{"id":"https://openalex.org/W4401906324","doi":"https://doi.org/10.1109/access.2024.3450808","title":"Arborescent Orthogonal Least Squares Regression for NARMAX-Based Black-Box Fitting","display_name":"Arborescent Orthogonal Least Squares Regression for NARMAX-Based Black-Box Fitting","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4401906324","doi":"https://doi.org/10.1109/access.2024.3450808"},"language":"en","primary_location":{"id":"doi:10.1109/access.2024.3450808","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1109/access.2024.3450808","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://dx.doi.org/10.1109/access.2024.3450808","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5106754857","display_name":"St\u00e9phane J. P. S. Thunus","orcid":"https://orcid.org/0009-0009-2494-0893"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"St\u00e9phane J. P. S. Thunus","raw_affiliation_strings":["Audio Communication Group, Technische Universität Berlin, Berlin, Germany"],"raw_orcid":"https://orcid.org/0009-0009-2494-0893","affiliations":[{"raw_affiliation_string":"Audio Communication Group, Technische Universität Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034175373","display_name":"Julian D. Parker","orcid":null},"institutions":[{"id":"https://openalex.org/I4210095073","display_name":"Sustainability Institute","ror":"https://ror.org/00q3tc787","country_code":"ZA","type":"nonprofit","lineage":["https://openalex.org/I4210095073"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Julian D. Parker","raw_affiliation_strings":["Stability AI, London, U.K"],"raw_orcid":"https://orcid.org/0009-0003-7261-4271","affiliations":[{"raw_affiliation_string":"Stability AI, London, U.K","institution_ids":["https://openalex.org/I4210095073"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101993170","display_name":"Stefan Weinzierl","orcid":"https://orcid.org/0000-0002-9427-9932"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Stefan Weinzierl","raw_affiliation_strings":["Audio Communication Group, Technische Universität Berlin, Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0002-9427-9932","affiliations":[{"raw_affiliation_string":"Audio Communication Group, Technische Universität Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.1622,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.4266455,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"12","issue":null,"first_page":"155578","last_page":"155597"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9988999962806702,"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"}},"topics":[{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9988999962806702,"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9988999962806702,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9983000159263611,"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/total-least-squares","display_name":"Total least squares","score":0.6134923696517944},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.5292182564735413},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.46331334114074707},{"id":"https://openalex.org/keywords/generalized-least-squares","display_name":"Generalized least squares","score":0.4480642080307007},{"id":"https://openalex.org/keywords/regression-analysis","display_name":"Regression analysis","score":0.44401827454566956},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4295156002044678},{"id":"https://openalex.org/keywords/non-linear-least-squares","display_name":"Non-linear least squares","score":0.42034676671028137},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.4050379991531372},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4032893776893616},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3751145601272583},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.328579306602478},{"id":"https://openalex.org/keywords/explained-sum-of-squares","display_name":"Explained sum of squares","score":0.20809122920036316}],"concepts":[{"id":"https://openalex.org/C169241690","wikidata":"https://www.wikidata.org/wiki/Q7828122","display_name":"Total least squares","level":3,"score":0.6134923696517944},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.5292182564735413},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.46331334114074707},{"id":"https://openalex.org/C188649462","wikidata":"https://www.wikidata.org/wiki/Q2246261","display_name":"Generalized least squares","level":3,"score":0.4480642080307007},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.44401827454566956},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4295156002044678},{"id":"https://openalex.org/C45923927","wikidata":"https://www.wikidata.org/wiki/Q3319230","display_name":"Non-linear least squares","level":3,"score":0.42034676671028137},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4050379991531372},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4032893776893616},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3751145601272583},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.328579306602478},{"id":"https://openalex.org/C49847556","wikidata":"https://www.wikidata.org/wiki/Q3964631","display_name":"Explained sum of