{"id":"https://openalex.org/W2884159946","doi":"https://doi.org/10.1109/tnnls.2018.2851612","title":"A Fused CP Factorization Method for Incomplete Tensors","display_name":"A Fused CP Factorization Method for Incomplete Tensors","publication_year":2018,"publication_date":"2018-07-26","ids":{"openalex":"https://openalex.org/W2884159946","doi":"https://doi.org/10.1109/tnnls.2018.2851612","mag":"2884159946","pmid":"https://pubmed.ncbi.nlm.nih.gov/30047907"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2018.2851612","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2018.2851612","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/A5100370856","display_name":"Yuankai Wu","orcid":"https://orcid.org/0000-0003-4435-9413"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuankai Wu","raw_affiliation_strings":["School of Mechanical Engineering, Beijing Institute of Technology, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100751506","display_name":"Huachun Tan","orcid":"https://orcid.org/0000-0001-5968-103X"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huachun Tan","raw_affiliation_strings":["School of Mechanical Engineering, Beijing Institute of Technology, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0001-5968-103X","affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100355325","display_name":"Yong Li","orcid":"https://orcid.org/0000-0001-9685-2571"},"institutions":[{"id":"https://openalex.org/I139759216","display_name":"Beijing University of Posts and Telecommunications","ror":"https://ror.org/04w9fbh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I139759216"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yong Li","raw_affiliation_strings":["School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0001-9685-2571","affiliations":[{"raw_affiliation_string":"School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing, China","institution_ids":["https://openalex.org/I139759216"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100410024","display_name":"Jian Zhang","orcid":"https://orcid.org/0000-0002-9086-7622"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian Zhang","raw_affiliation_strings":["Research Center for Internet of Mobility, School of Transportation, Southeast University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-9086-7622","affiliations":[{"raw_affiliation_string":"Research Center for Internet of Mobility, School of Transportation, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100628255","display_name":"Xiaoxuan Chen","orcid":"https://orcid.org/0000-0002-2029-2448"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiaoxuan Chen","raw_affiliation_strings":["Department of Civil and Environmental Engineering, University of Wisconsin\u2013Madison, Madison, WI, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Civil and Environmental Engineering, University of Wisconsin\u2013Madison, Madison, WI, USA","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.5642,"has_fulltext":false,"cited_by_count":66,"citation_normalized_percentile":{"value":0.94390716,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"30","issue":"3","first_page":"751","last_page":"764"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9970999956130981,"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"}},{"id":"https://openalex.org/T11304","display_name":"Advanced Neuroimaging Techniques and Applications","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/2741","display_name":"Radiology, Nuclear Medicine and Imaging"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/prior-probability","display_name":"Prior probability","score":0.6296396255493164},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.6081116199493408},{"id":"https://openalex.org/keywords/coordinate-descent","display_name":"Coordinate descent","score":0.5977684259414673},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5593022704124451},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5389178395271301},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.48833319544792175},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4860875904560089},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.48024991154670715},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4429360330104828},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.44278544187545776},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4043985605239868},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40345415472984314},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36908721923828125},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2839031517505646},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12228226661682129},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10369241237640381}],"concepts":[{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.6296396255493164},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.6081116199493408},{"id":"https://openalex.org/C157553263","wikidata":"https://www.wikidata.org/wiki/Q5168004","display_name":"Coordinate descent","level":2,"score":0.5977684259414673},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5593022704124451},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5389178395271301},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.48833319544792175},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4860875904560089},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.48024991154670715},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4429360330104828},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.44278544187545776},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4043985605239868},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40345415472984314},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36908721923828125},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2839031517505646},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12228226661682129},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10369241237640381},