{"id":"https://openalex.org/W4312607144","doi":"https://doi.org/10.1109/tsp.2022.3221661","title":"Learning Unbalanced and Sparse Low-Order Tensors","display_name":"Learning Unbalanced and Sparse Low-Order Tensors","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4312607144","doi":"https://doi.org/10.1109/tsp.2022.3221661"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2022.3221661","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2022.3221661","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/A5005131372","display_name":"Pham Minh Hoang","orcid":null},"institutions":[{"id":"https://openalex.org/I123565023","display_name":"Vietnam National University Ho Chi Minh City","ror":"https://ror.org/00waaqh38","country_code":"VN","type":"education","lineage":["https://openalex.org/I123565023"]},{"id":"https://openalex.org/I23582244","display_name":"Ho Chi Minh City University of Science","ror":"https://ror.org/05jfbgm49","country_code":"VN","type":"education","lineage":["https://openalex.org/I123565023","https://openalex.org/I23582244"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"Pham Minh Hoang","raw_affiliation_strings":["Faculty of Information Technology, University of Science, VNU-HCM, Hochiminh, Vietnam"],"affiliations":[{"raw_affiliation_string":"Faculty of Information Technology, University of Science, VNU-HCM, Hochiminh, Vietnam","institution_ids":["https://openalex.org/I23582244","https://openalex.org/I123565023"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046645515","display_name":"Hoang Duong Tuan","orcid":"https://orcid.org/0000-0003-0292-6061"},"institutions":[{"id":"https://openalex.org/I114017466","display_name":"University of Technology Sydney","ror":"https://ror.org/03f0f6041","country_code":"AU","type":"education","lineage":["https://openalex.org/I114017466"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Hoang Duong Tuan","raw_affiliation_strings":["School of Electrical and Data Engineering, University of Technology Sydney, Ultimo, NSW, Australia"],"affiliations":[{"raw_affiliation_string":"School of Electrical and Data Engineering, University of Technology Sydney, Ultimo, NSW, Australia","institution_ids":["https://openalex.org/I114017466"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067418754","display_name":"Tr\u1ea7n Th\u00e1i S\u01a1n","orcid":"https://orcid.org/0000-0002-4063-7095"},"institutions":[{"id":"https://openalex.org/I123565023","display_name":"Vietnam National University Ho Chi Minh City","ror":"https://ror.org/00waaqh38","country_code":"VN","type":"education","lineage":["https://openalex.org/I123565023"]},{"id":"https://openalex.org/I23582244","display_name":"Ho Chi Minh City University of Science","ror":"https://ror.org/05jfbgm49","country_code":"VN","type":"education","lineage":["https://openalex.org/I123565023","https://openalex.org/I23582244"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Tran Thai Son","raw_affiliation_strings":["Faculty of Information Technology, University of Science, VNU-HCM, Hochiminh, Vietnam"],"affiliations":[{"raw_affiliation_string":"Faculty of Information Technology, University of Science, VNU-HCM, Hochiminh, Vietnam","institution_ids":["https://openalex.org/I23582244","https://openalex.org/I123565023"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042307561","display_name":"H. Vincent Poor","orcid":"https://orcid.org/0000-0002-2062-131X"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"H. Vincent Poor","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ, USA"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Princeton University, Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091122305","display_name":"Lajos Hanzo","orcid":"https://orcid.org/0000-0002-2636-5214"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Lajos Hanzo","raw_affiliation_strings":["School of Electronics and Computer Science, University of Southampton, Southampton, U.K"],"affiliations":[{"raw_affiliation_string":"School of Electronics and Computer Science, University of Southampton, Southampton, U.K","institution_ids":["https://openalex.org/I43439940"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5005131372"],"corresponding_institution_ids":["https://openalex.org/I123565023","https://openalex.org/I23582244"],"apc_list":null,"apc_paid":null,"fwci":0.5463,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.62064826,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"70","issue":null,"first_page":"5624","last_page":"5638"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9969000220298767,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9534000158309937,"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/tensor","display_name":"Tensor (intrinsic definition)","score":0.7781785726547241},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.6303767561912537},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5535795092582703},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5204113721847534},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.5106099247932434},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.5079813599586487},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4798116981983185},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46817225217819214},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.46254345774650574},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.45701175928115845},{"id":"https://openalex.org/keywords/pixel","display_name":"Pixel","score":0.42341822385787964},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39701181650161743},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3499719500541687},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34414419531822205},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33317452669143677},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2965209484100342},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2519952058792114},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.23507460951805115},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.1115296483039856},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.1000126302242279}],"concepts":[{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.7781785726547241},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6303767561912537},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