{"id":"https://openalex.org/W3189899116","doi":"https://doi.org/10.3390/e23081012","title":"A Factor Analysis Perspective on Linear Regression in the \u2018More Predictors than Samples\u2019 Case","display_name":"A Factor Analysis Perspective on Linear Regression in the \u2018More Predictors than Samples\u2019 Case","publication_year":2021,"publication_date":"2021-08-03","ids":{"openalex":"https://openalex.org/W3189899116","doi":"https://doi.org/10.3390/e23081012","mag":"3189899116","pmid":"https://pubmed.ncbi.nlm.nih.gov/34441152"},"language":"en","primary_location":{"id":"doi:10.3390/e23081012","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23081012","pdf_url":"https://www.mdpi.com/1099-4300/23/8/1012/pdf?version=1628485192","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/1099-4300/23/8/1012/pdf?version=1628485192","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085225238","display_name":"Sebastian Ciobanu","orcid":"https://orcid.org/0000-0003-1873-3563"},"institutions":[{"id":"https://openalex.org/I138164181","display_name":"Alexandru Ioan Cuza University","ror":"https://ror.org/022kvet57","country_code":"RO","type":"education","lineage":["https://openalex.org/I138164181"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Sebastian Ciobanu","raw_affiliation_strings":["Faculty of Computer Science, Alexandru Ioan Cuza University of Ia\u015fi, 700506 Ia\u015fi, Romania"],"affiliations":[{"raw_affiliation_string":"Faculty of Computer Science, Alexandru Ioan Cuza University of Ia\u015fi, 700506 Ia\u015fi, Romania","institution_ids":["https://openalex.org/I138164181"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030108094","display_name":"Liviu Ciortuz","orcid":null},"institutions":[{"id":"https://openalex.org/I138164181","display_name":"Alexandru Ioan Cuza University","ror":"https://ror.org/022kvet57","country_code":"RO","type":"education","lineage":["https://openalex.org/I138164181"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Liviu Ciortuz","raw_affiliation_strings":["Faculty of Computer Science, Alexandru Ioan Cuza University of Ia\u015fi, 700506 Ia\u015fi, Romania"],"affiliations":[{"raw_affiliation_string":"Faculty of Computer Science, Alexandru Ioan Cuza University of Ia\u015fi, 700506 Ia\u015fi, Romania","institution_ids":["https://openalex.org/I138164181"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030108094","https://openalex.org/A5085225238"],"corresponding_institution_ids":["https://openalex.org/I138164181"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.14,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.55164354,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"23","issue":"8","first_page":"1012","last_page":"1012"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.996999979019165,"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"}},"topics":[{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.996999979019165,"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"}},{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9945999979972839,"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/mathematics","display_name":"Mathematics","score":0.5505021214485168},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.5353881120681763},{"id":"https://openalex.org/keywords/kullback\u2013leibler-divergence","display_name":"Kullback\u2013Leibler divergence","score":0.4821576476097107},{"id":"https://openalex.org/keywords/linear-regression","display_name":"Linear regression","score":0.44814348220825195},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.43499305844306946},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4326431453227997},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.4152193069458008},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3826570212841034},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36040616035461426},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2594909071922302}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5505021214485168},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.5353881120681763},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.4821576476097107},{"id":"https://openalex.org/C48921125","wikidata":"https://www.wikidata.org/wiki/Q10861030","display_name":"Linear