{"id":"https://openalex.org/W4289132425","doi":"https://doi.org/10.3390/e24081057","title":"Multivariate Time Series Imputation: An Approach Based on Dictionary Learning","display_name":"Multivariate Time Series Imputation: An Approach Based on Dictionary Learning","publication_year":2022,"publication_date":"2022-07-31","ids":{"openalex":"https://openalex.org/W4289132425","doi":"https://doi.org/10.3390/e24081057","pmid":"https://pubmed.ncbi.nlm.nih.gov/36010721"},"language":"en","primary_location":{"id":"doi:10.3390/e24081057","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24081057","pdf_url":"https://www.mdpi.com/1099-4300/24/8/1057/pdf?version=1661388379","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/24/8/1057/pdf?version=1661388379","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069502299","display_name":"Xiaomeng Zheng","orcid":"https://orcid.org/0000-0002-0953-0441"},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Xiaomeng Zheng","raw_affiliation_strings":["Department of Statistics, University of Auckland, Auckland 1142, New Zealand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, University of Auckland, Auckland 1142, New Zealand","institution_ids":["https://openalex.org/I154130895"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023994037","display_name":"Bogdan Dumitrescu","orcid":"https://orcid.org/0000-0003-4555-1714"},"institutions":[{"id":"https://openalex.org/I61641377","display_name":"Universitatea Na\u021bional\u0103 de \u0218tiin\u021b\u0103 \u0219i Tehnologie Politehnica Bucure\u0219ti","ror":"https://ror.org/0558j5q12","country_code":"RO","type":"education","lineage":["https://openalex.org/I61641377"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Bogdan Dumitrescu","raw_affiliation_strings":["Department of Automatic Control and Computers, University Politehnica of Bucharest, 060042 Bucharest, Romania"],"raw_orcid":"https://orcid.org/0000-0003-4555-1714","affiliations":[{"raw_affiliation_string":"Department of Automatic Control and Computers, University Politehnica of Bucharest, 060042 Bucharest, Romania","institution_ids":["https://openalex.org/I61641377"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083914998","display_name":"Jiamou Liu","orcid":"https://orcid.org/0000-0002-0824-0899"},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Jiamou Liu","raw_affiliation_strings":["School of Computer Science, University of Auckland, Auckland 1142, New Zealand"],"raw_orcid":"https://orcid.org/0000-0002-0824-0899","affiliations":[{"raw_affiliation_string":"School of Computer Science, University of Auckland, Auckland 1142, New Zealand","institution_ids":["https://openalex.org/I154130895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006344024","display_name":"Ciprian Doru Giurc\u0103neanu","orcid":"https://orcid.org/0000-0001-5512-0868"},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":true,"raw_author_name":"Ciprian Doru Giurc\u0103neanu","raw_affiliation_strings":["Department of Statistics, University of Auckland, Auckland 1142, New Zealand"],"raw_orcid":"https://orcid.org/0000-0001-5512-0868","affiliations":[{"raw_affiliation_string":"Department of Statistics, University of Auckland, Auckland 1142, New Zealand","institution_ids":["https://openalex.org/I154130895"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5006344024"],"corresponding_institution_ids":["https://openalex.org/I154130895"],"apc_list":{"value":1800,"currency":"CHF","value_usd":1885},"apc_paid":{"value":1800,"currency":"CHF","value_usd":1885},"fwci":0.2834,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.42856103,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"24","issue":"8","first_page":"1057","last_page":"1057"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9995999932289124,"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":0.9994000196456909,"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/T10320","display_name":"Neural Networks and Applications","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/computer-science","display_name":"Computer science","score":0.6798985004425049},{"id":"https://openalex.org/keywords/imputation","display_name":"Imputation (statistics)","score":0.6564434170722961},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.5770732164382935},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5646237134933472},{"id":"https://openalex.org/keywords/missing-data","display_name":"Missing data","score":0.562410295009613},{"id":"https://openalex.org/keywords/k-svd","display_name":"K-SVD","score":0.5401439070701599},{"id":"https://openalex.org/keywords/sparse-approximation","display_name":"Sparse