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2018.2851612","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2018.2851612","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:30047907","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/30047907","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/G1938823714","display_name":null,"funder_award_id":"61620106002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4880811201","display_name":"\u57fa\u4e8e\u5f20\u91cf\u6a21\u578b\u7684\u4ea4\u901a\u6570\u636e\u91cd\u5efa\u65b9\u6cd5\u7814\u7a76","funder_award_id":"61271376","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":66,"referenced_works":["https://openalex.org/W331119053","https://openalex.org/W792141054","https://openalex.org/W1487940008","https://openalex.org/W1521672915","https://openalex.org/W1539811621","https://openalex.org/W1568416770","https://openalex.org/W1798398164","https://openalex.org/W1814521481","https://openalex.org/W1968080575","https://openalex.org/W1968154520","https://openalex.org/W1971787101","https://openalex.org/W1989060270","https://openalex.org/W1993482030","https://openalex.org/W2013912476","https://openalex.org/W2020641160","https://openalex.org/W2024165284","https://openalex.org/W2027047167","https://openalex.org/W2030628896","https://openalex.org/W2030928609","https://openalex.org/W2033560557","https://openalex.org/W2040006565","https://openalex.org/W2048997552","https://openalex.org/W2049588365","https://openalex.org/W2058252247","https://openalex.org/W2064321206","https://openalex.org/W2068078373","https://openalex.org/W2078677240","https://openalex.org/W2082600181","https://openalex.org/W2086261631","https://openalex.org/W2091449379","https://openalex.org/W2098251381","https://openalex.org/W2102760656","https://openalex.org/W2103559027","https://openalex.org/W2108119513","https://openalex.org/W2117587045","https://openalex.org/W2122825543","https://openalex.org/W2135046866","https://openalex.org/W2147512299","https://openalex.org/W2155151262","https://openalex.org/W2164799551","https://openalex.org/W2167732364","https://openalex.org/W2171250816","https://openalex.org/W2179076887","https://openalex.org/W2231011007","https://openalex.org/W2258054274","https://openalex.org/W2270082749","https://openalex.org/W2302604136","https://openalex.org/W2342432191","https://openalex.org/W2342643507","https://openalex.org/W2345068797","https://openalex.org/W2403959208","https://openalex.org/W2475436493","https://openalex.org/W2481706124","https://openalex.org/W2527153419","https://openalex.org/W2547812180","https://openalex.org/W2583110309","https://openalex.org/W2584613988","https://openalex.org/W2606967921","https://openalex.org/W2793820729","https://openalex.org/W2936995161","https://openalex.org/W2963544062","https://openalex.org/W3101782091","https://openalex.org/W4242209908","https://openalex.org/W4247649469","https://openalex.org/W6631323259","https://openalex.org/W6761030284"],"related_works":["https://openalex.org/W2580650124","https://openalex.org/W4386190339","https://openalex.org/W2968424575","https://openalex.org/W3142333283","https://openalex.org/W3122088529","https://openalex.org/W3185235544","https://openalex.org/W4297791327","https://openalex.org/W3041320102","https://openalex.org/W2947416323","https://openalex.org/W4288346661"],"abstract_inverted_index":{"Low-rank":[0],"tensor":[1,29,88,99,148,210],"completion":[2,211],"methods":[3],"have":[4],"been":[5],"advanced":[6],"recently":[7],"for":[8,87,209],"modeling":[9],"sparsely":[10],"observed":[11],"data":[12,173,180],"with":[13,44],"a":[14,64,67,96,120,135,213],"multimode":[15],"structure.":[16],"However,":[17,48],"low-rank":[18,46],"priors":[19],"may":[20],"fail":[21],"to":[22,35,40,50,138,222],"interpret":[23],"the":[24,45,51,61,82,104,139,147,153,158,164,187,195,198,202],"model":[25],"factors":[26],"of":[27,57,63,84,122,181,189,204],"general":[28],"objects.":[30],"The":[31,114],"most":[32],"common":[33],"method":[34,127,191],"address":[36],"this":[37],"drawback":[38],"is":[39,117,150,161,192],"use":[41,62,223],"regularizations":[42,69,86,208],"together":[43],"priors.":[47],"due":[49],"complex":[52],"nature":[53],"and":[54,74,110,128,141,145,178,186,216],"diverse":[55],"characteristics":[56,203],"real-world":[58],"multiway":[59],"data,":[60,171],"single":[65],"or":[66],"few":[68],"remains":[70],"far":[71],"from":[72],"efficient,":[73],"there":[75],"are":[76,184],"limited":[77],"systematic":[78],"experimental":[79,218],"reports":[80],"on":[81,169],"advantages":[83],"these":[85,92,205],"completion.":[89],"To":[90],"fill":[91],"gaps,":[93],"we":[94,133],"propose":[95],"modified":[97],"CP":[98],"factorization":[100,115],"framework":[101],"that":[102],"fuses":[103],"l2norm":[105],"constraint,":[106],"sparseness":[107],"(l1norm),":[108],"manifold,":[109],"smooth":[111,136],"information":[112],"simultaneously.":[113],"problem":[116],"addressed":[118],"through":[119],"combination":[121],"Nesterov's":[123],"optimal":[124],"gradient":[125,155],"descent":[126],"block":[129],"coordinate":[130],"descent.":[131],"Here,":[132],"construct":[134],"approximation":[137],"l1norm":[140],"TV":[142],"norm":[143],"regularizations,":[144],"then,":[146],"factor":[149],"updated":[151],"using":[152],"projected":[154],"method,":[156],"where":[157],"step":[159],"size":[160],"determined":[162],"by":[163,194],"Lipschitz":[165],"constant.":[166],"Extensive":[167],"experiments":[168],"simulation":[170],"visual":[172],"completion,":[174],"intelligent":[175],"transportation":[176],"systems,":[177],"GPS":[179],"user":[182],"involvement":[183],"conducted,":[185],"efficiency":[188],"our":[190],"confirmed":[193],"results.":[196],"Moreover,":[197],"obtained":[199],"results":[200],"reveal":[201],"commonly":[206],"used":[207],"in":[212],"certain":[214],"sense":[215],"give":[217],"guidance":[219],"concerning":[220],"how":[221],"them.":[224]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":16},{"year":2019,"cited_by_count":7}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}