regression","level":2,"score":0.44814348220825195},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.43499305844306946},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4326431453227997},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.4152193069458008},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3826570212841034},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36040616035461426},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2594909071922302}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e23081012","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23081012","pdf_url":"https://www.mdpi.com/1099-4300/23/8/1012/pdf?version=1628485192","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:34441152","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34441152","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:doaj.org/article:4c2dd4b88eb24d05a1caad08f4ab2725","is_oa":true,"landing_page_url":"https://doaj.org/article/4c2dd4b88eb24d05a1caad08f4ab2725","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 23, Iss 8, p 1012 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/23/8/1012/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e23081012","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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; Volume 23; Issue 8; Pages: 1012","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:8394575","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8394575","pdf_url":null,"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"}],"best_oa_location":{"id":"doi:10.3390/e23081012","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23081012","pdf_url":"https://www.mdpi.com/1099-4300/23/8/1012/pdf?version=1628485192","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3189899116.pdf","grobid_xml":"https://content.openalex.org/works/W3189899116.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1662191912","https://openalex.org/W1822348759","https://openalex.org/W2049633694","https://openalex.org/W2089174218","https://openalex.org/W2108193616","https://openalex.org/W2115098571","https://openalex.org/W2125027820","https://openalex.org/W2169779569","https://openalex.org/W2542459869","https://openalex.org/W2794523151","https://openalex.org/W4298826872","https://openalex.org/W6676390387"],"related_works":["https://openalex.org/W1995622179","https://openalex.org/W1484111231","https://openalex.org/W1552543208","https://openalex.org/W2074396517","https://openalex.org/W2166963679","https://openalex.org/W2187269125","https://openalex.org/W1641615907","https://openalex.org/W3089231081","https://openalex.org/W2093956241","https://openalex.org/W2354420595"],"abstract_inverted_index":{"Linear":[0],"regression":[1,13,190],"(LR)":[2],"is":[3,43,59,75,97,142,163,217],"a":[4,12,36,55,90,103,109,132,207,224,227,235],"core":[5],"model":[6,19,93],"in":[7,99,126],"supervised":[8,157],"machine":[9,91],"learning":[10,92,101],"performing":[11,102],"task.":[14],"One":[15],"can":[16,130],"fit":[17,131],"this":[18,73,95,127,152],"using":[20,76],"either":[21,206],"an":[22,26,186,211],"analytic/closed-form":[23],"formula":[24,34],"or":[25,80,107,210,231],"iterative":[27],"algorithm.":[28,214],"Fitting":[29],"it":[30,129,177],"via":[31],"the":[32,39,46,51,77,81,137,140,145,156,198,232],"analytic":[33],"becomes":[35],"problem":[37],"when":[38,62,154],"number":[40,47,146],"of":[41,48,139,147,159,197,234],"predictors":[42,65],"greater":[44,143],"than":[45,66,144],"samples":[49],"because":[50],"closed-form":[52,208],"solution":[53,87,209],"contains":[54],"matrix":[56],"inverse":[57,79],"that":[58],"not":[60],"defined":[61],"having":[63],"more":[64],"samples.":[67],"The":[68,118,202,215],"standard":[69],"approach":[70],"to":[71,165,178,188,219],"solve":[72],"issue":[74],"Moore-Penrose":[78],"L2":[82],"regularization.":[83],"We":[84,168,184],"propose":[85],"another":[86],"starting":[88],"from":[89],"that,":[94],"time,":[96],"used":[98],"unsupervised":[100],"dimensionality":[104,138],"reduction":[105],"task":[106,121],"just":[108],"density":[110,119],"estimation":[111,120],"one-factor":[112],"analysis":[113,200],"(FA)-with":[114],"one-dimensional":[115],"latent":[116],"space.":[117],"represents":[122],"our":[123],"focus":[124],"since,":[125],"case,":[128],"Gaussian":[133],"distribution":[134],"even":[135],"if":[136],"data":[141],"samples;":[148],"hence,":[149],"we":[150],"obtain":[151],"advantage":[153],"creating":[155],"counterpart":[158,173],"factor":[160,199],"analysis,":[161],"which":[162],"linked":[164,218],"linear":[166,189],"regression.":[167],"also":[169],"create":[170,192],"its":[171],"semisupervised":[172],"and":[174,191],"then":[175],"extend":[176],"be":[179],"usable":[180],"with":[181],"missing":[182],"data.":[183],"prove":[185],"equivalence":[187],"experiments":[193],"for":[194],"each":[195],"extension":[196],"model.":[201],"resulting":[203],"algorithms":[204],"are":[205],"expectation-maximization":[212],"(EM)":[213],"latter":[216],"information":[220],"theory":[221],"by":[222],"optimizing":[223],"function":[225],"containing":[226],"Kullback-Leibler":[228],"(KL)":[229],"divergence":[230],"entropy":[233],"random":[236],"variable.":[237]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}