{"id":"https://openalex.org/W2133740040","doi":"https://doi.org/10.1162/089976601753196049","title":"The Whitney Reduction Network: A Method for Computing Autoassociative Graphs","display_name":"The Whitney Reduction Network: A Method for Computing Autoassociative Graphs","publication_year":2001,"publication_date":"2001-11-01","ids":{"openalex":"https://openalex.org/W2133740040","doi":"https://doi.org/10.1162/089976601753196049","mag":"2133740040","pmid":"https://pubmed.ncbi.nlm.nih.gov/11674853"},"language":"en","primary_location":{"id":"doi:10.1162/089976601753196049","is_oa":false,"landing_page_url":"https://doi.org/10.1162/089976601753196049","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","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/A5110112678","display_name":"D.S. Broomhead","orcid":null},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]},{"id":"https://openalex.org/I87253917","display_name":"Manchester University","ror":"https://ror.org/02aswte26","country_code":"US","type":"education","lineage":["https://openalex.org/I87253917"]}],"countries":["GB","US"],"is_corresponding":true,"raw_author_name":"D. S. Broomhead","raw_affiliation_strings":["Department of Mathematics, University of Manchester Institute of Science and Technology, Manchester M60 1QD, U.K"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Manchester Institute of Science and Technology, Manchester M60 1QD, U.K","institution_ids":["https://openalex.org/I28407311","https://openalex.org/I87253917"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061567476","display_name":"Michael Kirby","orcid":"https://orcid.org/0000-0001-9802-9263"},"institutions":[{"id":"https://openalex.org/I92446798","display_name":"Colorado State University","ror":"https://ror.org/03k1gpj17","country_code":"US","type":"education","lineage":["https://openalex.org/I92446798"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. J. Kirby","raw_affiliation_strings":["Department of Mathematics, Colorado State University, Fort Collins, CO80523, U.S.A","Department of Mathematics , Colorado State University , Fort Collins, CO, 80523, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Colorado State University, Fort Collins, CO80523, U.S.A","institution_ids":["https://openalex.org/I92446798"]},{"raw_affiliation_string":"Department of Mathematics , Colorado State University , Fort Collins, CO, 80523, U.S.A","institution_ids":["https://openalex.org/I92446798"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110112678"],"corresponding_institution_ids":["https://openalex.org/I28407311","https://openalex.org/I87253917"],"apc_list":null,"apc_paid":null,"fwci":1.6354,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.87735355,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"13","issue":"11","first_page":"2595","last_page":"2616"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9957000017166138,"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":0.9957000017166138,"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":0.9711999893188477,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9587000012397766,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.7521772384643555},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5469276905059814},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.5217412710189819},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5166988372802734},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5140248537063599},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.49333515763282776},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.4544858932495117},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43277400732040405},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.41793811321258545},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.41228705644607544},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4106071889400482},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3898554742336273},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3281654119491577},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1575467586517334}],"concepts":[{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.7521772384643555},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5469276905059814},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5217412710189819},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5166988372802734},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5140248537063599},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.49333515763282776},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.4544858932495117},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43277400732040405},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.41793811321258545},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.41228705644607544},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4106071889400482},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3898554742336273},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3281654119491577},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1575467586517334},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1162/089976601753196049","is_oa":false,"landing_page_url":"https://doi.org/10.1162/089976601753196049","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},{"id":"pmid:11674853","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/11674853","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":"Neural computation","raw_type":null},{"id":"pmh:oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:713","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400452","display_name":"MIMS EPrints (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W94523489","https://openalex.org/W1576347883","https://openalex.org/W1967538548","https://openalex.org/W1992620213","https://openalex.org/W2032121576","https://openalex.org/W2093399550","https://openalex.org/W2108496475","https://openalex.org/W2120101088","https://openalex.org/W2130259898","https://openalex.org/W2135463994","https://openalex.org/W4256400128"],"related_works":["https://openalex.org/W2081900870","https://openalex.org/W3162204513","https://openalex.org/W3176621072","https://openalex.org/W2371138613","https://openalex.org/W2048963458","https://openalex.org/W43109613","https://openalex.org/W2359952343","https://openalex.org/W2080152487","https://openalex.org/W2994280181","https://openalex.org/W4238233526"],"abstract_inverted_index":{"This":[0],"article":[1],"introduces":[2],"a":[3,51,55,58,91],"new":[4],"architecture":[5],"and":[6,101],"associated":[7],"algorithms":[8],"ideal":[9],"for":[10,73],"implementing":[11],"the":[12,35,41,45,48,63,67,88,95,99],"dimensionality":[13],"reduction":[14,56],"of":[15,39,47,50,66,90,98,112],"an":[16,22,102],"m-dimensional":[17],"manifold":[18],"initially":[19],"residing":[20],"in":[21],"n-dimensional":[23],"Euclidean":[24],"space":[25],"where":[26],"n":[27],">>":[28],"m.":[29],"Motivated":[30],"by":[31],"Whitney's":[32],"embedding":[33],"theorem,":[34],"network":[36],"is":[37,117,122],"capable":[38],"training":[40],"identity":[42],"mapping":[43],"employing":[44],"idea":[46,89],"graph":[49],"function.":[52],"In":[53],"theory,":[54],"to":[57,107],"dimension":[59],"d":[60,75],"that":[61],"retains":[62],"differential":[64],"structure":[65],"original":[68],"data":[69],"may":[70],"be":[71],"achieved":[72],"some":[74],"<":[76],"or":[77],"=":[78],"2m":[79],"+":[80],"1.":[81],"To":[82],"implement":[83],"this":[84,115],"network,":[85,100],"we":[86],"propose":[87],"good-projection,":[92],"which":[93],"enhances":[94],"generalization":[96],"capabilities":[97],"adaptive":[103],"secant":[104],"basis":[105],"algorithm":[106],"achieve":[108],"it.":[109],"The":[110,120],"effect":[111],"noise":[113],"on":[114],"procedure":[116],"also":[118],"considered.":[119],"approach":[121],"illustrated":[123],"with":[124],"several":[125],"examples.":[126]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}