{"id":"https://openalex.org/W2136146792","doi":"https://doi.org/10.1109/tsmcb.2011.2151187","title":"Manifold Learning by Graduated Optimization","display_name":"Manifold Learning by Graduated Optimization","publication_year":2011,"publication_date":"2011-05-27","ids":{"openalex":"https://openalex.org/W2136146792","doi":"https://doi.org/10.1109/tsmcb.2011.2151187","mag":"2136146792","pmid":"https://pubmed.ncbi.nlm.nih.gov/21622074"},"language":"en","primary_location":{"id":"doi:10.1109/tsmcb.2011.2151187","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmcb.2011.2151187","pdf_url":null,"source":{"id":"https://openalex.org/S4210170378","display_name":"IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics)","issn_l":"1083-4419","issn":["1083-4419","1941-0492"],"is_oa":false,"is_in_doaj":false,"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 Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics)","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5003595274","display_name":"Michael S. Gashler","orcid":"https://orcid.org/0000-0001-8991-8907"},"institutions":[{"id":"https://openalex.org/I100005738","display_name":"Brigham Young University","ror":"https://ror.org/047rhhm47","country_code":"US","type":"education","lineage":["https://openalex.org/I100005738"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"M. Gashler","raw_affiliation_strings":["Department of Computer Science, Brigham Young University, Provo, UT, USA","[Department of Computer Science, Brigham Young University, Provo, UT, USA]"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Brigham Young University, Provo, UT, USA","institution_ids":["https://openalex.org/I100005738"]},{"raw_affiliation_string":"[Department of Computer Science, Brigham Young University, Provo, UT, USA]","institution_ids":["https://openalex.org/I100005738"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064318273","display_name":"Dan Ventura","orcid":"https://orcid.org/0000-0002-3111-2238"},"institutions":[{"id":"https://openalex.org/I100005738","display_name":"Brigham Young University","ror":"https://ror.org/047rhhm47","country_code":"US","type":"education","lineage":["https://openalex.org/I100005738"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D. Ventura","raw_affiliation_strings":["Department of Computer Science, Brigham Young University, Provo, UT, USA","[Department of Computer Science, Brigham Young University, Provo, UT, USA]"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Brigham Young University, Provo, UT, USA","institution_ids":["https://openalex.org/I100005738"]},{"raw_affiliation_string":"[Department of Computer Science, Brigham Young University, Provo, UT, USA]","institution_ids":["https://openalex.org/I100005738"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111465095","display_name":"Tony Martinez","orcid":"https://orcid.org/0009-0009-5855-5459"},"institutions":[{"id":"https://openalex.org/I100005738","display_name":"Brigham Young University","ror":"https://ror.org/047rhhm47","country_code":"US","type":"education","lineage":["https://openalex.org/I100005738"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"T. Martinez","raw_affiliation_strings":["Department of Computer Science, Brigham Young University, Provo, UT, USA","[Department of Computer Science, Brigham Young University, Provo, UT, USA]"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Brigham Young University, Provo, UT, USA","institution_ids":["https://openalex.org/I100005738"]},{"raw_affiliation_string":"[Department of Computer Science, Brigham Young University, Provo, UT, USA]","institution_ids":["https://openalex.org/I100005738"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5003595274"],"corresponding_institution_ids":["https://openalex.org/I100005738"],"apc_list":null,"apc_paid":null,"fwci":1.5682,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.86440468,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"41","issue":"6","first_page":"1458","last_page":"1470"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9987999796867371,"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":0.9987999796867371,"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/T11309","display_name":"Music and Audio Processing","score":0.991599977016449,"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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.9905999898910522,"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/isomap","display_name":"Isomap","score":0.8590250015258789},{"id":"https://openalex.org/keywords/nonlinear-dimensionality-reduction","display_name":"Nonlinear dimensionality reduction","score":0.8548975586891174},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.847183108329773},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.7469087839126587},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.700568437576294},{"id":"https://openalex.org/keywords/manifold-alignment","display_name":"Manifold alignment","score":0.57319176197052},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5329540371894836},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.500877857208252},{"id":"https://openalex.org/keywords/statistical-manifold","display_name":"Statistical manifold","score":0.427840918302536},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3919485807418823},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3691469728946686},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3380722403526306},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.33593738079071045},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.23316916823387146},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.16126954555511475},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16056311130523682},{"id":"https://openalex.org/keywords/information-geometry","display_name":"Information