{"id":"https://openalex.org/W4391133614","doi":"https://doi.org/10.3390/e26010092","title":"Robust Multi-Dimensional Time Series Forecasting","display_name":"Robust Multi-Dimensional Time Series Forecasting","publication_year":2024,"publication_date":"2024-01-22","ids":{"openalex":"https://openalex.org/W4391133614","doi":"https://doi.org/10.3390/e26010092","pmid":"https://pubmed.ncbi.nlm.nih.gov/38275500"},"language":"en","primary_location":{"id":"doi:10.3390/e26010092","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26010092","pdf_url":"https://www.mdpi.com/1099-4300/26/1/92/pdf?version=1706005710","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/1099-4300/26/1/92/pdf?version=1706005710","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081367857","display_name":"Chen Shen","orcid":"https://orcid.org/0009-0001-4765-7531"},"institutions":[{"id":"https://openalex.org/I178232147","display_name":"Guizhou University","ror":"https://ror.org/02wmsc916","country_code":"CN","type":"education","lineage":["https://openalex.org/I178232147"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen Shen","raw_affiliation_strings":["State Key Laboratory of Public Big Data, College of Computer Science and Technology, Guizhou University, Guiyang 550025, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Public Big Data, College of Computer Science and Technology, Guizhou University, Guiyang 550025, China","institution_ids":["https://openalex.org/I178232147"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100342968","display_name":"Yong He","orcid":"https://orcid.org/0000-0001-6752-1757"},"institutions":[{"id":"https://openalex.org/I178232147","display_name":"Guizhou University","ror":"https://ror.org/02wmsc916","country_code":"CN","type":"education","lineage":["https://openalex.org/I178232147"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yong He","raw_affiliation_strings":["State Key Laboratory of Public Big Data, College of Computer Science and Technology, Guizhou University, Guiyang 550025, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Public Big Data, College of Computer Science and Technology, Guizhou University, Guiyang 550025, China","institution_ids":["https://openalex.org/I178232147"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100662807","display_name":"Jing Qin","orcid":"https://orcid.org/0000-0002-7059-0929"},"institutions":[{"id":"https://openalex.org/I178232147","display_name":"Guizhou University","ror":"https://ror.org/02wmsc916","country_code":"CN","type":"education","lineage":["https://openalex.org/I178232147"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jin Qin","raw_affiliation_strings":["State Key Laboratory of Public Big Data, College of Computer Science and Technology, Guizhou University, Guiyang 550025, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Public Big Data, College of Computer Science and Technology, Guizhou University, Guiyang 550025, China","institution_ids":["https://openalex.org/I178232147"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100342968"],"corresponding_institution_ids":["https://openalex.org/I178232147"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.7883,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.83774484,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"26","issue":"1","first_page":"92","last_page":"92"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12205","display_name":"Time Series Analysis and Forecasting","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T12205","display_name":"Time Series Analysis and Forecasting","score":0.9994999766349792,"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/T11052","display_name":"Energy Load and Power Forecasting","score":0.991599977016449,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T11344","display_name":"Traffic Prediction and Management Techniques","score":0.9909999966621399,"subfield":{"id":"https://openalex.org/subfields/2215","display_name":"Building and Construction"},"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/computer-science","display_name":"Computer science","score":0.7338990569114685},{"id":"https://openalex.org/keywords/non-negative-matrix-factorization","display_name":"Non-negative matrix factorization","score":0.6862517595291138},{"id":"https://openalex.org/keywords/outlier","display_name":"Outlier","score":0.6465693712234497},{"id":"https://openalex.org/keywords/missing-data","display_name":"Missing data","score":0.611878514289856},{"id":"https://openalex.org/keywords/overfitting","display_name":"Overfitting","score":0.5953739881515503},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5601283311843872},{"id":"https://openalex.org/keywords/time-series","display_name":"Time series","score":0.5516369342803955},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.5212053060531616},{"id":"https://openalex.org/keywords/autoregressive-integrated-moving-average","display_name":"Autoregressive integrated moving average","score":0.5105181932449341},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5001447200775146},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.48889604210853577},{"id":"https://openalex.org/keywords/matrix-decomposition","display_name":"Matrix decomposition","score":0.48500916361808777},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.43855366110801697},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3391685485839844},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.2821289896965027},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.14816030859947205}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7338990569114685},{"id":"https://openalex.org/C152671427","wikidata":"https://www.wikidata.org/wiki/Q10843505","display_name":"Non-negative matrix factorization","level":4,"score":0.6862517595291138},{"id":"https://openalex.org/C79337645","wikidata":"https://www.wikidata.org/wiki/Q779824","display_name":"Outlier","level":2,"score":0.6465693712234497},{"id":"https://openalex.org/C9357733","wikidata":"https://www.wikidata.org/wiki/Q6878417","display_name":"Missing