{"id":"https://openalex.org/W2020523929","doi":"https://doi.org/10.1109/tnn.2011.2171991","title":"Quantitative Analysis of Nonlinear Embedding","display_name":"Quantitative Analysis of Nonlinear Embedding","publication_year":2011,"publication_date":"2011-11-01","ids":{"openalex":"https://openalex.org/W2020523929","doi":"https://doi.org/10.1109/tnn.2011.2171991","mag":"2020523929","pmid":"https://pubmed.ncbi.nlm.nih.gov/22057061"},"language":"en","primary_location":{"id":"doi:10.1109/tnn.2011.2171991","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnn.2011.2171991","pdf_url":null,"source":{"id":"https://openalex.org/S42080949","display_name":"IEEE Transactions on Neural Networks","issn_l":"1045-9227","issn":["1045-9227","1941-0093"],"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 Neural Networks","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/A5115604692","display_name":"Junping Zhang","orcid":"https://orcid.org/0000-0002-3848-8430"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Junping Zhang","raw_affiliation_strings":["School of Intelligent Information Processing and Computer Science, Fudan University, Shanghai 200433, China. jpzhang@fudan.edu.cn","Shanghai Key Lab., Fudan Univ., Shanghai, China"],"affiliations":[{"raw_affiliation_string":"School of Intelligent Information Processing and Computer Science, Fudan University, Shanghai 200433, China. jpzhang@fudan.edu.cn","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"Shanghai Key Lab., Fudan Univ., Shanghai, China","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085545717","display_name":"Qi Wang","orcid":"https://orcid.org/0000-0003-3249-8459"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qi Wang","raw_affiliation_strings":["Shanghai Key Laboratory, School of Intelligent Information Processing and Computer Science, Fudan University, Shanghai, China","Shanghai Key Lab., Fudan Univ., Shanghai, China"],"affiliations":[{"raw_affiliation_string":"Shanghai Key Laboratory, School of Intelligent Information Processing and Computer Science, Fudan University, Shanghai, China","institution_ids":["https://openalex.org/I24943067"]},{"raw_affiliation_string":"Shanghai Key Lab., Fudan Univ., Shanghai, China","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100719321","display_name":"Li He","orcid":"https://orcid.org/0000-0003-0261-4068"},"institutions":[{"id":"https://openalex.org/I1325784139","display_name":"Yahoo (United Kingdom)","ror":"https://ror.org/038p3gq39","country_code":"GB","type":"company","lineage":["https://openalex.org/I1325784139","https://openalex.org/I4210134091"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Li He","raw_affiliation_strings":["Yahoo Laboratories China, Beijing, China","Yahoo Labs China, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Yahoo Laboratories China, Beijing, China","institution_ids":[]},{"raw_affiliation_string":"Yahoo Labs China, Beijing, China","institution_ids":["https://openalex.org/I1325784139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100621138","display_name":"Zhi\u2010Hua Zhou","orcid":"https://orcid.org/0000-0003-0746-1494"},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhi-Hua Zhou","raw_affiliation_strings":["National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China","[National Key Lab for Novel Software Technology, Nanjing University, Nanjing, China]"],"affiliations":[{"raw_affiliation_string":"National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China","institution_ids":["https://openalex.org/I881766915"]},{"raw_affiliation_string":"[National Key Lab for Novel Software Technology, Nanjing University, Nanjing, China]","institution_ids":["https://openalex.org/I881766915"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5115604692"],"corresponding_institution_ids":["https://openalex.org/I24943067"],"apc_list":null,"apc_paid":null,"fwci":1.2878,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.8259917,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"22","issue":"12","first_page":"1987","last_page":"1998"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9951000213623047,"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":0.9951000213623047,"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/T10638","display_name":"Optical measurement and interference techniques","score":0.991599977016449,"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/T10531","display_name":"Advanced Vision and