{"id":"https://openalex.org/W2906811498","doi":"https://doi.org/10.1137/17m1140662","title":"Modified Active Subspaces Using the Average of Gradients","display_name":"Modified Active Subspaces Using the Average of Gradients","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2906811498","doi":"https://doi.org/10.1137/17m1140662","mag":"2906811498"},"language":"en","primary_location":{"id":"doi:10.1137/17m1140662","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1140662","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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/ASA Journal on Uncertainty Quantification","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/A5030964122","display_name":"Minyong R. Lee","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Minyong R. Lee","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5030964122"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7025,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.82068226,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"7","issue":"1","first_page":"53","last_page":"66"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.994700014591217,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.994700014591217,"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/T11525","display_name":"Piezoelectric Actuators and Control","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9914000034332275,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.8631531596183777},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.8630927801132202},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6274533271789551},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5612281560897827},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.5223970413208008},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5213324427604675},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.49446606636047363},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4803163409233093},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.4676629602909088},{"id":"https://openalex.org/keywords/orthogonal-complement","display_name":"Orthogonal complement","score":0.4473428726196289},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.4427978992462158},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4263421297073364},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4118644595146179},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3915570378303528},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3231028616428375},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1981593370437622},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18255841732025146},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.15515685081481934},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1276501715183258},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1214967668056488}],"concepts":[{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.8631531596183777},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.8630927801132202},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6274533271789551},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5612281560897827},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5223970413208008},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5213324427604675},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.49446606636047363},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4803163409233093},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.4676629602909088},{"id":"https://openalex.org/C154399039","wikidata":"https://www.wikidata.org/wiki/Q1780921","display_name":"Orthogonal complement","level":3,"score":0.4473428726196289},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.4427978992462158},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4263421297073364},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4118644595146179},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3915570378303528},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3231028616428375},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1981593370437622},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18255841732025146},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.15515685081481934},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1276501715183258},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1214967668056488},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"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/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"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:10.1137/17m1140662","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1140662","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7822220147","display_name":null,"funder_award_id":"DMS-1521145","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G8631355626","display_name":null,"funder_award_id":"DMS-1407397","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"}],"funders":[{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1612404967","https://openalex.org/W1988219946","https://openalex.org/W2012176413","https://openalex.org/W2019970588","https://openalex.org/W2031534006","https://openalex.org/W2090492278","https://openalex.org/W2171050905","https://openalex.org/W2412182992","https://openalex.org/W4249991458","https://openalex.org/W4254114241"],"related_works":["https://openalex.org/W3100286349","https://openalex.org/W2896134808","https://openalex.org/W4289378085","https://openalex.org/W4294291164","https://openalex.org/W3172436493","https://openalex.org/W1887135636","https://openalex.org/W4287164812","https://openalex.org/W2386063599","https://openalex.org/W1975884855","https://openalex.org/W3213150849"],"abstract_inverted_index":{"The":[0],"active":[1,23,44,91,96],"subspace":[2,24,45,92],"is":[3,64],"useful":[4],"in":[5],"reducing":[6],"the":[7,10,22,29,36,42,51,62,78,83,89,95],"dimensionality":[8],"of":[9,13,21,35,94],"input":[11],"space":[12],"a":[14,19],"function.":[15,37],"This":[16],"article":[17],"proposes":[18],"modification":[20,63],"that":[25,61,68,85],"can":[26],"substantially":[27],"improve":[28],"dimension":[30],"reduction,":[31],"concerning":[32],"explained":[33,53],"variance":[34,52],"For":[38],"general":[39],"quadratic":[40,75],"functions,":[41],"modified":[43,90],"minimizes":[46],"an":[47],"upper":[48],"bound":[49],"on":[50],"by":[54],"its":[55],"complement.":[56],"A":[57],"two-dimensional":[58],"example":[59],"demonstrates":[60],"effective":[65],"for":[66],"functions":[67],"have":[69],"both":[70],"strong":[71],"linear":[72],"trend":[73],"and":[74],"trend.":[76],"Finally,":[77],"numerical":[79],"examples":[80],"empirically":[81],"demonstrate":[82],"improvements":[84],"result":[86],"from":[87],"using":[88],"instead":[93],"subspace.":[97]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
