{"id":"https://openalex.org/W2076918381","doi":"https://doi.org/10.1137/050646457","title":"Towards a Black Box Algorithm for Nonlinear Function Approximation over High\u2010Dimensional Domains","display_name":"Towards a Black Box Algorithm for Nonlinear Function Approximation over High\u2010Dimensional Domains","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2076918381","doi":"https://doi.org/10.1137/050646457","mag":"2076918381"},"language":"en","primary_location":{"id":"doi:10.1137/050646457","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050646457","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","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/A5009102574","display_name":"Arta A. Jamshidi","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Arta A. Jamshidi","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5061567476","display_name":"Michael Kirby","orcid":"https://orcid.org/0000-0001-9802-9263"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael J. Kirby","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5009102574"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8774,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.87813113,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"29","issue":"3","first_page":"941","last_page":"963"},"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9498000144958496,"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/T12205","display_name":"Time Series Analysis and Forecasting","score":0.9307000041007996,"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/algorithm","display_name":"Algorithm","score":0.7168670892715454},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.620049774646759},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.531511664390564},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5210877656936646},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.48349621891975403},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.4776519536972046},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.4756835699081421},{"id":"https://openalex.org/keywords/perceptron","display_name":"Perceptron","score":0.4406304955482483},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.42989209294319153},{"id":"https://openalex.org/keywords/radial-basis-function","display_name":"Radial basis function","score":0.42427244782447815},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3814832866191864},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3755022883415222},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3729932904243469},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.21934270858764648},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15298444032669067}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7168670892715454},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.620049774646759},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.531511664390564},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5210877656936646},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.48349621891975403},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.4776519536972046},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4756835699081421},{"id":"https://openalex.org/C60908668","wikidata":"https://www.wikidata.org/wiki/Q690207","display_name":"Perceptron","level":3,"score":0.4406304955482483},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.42989209294319153},{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.42427244782447815},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3814832866191864},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3755022883415222},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3729932904243469},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.21934270858764648},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15298444032669067},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/050646457","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050646457","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Decent work and economic growth","id":"https://metadata.un.org/sdg/8","score":0.49000000953674316}],"awards":[],"funders":[{"id":"https://openalex.org/F4320315254","display_name":"Innovative Research Group Project of the National Natural Science Foundation of China","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W94523489","https://openalex.org/W101956566","https://openalex.org/W150219436","https://openalex.org/W1525133979","https://openalex.org/W1532480015","https://openalex.org/W1535810436","https://openalex.org/W1554663460","https://openalex.org/W1579878850","https://openalex.org/W1965198822","https://openalex.org/W1968747946","https://openalex.org/W1981025032","https://openalex.org/W1984049995","https://openalex.org/W2023183448","https://openalex.org/W2093248416","https://openalex.org/W2093399550","https://openalex.org/W2096278047","https://openalex.org/W2099244771","https://openalex.org/W2109779438","https://openalex.org/W2111051539","https://openalex.org/W2113825526","https://openalex.org/W2114766824","https://openalex.org/W2114865067","https://openalex.org/W2122146783","https://openalex.org/W2124776405","https://openalex.org/W2128033389","https://openalex.org/W2133740040","https://openalex.org/W2140971281","https://openalex.org/W2141652754","https://openalex.org/W2142635246","https://openalex.org/W2158071659","https://openalex.org/W2171277043","https://openalex.org/W2254441538","https://openalex.org/W2330755614"],"related_works":["https://openalex.org/W2006953814","https://openalex.org/W2542637001","https://openalex.org/W1972782945","https://openalex.org/W2096715552","https://openalex.org/W3212981098","https://openalex.org/W4221090543","https://openalex.org/W2130622405","https://openalex.org/W2374946871","https://openalex.org/W2109887391","https://openalex.org/W1598419248"],"abstract_inverted_index":{"We":[0,110],"propose":[1],"an":[2,101],"algorithm":[3,13,130],"for":[4,78,100,149],"constructing":[5],"nonlinear":[6,79],"models":[7],"from":[8],"high\u2010dimensional":[9],"scattered":[10,83],"data.":[11],"The":[12,27,129],"progresses":[14],"iteratively,":[15],"adding":[16],"a":[17,35,58],"new":[18],"function":[19,51,80,150],"at":[20],"each":[21,47],"step":[22,48],"to":[23,54,63],"refine":[24],"the":[25,30,49,65,68,71,85,94,108,112,124,134],"model.":[26,73],"placement":[28],"of":[29,70,96,126,136],"functions":[31,98,139],"is":[32,52,104,131],"driven":[33],"by":[34,107],"statistical":[36],"hypothesis":[37],"test":[38],"that":[39],"reveals":[40],"geometric":[41],"structure":[42],"when":[43],"it":[44],"fails.":[45],"At":[46],"added":[50],"fit":[53,103],"data":[55,120],"contained":[56],"in":[57,133,141],"spatio\u2010temporally":[59],"defined":[60],"local":[61,72],"region":[62],"determine":[64],"parameters,":[66],"particularly":[67],"scale":[69],"Unlike":[74],"currently":[75],"available":[76],"techniques":[77],"fitting":[81],"over":[82],"data,":[84],"proposed":[86],"method":[87],"requires":[88],"no":[89],"ad":[90],"hoc":[91],"parameters.":[92],"Thus,":[93],"number":[95],"basis":[97,138],"required":[99],"accurate":[102],"determined":[105],"automatically":[106],"algorithm.":[109],"illustrate":[111],"approach":[113],"using":[114],"several":[115],"illustrative":[116],"problems":[117],"including":[118],"modeling":[119],"on":[121],"manifolds":[122],"and":[123],"prediction":[125],"financial":[127],"time\u2010series.":[128],"presented":[132],"context":[135],"radial":[137],"but":[140],"principle":[142],"can":[143],"be":[144],"employed":[145],"with":[146],"other":[147],"methods":[148],"approximation,":[151],"such":[152],"as":[153],"multilayer":[154],"perceptrons.":[155]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