data","level":2,"score":0.611878514289856},{"id":"https://openalex.org/C22019652","wikidata":"https://www.wikidata.org/wiki/Q331309","display_name":"Overfitting","level":3,"score":0.5953739881515503},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5601283311843872},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.5516369342803955},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.5212053060531616},{"id":"https://openalex.org/C24338571","wikidata":"https://www.wikidata.org/wiki/Q2566298","display_name":"Autoregressive integrated moving average","level":3,"score":0.5105181932449341},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5001447200775146},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.48889604210853577},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.48500916361808777},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.43855366110801697},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3391685485839844},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.2821289896965027},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.14816030859947205},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e26010092","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26010092","pdf_url":"https://www.mdpi.com/1099-4300/26/1/92/pdf?version=1706005710","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:38275500","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/38275500","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":null},{"id":"pmh:oai:pubmedcentral.nih.gov:11154447","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/11154447","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC11154447/pdf/entropy-26-00092.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","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":"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:17cf44fa0d4941bab9b8eb555f64073c","is_oa":true,"landing_page_url":"https://doaj.org/article/17cf44fa0d4941bab9b8eb555f64073c","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 26, Iss 1, p 92 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e26010092","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e26010092","pdf_url":"https://www.mdpi.com/1099-4300/26/1/92/pdf?version=1706005710","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4391133614.pdf"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W45565856","https://openalex.org/W901288969","https://openalex.org/W1996452481","https://openalex.org/W2002469984","https://openalex.org/W2131830135","https://openalex.org/W2144359569","https://openalex.org/W2149409084","https://openalex.org/W2159586267","https://openalex.org/W2171837816","https://openalex.org/W2186878252","https://openalex.org/W2529086294","https://openalex.org/W2541338223","https://openalex.org/W2552480641","https://openalex.org/W2775387120","https://openalex.org/W2889443148","https://openalex.org/W2889512547","https://openalex.org/W2892452712","https://openalex.org/W2917733937","https://openalex.org/W2921378610","https://openalex.org/W2943921667","https://openalex.org/W2944772978","https://openalex.org/W2964010366","https://openalex.org/W2980537499","https://openalex.org/W2992324966","https://openalex.org/W3002604753","https://openalex.org/W3022643593","https://openalex.org/W3036366020","https://openalex.org/W3132782787","https://openalex.org/W3132963454","https://openalex.org/W3157233913","https://openalex.org/W3167202680","https://openalex.org/W3204962186","https://openalex.org/W3209621300","https://openalex.org/W4220735084","https://openalex.org/W4292671038","https://openalex.org/W4378697508","https://openalex.org/W4388140199","https://openalex.org/W6601848474","https://openalex.org/W6638285678","https://openalex.org/W6680012447","https://openalex.org/W6728665592","https://openalex.org/W6768842840"],"related_works":["https://openalex.org/W2127243424","https://openalex.org/W4390394189","https://openalex.org/W2037504162","https://openalex.org/W2792706544","https://openalex.org/W1568451138","https://openalex.org/W2539013788","https://openalex.org/W2156699640","https://openalex.org/W2045265907","https://openalex.org/W2972997031","https://openalex.org/W2075222291"],"abstract_inverted_index":{"Large-scale":[0],"and":[1,16,26,134,196],"high-dimensional":[2],"time":[3,61,88,109,164,172],"series":[4,62,89],"data":[5,21,41],"are":[6],"widely":[7],"generated":[8],"in":[9,128],"modern":[10],"applications":[11],"such":[12,20,38],"as":[13,166,168],"intelligent":[14],"transportation":[15],"environmental":[17],"monitoring.":[18],"However,":[19],"contains":[22],"much":[23],"noise,":[24],"outliers,":[25],"missing":[27,152],"values":[28],"due":[29],"to":[30,52,57,138,143,170],"interference":[31],"during":[32],"measurement":[33],"or":[34,67],"transmission.":[35],"Directly":[36],"forecasting":[37,90,104],"types":[39],"of":[40,124,147],"(i.e.,":[42],"anomalous":[43,64,96],"data)":[44],"can":[45,93],"be":[46],"extremely":[47],"challenging.":[48],"The":[49],"traditional":[50],"method":[51],"deal":[53],"with":[54,63,121,174],"anomalies":[55],"is":[56],"cut":[58],"out":[59],"the":[60,69,78,98,113,122,125,145,162,171,180,183],"value":[65],"entries":[66],"replace":[68],"data.":[70,80],"Both":[71],"methods":[72],"may":[73],"lose":[74],"important":[75],"knowledge":[76],"from":[77],"original":[79],"In":[81,141],"this":[82],"paper,":[83],"we":[84,154,178],"propose":[85,155],"a":[86,156],"multidimensional":[87],"framework":[91],"that":[92,160,191],"better":[94,194,197],"handle":[95],"values:":[97],"robust":[99],"temporal":[100],"nonnegative":[101,117],"matrix":[102,118],"factorization":[103,119],"model":[105,148,181],"(RTNMFFM)":[106],"for":[107],"multi-dimensional":[108],"series.":[110],"RTNMFFM":[111,192],"integrates":[112],"autoregressive":[114],"regularizer":[115],"into":[116],"(NMF)":[120],"application":[123],"L2,1":[126],"norm":[127],"NMF.":[129],"This":[130],"approach":[131],"improves":[132],"robustness":[133,195],"alleviates":[135],"overfitting":[136],"compared":[137],"standard":[139],"methods.":[140],"addition,":[142],"improve":[144],"accuracy":[146],"forecasts":[149],"on":[150],"severely":[151],"data,":[153],"periodic":[157],"smoothing":[158],"penalty":[159],"keeps":[161],"sparse":[163],"slices":[165],"close":[167],"possible":[169],"slice":[173],"high":[175],"confidence.":[176],"Finally,":[177],"train":[179],"using":[182],"alternating":[184],"gradient":[185],"descent":[186],"algorithm.":[187],"Numerous":[188],"experiments":[189],"demonstrate":[190],"provides":[193],"prediction":[198],"accuracy.":[199]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