geometry","score":0.13821706175804138},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.07623502612113953},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07143053412437439}],"concepts":[{"id":"https://openalex.org/C2778626561","wikidata":"https://www.wikidata.org/wiki/Q6086067","display_name":"Isomap","level":4,"score":0.8590250015258789},{"id":"https://openalex.org/C151876577","wikidata":"https://www.wikidata.org/wiki/Q7049464","display_name":"Nonlinear dimensionality reduction","level":3,"score":0.8548975586891174},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.847183108329773},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.7469087839126587},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.700568437576294},{"id":"https://openalex.org/C153120616","wikidata":"https://www.wikidata.org/wiki/Q17068315","display_name":"Manifold alignment","level":4,"score":0.57319176197052},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5329540371894836},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.500877857208252},{"id":"https://openalex.org/C169391604","wikidata":"https://www.wikidata.org/wiki/Q7604402","display_name":"Statistical manifold","level":5,"score":0.427840918302536},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3919485807418823},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3691469728946686},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3380722403526306},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.33593738079071045},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.23316916823387146},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.16126954555511475},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16056311130523682},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.13821706175804138},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.07623502612113953},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07143053412437439},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tsmcb.2011.2151187","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmcb.2011.2151187","pdf_url":null,"source":{"id":"https://openalex.org/S4210170378","display_name":"IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics)","issn_l":"1083-4419","issn":["1083-4419","1941-0492"],"is_oa":false,"is_in_doaj":false,"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 Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics)","raw_type":"journal-article"},{"id":"pmid:21622074","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/21622074","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":"IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society","raw_type":null},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.221.3729","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.221.3729","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://axon.cs.byu.edu/papers/gashler2011smc.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W4211794","https://openalex.org/W119967642","https://openalex.org/W1604938182","https://openalex.org/W1651008648","https://openalex.org/W1965061793","https://openalex.org/W2001141328","https://openalex.org/W2017588182","https://openalex.org/W2053186076","https://openalex.org/W2063078340","https://openalex.org/W2071128523","https://openalex.org/W2074163268","https://openalex.org/W2074738960","https://openalex.org/W2098162425","https://openalex.org/W2112148214","https://openalex.org/W2118217205","https://openalex.org/W2118527389","https://openalex.org/W2124728898","https://openalex.org/W2134312057","https://openalex.org/W2138886673","https://openalex.org/W2142781195","https://openalex.org/W2150711601","https://openalex.org/W2156287497","https://openalex.org/W2156718197","https://openalex.org/W2156838815","https://openalex.org/W2157169955","https://openalex.org/W2158867000","https://openalex.org/W2158930984","https://openalex.org/W2161366100","https://openalex.org/W2169507824","https://openalex.org/W2171029115","https://openalex.org/W2595697910","https://openalex.org/W2914776604","https://openalex.org/W2978983090","https://openalex.org/W2990138404","https://openalex.org/W2999905431","https://openalex.org/W3002694247","https://openalex.org/W3122936144","https://openalex.org/W4237171445","https://openalex.org/W4238805501","https://openalex.org/W6600155594","https://openalex.org/W6636889064"],"related_works":["https://openalex.org/W2375518579","https://openalex.org/W2366334780","https://openalex.org/W2383781046","https://openalex.org/W2014252850","https://openalex.org/W2385862161","https://openalex.org/W3089741428","https://openalex.org/W2283921858","https://openalex.org/W2129138585","https://openalex.org/W2170058261","https://openalex.org/W2164397368"],"abstract_inverted_index":{"We":[0],"present":[1],"an":[2,17],"algorithm":[3],"for":[4],"manifold":[5,8,19,29,33],"learning":[6],"called":[7],"sculpting":[9,34,70],",":[10],"which":[11],"utilizes":[12],"graduated":[13],"optimization":[14],"to":[15,75],"seek":[16],"accurate":[18,37],"embedding.":[20],"An":[21],"empirical":[22],"analysis":[23],"across":[24],"a":[25,40],"wide":[26],"range":[27],"of":[28,42],"problems":[30],"indicates":[31],"that":[32],"yields":[35],"more":[36,63],"results":[38],"than":[39,65],"number":[41],"existing":[43],"algorithms,":[44],"including":[45],"Isomap,":[46],"locally":[47],"linear":[48],"embedding":[49],"(LLE),":[50],"Hessian":[51],"LLE":[52],"(HLLE),":[53],"and":[54,60,67],"landmark":[55],"maximum":[56],"variance":[57],"unfolding":[58],"(L-MVU),":[59],"is":[61],"significantly":[62],"efficient":[64],"HLLE":[66],"L-MVU.":[68],"Manifold":[69],"also":[71],"has":[72],"the":[73],"ability":[74],"benefit":[76],"from":[77],"prior":[78],"knowledge":[79],"about":[80],"expected":[81],"results.":[82]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
