W1988720938","https://openalex.org/W1989811026","https://openalex.org/W2008972618","https://openalex.org/W2024356620","https://openalex.org/W2026034143","https://openalex.org/W2039844283","https://openalex.org/W2054137409","https://openalex.org/W2057503509","https://openalex.org/W2063385922","https://openalex.org/W2070013413","https://openalex.org/W2070615500","https://openalex.org/W2071729267","https://openalex.org/W2114508388","https://openalex.org/W2119412403","https://openalex.org/W2130984546","https://openalex.org/W2131914626","https://openalex.org/W2135160607","https://openalex.org/W2149192061","https://openalex.org/W2159269332","https://openalex.org/W2164074203","https://openalex.org/W2469230926","https://openalex.org/W2569877296","https://openalex.org/W2791772015","https://openalex.org/W2924170235","https://openalex.org/W2944211990","https://openalex.org/W2970592101","https://openalex.org/W2988608730","https://openalex.org/W3005990752","https://openalex.org/W3098758500","https://openalex.org/W3098973674","https://openalex.org/W3103400026","https://openalex.org/W3105254673","https://openalex.org/W4301014524","https://openalex.org/W6762796666"],"related_works":["https://openalex.org/W2611031068","https://openalex.org/W1704347466","https://openalex.org/W1996936972","https://openalex.org/W4283017538","https://openalex.org/W1545275724","https://openalex.org/W2802707792","https://openalex.org/W2569979269","https://openalex.org/W781002220","https://openalex.org/W4299069794","https://openalex.org/W2796380742"],"abstract_inverted_index":{"The":[0,115],"canonical":[1],"polyadic":[2],"decomposition":[3,171],"(CPD)":[4],"can":[5,143],"be":[6,144],"used":[7],"to":[8,91,109,123,147],"extract":[9],"meaningful":[10],"components":[11],"from":[12,84],"a":[13,130,151],"tensor.":[14],"Most":[15],"existing":[16],"optimization":[17,71],"methods":[18,72],"for":[19,49,57],"fitting":[20],"the":[21,27,31,37,45,85,88,104,119,125,148,161,170],"CPD":[22],"use":[23,82],"as":[24],"cost":[25,41,62,67,89,113,127,134,154],"function":[26,42,90],"least-squares":[28,107],"distance":[29],"between":[30],"tensor":[32],"and":[33,157],"its":[34],"CPD.":[35],"While":[36],"minimum":[38],"of":[39,87,118,169],"this":[40,100],"coincides":[43],"with":[44,51,150],"maximum":[46],"likelihood":[47],"estimator":[48],"data":[50],"additive":[52],"i.i.d.":[53],"Gaussian":[54],"distributed":[55],"noise,":[56],"other":[58],"noise":[59],"distributions,":[60],"better-suited":[61],"functions":[63,135],"exist.":[64],"For":[65],"such":[66],"functions,":[68],"first-order,":[69],"gradient-based":[70],"have":[73],"been":[74],"proposed.":[75],"However,":[76],"(approximate)":[77],"second-order":[78],"methods,":[79],"which":[80],"additionally":[81],"information":[83],"Hessian":[86],"achieve":[92],"faster":[93],"convergence,":[94],"are":[95,136],"still":[96],"largely":[97],"unexplored.":[98],"In":[99],"paper,":[101],"we":[102],"generalize":[103],"Gauss-Newton":[105],"nonlinear":[106],"algorithm":[108],"twice":[110],"differentiable":[111],"entry-wise":[112],"functions.":[114],"low-rank":[116],"structure":[117],"problem":[120],"is":[121,172],"exploited":[122],"keep":[124],"computational":[126],"low.":[128],"As":[129],"special":[131],"case,":[132],"$\\beta$-divergence":[133],"examined.":[137],"We":[138],"show":[139],"that":[140],"quadratic":[141],"convergence":[142],"obtained":[145],"close":[146],"solution":[149],"reasonable":[152],"extra":[153],"in":[155],"memory":[156],"computation":[158],"time,":[159],"making":[160],"proposed":[162],"method":[163],"particularly":[164],"useful":[165],"when":[166],"high":[167],"accuracy":[168],"desired.":[173]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