5535795092582703},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5204113721847534},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.5106099247932434},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.5079813599586487},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4798116981983185},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46817225217819214},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.46254345774650574},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.45701175928115845},{"id":"https://openalex.org/C160633673","wikidata":"https://www.wikidata.org/wiki/Q355198","display_name":"Pixel","level":2,"score":0.42341822385787964},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39701181650161743},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3499719500541687},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34414419531822205},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33317452669143677},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2965209484100342},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2519952058792114},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23507460951805115},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.1115296483039856},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.1000126302242279},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tsp.2022.3221661","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2022.3221661","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:eprints.soton.ac.uk:472444","is_oa":false,"landing_page_url":"https://eprints.soton.ac.uk/472444/2/Learning_Unbalanced_and_Sparse_Low_Order_Tensors.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306401019","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1032414495","display_name":"Converged Optical and Wireless Access Networks (COALESCE)","funder_award_id":"EP/P003990/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1131370387","display_name":"UKRI-India Future Networks Initiative","funder_award_id":"EP/W016605/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1471839284","display_name":null,"funder_award_id":"EP/W016605/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2422336959","display_name":null,"funder_award_id":"EP/P003990/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7920959503","display_name":null,"funder_award_id":"CCF-1908308","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/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W1521672915","https://openalex.org/W1563049925","https://openalex.org/W1966661320","https://openalex.org/W1968080575","https://openalex.org/W1969648546","https://openalex.org/W1973397215","https://openalex.org/W1993482030","https://openalex.org/W2004026774","https://openalex.org/W2004544971","https://openalex.org/W2011359124","https://openalex.org/W2013912476","https://openalex.org/W2025666718","https://openalex.org/W2031993275","https://openalex.org/W2036604884","https://openalex.org/W2038891887","https://openalex.org/W2091449379","https://openalex.org/W2103972604","https://openalex.org/W2126119581","https://openalex.org/W2219888463","https://openalex.org/W2316339223","https://openalex.org/W2412278696","https://openalex.org/W2480971951","https://openalex.org/W2523623965","https://openalex.org/W2611328865","https://openalex.org/W2764347725","https://openalex.org/W2810325916","https://openalex.org/W2894900504","https://openalex.org/W2897298721","https://openalex.org/W2901836533","https://openalex.org/W2906988372","https://openalex.org/W2907368145","https://openalex.org/W2949419207","https://openalex.org/W2950952569","https://openalex.org/W3003365835","https://openalex.org/W3010834347","https://openalex.org/W3025598106","https://openalex.org/W3098683815","https://openalex.org/W3112409853","https://openalex.org/W3169524537","https://openalex.org/W3169984557","https://openalex.org/W4249840661","https://openalex.org/W6631323259","https://openalex.org/W6633544067","https://openalex.org/W6641162989","https://openalex.org/W6682042988","https://openalex.org/W6685089420","https://openalex.org/W6703949738"],"related_works":["https://openalex.org/W2781510240","https://openalex.org/W2950186459","https://openalex.org/W2170114491","https://openalex.org/W2897298721","https://openalex.org/W2242624680","https://openalex.org/W2136127937","https://openalex.org/W4290987221","https://openalex.org/W2216309014","https://openalex.org/W3199841771","https://openalex.org/W3006184558"],"abstract_inverted_index":{"Efficient":[0],"techniques":[1,21],"are":[2,109],"developed":[3,38],"for":[4,42,80,92],"completing":[5],"unbalanced":[6],"and":[7,89,119],"sparse":[8,90],"low-order":[9,51],"tensors,":[10],"which":[11,108],"cannot":[12],"be":[13],"effectively":[14],"completed":[15],"by":[16,53,111,114],"popular":[17],"matrix-rank":[18],"optimization":[19],"based":[20],"such":[22],"as":[23],"compressed":[24],"sensing":[25],"and/or":[26],"the":[27,69],"<inline-formula":[28],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[29],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[30],"notation=\"LaTeX\">$\\ell":[31],"_{q}$</tex-math></inline-formula>":[32],"-matrix-metric.":[33],"We":[34],"use":[35],"our":[36],"previously":[37],"2D-index":[39],"encoding":[40],"technique":[41],"tensor":[43,71,121],"augmentation":[44],"in":[45],"order":[46],"to":[47],"represent":[48],"these":[49,82],"incomplete":[50,70],"tensors":[52,57,84],"high-order":[54],"but":[55],"low-dimensional":[56],"with":[58],"their":[59],"modes":[60],"building":[61],"up":[62],"a":[63],"coarse-grained":[64],"hierachy":[65],"of":[66,75,87],"correlations":[67],"among":[68],"entries.":[72],"The":[73],"concept":[74],"tensor-trains":[76],"is":[77],"then":[78],"exploited":[79],"decomposing":[81],"augmented":[83],"into":[85],"trains":[86],"balanced":[88],"matrices":[91],"efficient":[93],"completion.":[94],"More":[95],"explicitly,":[96],"we":[97],"develop":[98],"powerful":[99],"algorithms":[100],"exhibiting":[101],"an":[102],"excellent":[103],"performance":[104],"vs.":[105],"complexity":[106],"trade-off,":[107],"supported":[110],"numerical":[112],"examples":[113],"relying":[115],"on":[116],"matrix":[117],"data":[118,122],"third-order":[120],"derived":[123],"from":[124],"color":[125],"image":[126],"pixels.":[127]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