approximation","score":0.5328769087791443},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.5311005711555481},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.5270928144454956},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.49769070744514465},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.46784958243370056},{"id":"https://openalex.org/keywords/time-series","display_name":"Time series","score":0.44652700424194336},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4389874041080475},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4182264804840088},{"id":"https://openalex.org/keywords/dictionary-learning","display_name":"Dictionary learning","score":0.41208553314208984},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.4024434983730316},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3308488130569458},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2492821216583252}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6798985004425049},{"id":"https://openalex.org/C58041806","wikidata":"https://www.wikidata.org/wiki/Q1660484","display_name":"Imputation (statistics)","level":3,"score":0.6564434170722961},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.5770732164382935},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5646237134933472},{"id":"https://openalex.org/C9357733","wikidata":"https://www.wikidata.org/wiki/Q6878417","display_name":"Missing data","level":2,"score":0.562410295009613},{"id":"https://openalex.org/C154771677","wikidata":"https://www.wikidata.org/wiki/Q17098361","display_name":"K-SVD","level":3,"score":0.5401439070701599},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.5328769087791443},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5311005711555481},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.5270928144454956},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.49769070744514465},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.46784958243370056},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.44652700424194336},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4389874041080475},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4182264804840088},{"id":"https://openalex.org/C2988886741","wikidata":"https://www.wikidata.org/wiki/Q25304494","display_name":"Dictionary learning","level":3,"score":0.41208553314208984},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.4024434983730316},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3308488130569458},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2492821216583252},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e24081057","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24081057","pdf_url":"https://www.mdpi.com/1099-4300/24/8/1057/pdf?version=1661388379","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},{"id":"pmid:36010721","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/36010721","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":"Entropy (Basel, Switzerland)","raw_type":"Journal Article"},{"id":"pmh:oai:pubmedcentral.nih.gov:9407201","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/9407201","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:cf1f5fdfd91f4e7e9a6ba7041fc961a9","is_oa":true,"landing_page_url":"https://doaj.org/article/cf1f5fdfd91f4e7e9a6ba7041fc961a9","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":"Entropy, Vol 24, Iss 8, p 1057 (2022)","raw_type":"article"},{"id":"pmh:oai:researchspace.auckland.ac.nz:2292/63378","is_oa":true,"landing_page_url":"https://hdl.handle.net/2292/63378","pdf_url":null,"source":{"id":"https://openalex.org/S7407055463","display_name":"ResearchSpace (University of Auckland)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I154130895","host_organization_name":"University of Auckland","host_organization_lineage":["https://openalex.org/I154130895"],"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":null,"raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.3390/e24081057","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e24081057","pdf_url":"https://www.mdpi.com/1099-4300/24/8/1057/pdf?version=1661388379","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6899999976158142,"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education"}],"awards":[{"id":"https://openalex.org/G3134238699","display_name":null,"funder_award_id":"PN-III-P4-PCE-2021-0154","funder_id":"https://openalex.org/F4320318622","funder_display_name":"Ministerul Cercet\u0103rii, Inov\u0103rii \u015fi