squares","level":2,"score":0.20809122920036316},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2024.3450808","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1109/access.2024.3450808","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:5306716f7896491eb452aaf2a9d20d33","is_oa":true,"landing_page_url":"https://doaj.org/article/5306716f7896491eb452aaf2a9d20d33","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":"IEEE Access, Vol 12, Pp 155578-155597 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2024.3450808","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1109/access.2024.3450808","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320324094","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1173784407","https://openalex.org/W1586945187","https://openalex.org/W1977458753","https://openalex.org/W1995614965","https://openalex.org/W2044235108","https://openalex.org/W2092587625","https://openalex.org/W2098955183","https://openalex.org/W2167898623","https://openalex.org/W2203914624","https://openalex.org/W2297177635","https://openalex.org/W2526589980","https://openalex.org/W2594379484","https://openalex.org/W2730108975","https://openalex.org/W2755371726","https://openalex.org/W2782893292","https://openalex.org/W2796292185","https://openalex.org/W2807052432","https://openalex.org/W2886985401","https://openalex.org/W2903797737","https://openalex.org/W2908403814","https://openalex.org/W2919157684","https://openalex.org/W2963813038","https://openalex.org/W2999833139","https://openalex.org/W3046390683","https://openalex.org/W3113231247","https://openalex.org/W3119558406","https://openalex.org/W3154678491","https://openalex.org/W3169901447","https://openalex.org/W3201558289","https://openalex.org/W4210963570","https://openalex.org/W4281630791","https://openalex.org/W4285007414","https://openalex.org/W4285110051","https://openalex.org/W4292072112","https://openalex.org/W4313307303","https://openalex.org/W4318147987","https://openalex.org/W4320026610","https://openalex.org/W4360987259","https://openalex.org/W4362699560","https://openalex.org/W4379116962","https://openalex.org/W4386245692","https://openalex.org/W4388806910","https://openalex.org/W4388806995","https://openalex.org/W4390493415"],"related_works":["https://openalex.org/W2030255580","https://openalex.org/W4380487384","https://openalex.org/W2034819163","https://openalex.org/W2123913166","https://openalex.org/W3150673294","https://openalex.org/W1959514624","https://openalex.org/W2394396033","https://openalex.org/W2125225254","https://openalex.org/W2374560502","https://openalex.org/W2368345218"],"abstract_inverted_index":{"This":[0,75],"paper":[1],"proposes":[2],"a":[3,59,77,150,168,197],"linear":[4,211],"algebra-based":[5],"supervised":[6],"machine":[7],"learning":[8],"algorithm":[9,100],"for":[10,171,209],"the":[11,25,47,67,72,82,93,103,120,144,172,186,201,218],"symbolic":[12,39],"representation":[13],"of":[14,28,62,85,188,200],"arbitrarily":[15],"non-linear":[16,56],"and":[17,50,55,65,114,130,140,162,205],"recursive":[18,117],"systems.":[19],"It":[20],"introduces":[21],"multiple":[22],"extensions":[23],"to":[24,70,87,105,128,133],"algorithmic":[26],"class":[27],"\u201cForward":[29],"Orthogonal":[30],"Least":[31],"Squares":[32],"Regressions\u201d":[33],"(FOrLSR),":[34],"which":[35,214],"performs":[36,52],"dictionary-based":[37],"sparse":[38,155],"regressions.":[40],"The":[41,97,176,203],"regression,":[42],"being":[43],"only":[44,195],"provided":[45],"with":[46],"system\u2019s":[48],"input":[49],"output,":[51],"variable":[53],"combinations":[54],"transformations":[57],"from":[58,123],"given":[60],"dictionary":[61,145],"analytic":[63],"expressions":[64],"selects":[66],"optimal":[68,191],"ones":[69],"represent":[71],"unknown":[73],"system.":[74],"yields":[76],"\u201csymbolic\u201d":[78],"system":[79,192],"representation,":[80,193],"having":[81],"minimum":[83],"number":[84],"terms":[86],"enforce":[88],"sparsity":[89,216],"($L_{0}$-norm),":[90],"while":[91,166,194],"keeping":[92],"highest":[94],"possible":[95],"precision.":[96],"first":[98],"proposed":[99,158,177],"(rFOrLSR)":[101],"restructures":[102],"FOrLSR":[104],"be":[106,134],"in":[107,125,217],"matrix":[108],"form":[109],"(for":[110],"large":[111,181],"scale":[112],"GPU":[113],"BLAS-like":[115],"optimizations),":[116],"(to":[118,136],"reduce":[119],"computational":[121],"complexity":[122],"quadratic":[124],"model":[126,174],"length":[127],"linear)":[129],"allows":[131],"regressors":[132],"imposed":[135],"include":[137],"user":[138],"expertise":[139],"perform":[141],"tree-searches).":[142],"Furthermore,":[143],"search":[146],"is":[147],"restructured":[148],"into":[149],"breadth-first":[151],"arborescence":[152,178,206],"traversal":[153],"kept":[154],"by":[156],"five":[157],"theorems,":[159],"four":[160],"corollaries":[161],"one":[163],"pruning":[164],"mechanism,":[165],"adding":[167],"validation":[169],"procedure":[170],"final":[173],"selection.":[175],"(AOrLSR)":[179],"scans":[180],"search-space":[182],"segments,":[183],"significantly":[184],"increasing":[185],"probability":[187],"finding":[189],"an":[190],"computing":[196],"marginal":[198],"fraction":[199],"search-space.":[202],"regression":[204],"are":[207],"solvers":[208],"arbitrarily-determined":[210],"equation":[212],"systems":[213],"maximize":[215],"solution":[219],"vectors.":[220]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}