Imaging","score":0.9894000291824341,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.9307847619056702},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7065812349319458},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6767705082893372},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5034195780754089},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.4857173562049866},{"id":"https://openalex.org/keywords/visualization","display_name":"Visualization","score":0.43983685970306396},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3921363353729248},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.329088032245636},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.29043635725975037}],"concepts":[{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.9307847619056702},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7065812349319458},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6767705082893372},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5034195780754089},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.4857173562049866},{"id":"https://openalex.org/C36464697","wikidata":"https://www.wikidata.org/wiki/Q451553","display_name":"Visualization","level":2,"score":0.43983685970306396},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3921363353729248},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.329088032245636},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29043635725975037},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":2,"locations":[{"id":"doi:10.1109/tnn.2011.2171991","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnn.2011.2171991","pdf_url":null,"source":{"id":"https://openalex.org/S42080949","display_name":"IEEE Transactions on Neural Networks","issn_l":"1045-9227","issn":["1045-9227","1941-0093"],"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 Neural Networks","raw_type":"journal-article"},{"id":"pmid:22057061","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/22057061","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 neural networks","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","display_name":"Life in Land","score":0.4099999964237213}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W28414123","https://openalex.org/W146900863","https://openalex.org/W1595132914","https://openalex.org/W1596641891","https://openalex.org/W1651008648","https://openalex.org/W1985188514","https://openalex.org/W2001141328","https://openalex.org/W2002597011","https://openalex.org/W2005473158","https://openalex.org/W2006554089","https://openalex.org/W2017588182","https://openalex.org/W2026164926","https://openalex.org/W2035990705","https://openalex.org/W2050098151","https://openalex.org/W2053186076","https://openalex.org/W2058486241","https://openalex.org/W2075336646","https://openalex.org/W2077776048","https://openalex.org/W2084809122","https://openalex.org/W2096022469","https://openalex.org/W2096683380","https://openalex.org/W2097308346","https://openalex.org/W2100656411","https://openalex.org/W2107636931","https://openalex.org/W2113442785","https://openalex.org/W2113751382","https://openalex.org/W2116931174","https://openalex.org/W2125003829","https://openalex.org/W2126185804","https://openalex.org/W2133368777","https://openalex.org/W2134312057","https://openalex.org/W2150711601","https://openalex.org/W2153934661","https://openalex.org/W2156838815","https://openalex.org/W2157444450","https://openalex.org/W2161951361","https://openalex.org/W2171461439","https://openalex.org/W2187089797","https://openalex.org/W6601161491","https://openalex.org/W6636889064","https://openalex.org/W6677188175"],"related_works":["https://openalex.org/W2393022482","https://openalex.org/W2377346130","https://openalex.org/W2081900870","https://openalex.org/W2361092061","https://openalex.org/W2319775965","https://openalex.org/W2357314690","https://openalex.org/W2068608913","https://openalex.org/W2191886813","https://openalex.org/W1986317414","https://openalex.org/W2163394011"],"abstract_inverted_index":{"A":[0],"lot":[1],"of":[2,81,112,129],"nonlinear":[3,83,114],"embedding":[4,31,51,84,115,128],"techniques":[5],"have":[6],"been":[7],"developed":[8],"to":[9,48,95,124],"recover":[10],"the":[11,17,21,50,75,82,113,127,130],"intrinsic":[12],"low-dimensional":[13],"manifolds":[14],"embedded":[15],"in":[16,28],"high-dimensional":[18],"space.":[19],"However,":[20],"quantitative":[22,71],"evaluation":[23,46],"criteria":[24,69,88,106],"are":[25,58,89],"less":[26],"studied":[27],"literature.":[29],"The":[30,43,86],"quality":[32],"is":[33,39],"usually":[34],"evaluated":[35],"by":[36,73],"visualization":[37],"which":[38],"subjective":[40],"and":[41,78,93,117],"qualitative.":[42],"few":[44],"existing":[45],"methods":[47],"estimate":[49],"quality,":[52],"neighboring":[53],"preservation":[54],"rate":[55],"for":[56,70],"example,":[57],"not":[59],"widely":[60],"applicable.":[61],"In":[62],"this":[63],"paper,":[64],"we":[65],"propose":[66],"several":[67],"novel":[68],"evaluation,":[72],"considering":[74],"global":[76],"smoothness":[77],"co-directional":[79],"consistence":[80],"algorithms.":[85],"proposed":[87],"geometrically":[90],"intuitive,":[91],"simple,":[92],"easy":[94],"implement":[96],"with":[97,126],"a":[98,122],"low":[99],"computational":[100],"cost.":[101],"Experiments":[102],"show":[103],"that":[104],"our":[105],"capture":[107],"some":[108],"new":[109],"geometrical":[110],"properties":[111],"algorithms,":[116],"can":[118],"be":[119],"used":[120],"as":[121],"guidance":[123],"deal":[125],"out-of-samples.":[131]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-01-13T01:12:25.745995","created_date":"2025-10-10T00:00:00"}