Digitaliz\u0103rii"}],"funders":[{"id":"https://openalex.org/F4320318622","display_name":"Ministerul Cercet\u0103rii, Inov\u0103rii \u015fi Digitaliz\u0103rii","ror":null},{"id":"https://openalex.org/F4320323471","display_name":"Universit\u00e9 de Fribourg","ror":"https://ror.org/022fs9h90"},{"id":"https://openalex.org/F4320323983","display_name":"Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii","ror":"https://ror.org/01q7jq182"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4289132425.pdf","grobid_xml":"https://content.openalex.org/works/W4289132425.grobid-xml"},"referenced_works_count":44,"referenced_works":["https://openalex.org/W282757658","https://openalex.org/W766589415","https://openalex.org/W2042096957","https://openalex.org/W2053061982","https://openalex.org/W2056758595","https://openalex.org/W2061615939","https://openalex.org/W2062799148","https://openalex.org/W2072356364","https://openalex.org/W2081411525","https://openalex.org/W2086962710","https://openalex.org/W2096863518","https://openalex.org/W2103972604","https://openalex.org/W2114122776","https://openalex.org/W2118990207","https://openalex.org/W2122119900","https://openalex.org/W2128659236","https://openalex.org/W2138144286","https://openalex.org/W2145962650","https://openalex.org/W2146130798","https://openalex.org/W2147104514","https://openalex.org/W2148102575","https://openalex.org/W2151188419","https://openalex.org/W2152061189","https://openalex.org/W2168175751","https://openalex.org/W2183805236","https://openalex.org/W2316934317","https://openalex.org/W2466801766","https://openalex.org/W2530163446","https://openalex.org/W2552480641","https://openalex.org/W2613687551","https://openalex.org/W2740917292","https://openalex.org/W2775056555","https://openalex.org/W2798056406","https://openalex.org/W2800431972","https://openalex.org/W2952071070","https://openalex.org/W2964044134","https://openalex.org/W2969874346","https://openalex.org/W2985213793","https://openalex.org/W3003365835","https://openalex.org/W3006713198","https://openalex.org/W3101447531","https://openalex.org/W3113847083","https://openalex.org/W4226184120","https://openalex.org/W6682042988"],"related_works":["https://openalex.org/W4297754234","https://openalex.org/W2890686416","https://openalex.org/W2157785665","https://openalex.org/W2074079618","https://openalex.org/W2786769798","https://openalex.org/W3113847083","https://openalex.org/W3121341047","https://openalex.org/W2159586267","https://openalex.org/W3134724422","https://openalex.org/W4310609493"],"abstract_inverted_index":{"The":[0,74,93,155],"problem":[1],"addressed":[2],"by":[3,88],"dictionary":[4,26],"learning":[5,98],"(DL)":[6],"is":[7,56,99],"the":[8,25,28,34,44,71,80,84,104,107,111,114,117,125,134,167,172,175,186,190,197],"representation":[9,85],"of":[10,17,19,46,58,76,83,106,113,116,127,148,169,174,177],"data":[11,153,157],"as":[12],"a":[13,20,52,66,145],"sparse":[14,29],"linear":[15],"combination":[16],"columns":[18],"matrix":[21],"called":[22],"dictionary.":[23],"Both":[24],"and":[27,65,79,171],"representations":[30],"are":[31,86,159,179,194],"learned":[32],"from":[33],"data.":[35],"We":[36,50,119],"show":[37],"how":[38,133],"DL":[39],"can":[40,137],"be":[41,138],"employed":[42],"in":[43,97,140,188],"imputation":[45],"multivariate":[47],"time":[48,63,72,129],"series.":[49,73,130],"use":[51],"structured":[53],"dictionary,":[54],"which":[55,189],"comprised":[57],"one":[59],"block":[60,68,78],"for":[61,69,124],"each":[62,77],"series":[64],"common":[67],"all":[70],"size":[75],"sparsity":[81],"level":[82],"selected":[87],"using":[89],"information":[90],"theoretic":[91],"criteria.":[92],"objective":[94],"function":[95],"used":[96,139],"designed":[100],"to":[101,162,184,196],"minimize":[102],"either":[103],"sum":[105,112],"squared":[108],"errors":[109],"or":[110],"magnitudes":[115],"errors.":[118],"propose":[120],"dimensionality":[121],"reduction":[122],"techniques":[123],"case":[126],"high-dimensional":[128],"For":[131],"demonstrating":[132],"new":[135],"algorithms":[136],"practical":[141],"applications,":[142],"we":[143],"conduct":[144],"large":[146],"set":[147],"experiments":[149],"on":[150],"five":[151],"real-life":[152],"sets.":[154],"missing":[156],"(MD)":[158],"simulated":[160],"according":[161],"various":[163],"scenarios":[164],"where":[165],"both":[166],"percentage":[168],"MD":[170,178],"length":[173],"sequences":[176],"considered.":[180],"This":[181],"allows":[182],"us":[183],"identify":[185],"situations":[187],"novel":[191],"DL-based":[192],"methods":[193],"superior":[195],"existing":[198],"methods.":[199]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}