{"id":"https://openalex.org/W2019045907","doi":"https://doi.org/10.1109/tip.2013.2297020","title":"A General Exponential Framework for Dimensionality Reduction","display_name":"A General Exponential Framework for Dimensionality Reduction","publication_year":2014,"publication_date":"2014-01-17","ids":{"openalex":"https://openalex.org/W2019045907","doi":"https://doi.org/10.1109/tip.2013.2297020","mag":"2019045907","pmid":"https://pubmed.ncbi.nlm.nih.gov/26270928"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2013.2297020","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2013.2297020","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"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 Image Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://ir.psych.ac.cn/handle/311026/14174","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066403927","display_name":"Sujing Wang","orcid":"https://orcid.org/0000-0002-8774-6328"},"institutions":[{"id":"https://openalex.org/I4210131870","display_name":"Institute of Psychology, Chinese Academy of Sciences","ror":"https://ror.org/03j7v5j15","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210131870"]},{"id":"https://openalex.org/I4210115644","display_name":"Chinese Institute for Brain Research","ror":"https://ror.org/029819q61","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210115644"]},{"id":"https://openalex.org/I4391767814","display_name":"State Key Laboratory of Brain and Cognitive Science","ror":"https://ror.org/048wy7h78","country_code":null,"type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210112540","https://openalex.org/I4391767814"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Su-Jing Wang","raw_affiliation_strings":["Institute of Psychology, State Key Laboratory of Brain and Cognitive Science, Beijing, China","State Key Lab. of Brain & Cognitive Sci., Inst. of Psychol., Beijing, China"],"affiliations":[{"raw_affiliation_string":"Institute of Psychology, State Key Laboratory of Brain and Cognitive Science, Beijing, China","institution_ids":["https://openalex.org/I4210131870","https://openalex.org/I4391767814"]},{"raw_affiliation_string":"State Key Lab. of Brain & Cognitive Sci., Inst. of Psychol., Beijing, China","institution_ids":["https://openalex.org/I4210115644"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100381753","display_name":"Shuicheng Yan","orcid":"https://orcid.org/0000-0001-8906-3777"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Shuicheng Yan","raw_affiliation_strings":["Department of Electrical and Computer Engineering, National University of Singapore, Singapore","[Dept. of Electr. & Comput. Eng., Nat. Univ. of Singapore, Singapore, Singapore]"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, National University of Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]},{"raw_affiliation_string":"[Dept. of Electr. & Comput. Eng., Nat. Univ. of Singapore, Singapore, Singapore]","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100726984","display_name":"Jian Yang","orcid":"https://orcid.org/0000-0003-4800-832X"},"institutions":[{"id":"https://openalex.org/I36399199","display_name":"Nanjing University of Science and Technology","ror":"https://ror.org/00xp9wg62","country_code":"CN","type":"education","lineage":["https://openalex.org/I36399199"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jian Yang","raw_affiliation_strings":["Nanjing University of Science and Technology, School of Computer Science and Technology, Nanjing, China","School of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing, China#TAB#"],"affiliations":[{"raw_affiliation_string":"Nanjing University of Science and Technology, School of Computer Science and Technology, Nanjing, China","institution_ids":["https://openalex.org/I36399199"]},{"raw_affiliation_string":"School of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing, China#TAB#","institution_ids":["https://openalex.org/I36399199"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079746101","display_name":"Chunguang Zhou","orcid":"https://orcid.org/0000-0002-5269-2526"},"institutions":[{"id":"https://openalex.org/I194450716","display_name":"Jilin University","ror":"https://ror.org/00js3aw79","country_code":"CN","type":"education","lineage":["https://openalex.org/I194450716"]},{"id":"https://openalex.org/I4210134929","display_name":"Jilin Province Science and Technology Department","ror":"https://ror.org/049x38272","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210134929"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chun-Guang Zhou","raw_affiliation_strings":["College of Computer Science and Technology, Jilin University, Changchun, China","College of Computer Science and Technology, Jilin University, Changchun, China;"],"affiliations":[{"raw_affiliation_string":"College of Computer Science and Technology, Jilin University, Changchun, China","institution_ids":["https://openalex.org/I4210134929","https://openalex.org/I194450716"]},{"raw_affiliation_string":"College of Computer Science and Technology, Jilin University, Changchun, China;","institution_ids":["https://openalex.org/I4210134929","https://openalex.org/I194450716"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015329251","display_name":"Xiaolan Fu","orcid":"https://orcid.org/0000-0002-6944-1037"},"institutions":[{"id":"https://openalex.org/I4391767814","display_name":"State Key Laboratory of Brain and Cognitive Science","ror":"https://ror.org/048wy7h78","country_code":null,"type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210112540","https://openalex.org/I4391767814"]},{"id":"https://openalex.org/I4210115644","display_name":"Chinese Institute for Brain Research","ror":"https://ror.org/029819q61","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210115644"]},{"id":"https://openalex.org/I4210131870","display_name":"Institute of Psychology, Chinese Academy of Sciences","ror":"https://ror.org/03j7v5j15","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210131870"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaolan Fu","raw_affiliation_strings":["Institute of Psychology, State Key Laboratory of Brain and Cognitive Science, Beijing, China","State Key Lab. of Brain & Cognitive Sci., Inst. of Psychol., Beijing, China"],"affiliations":[{"raw_affiliation_string":"Institute of Psychology, State Key Laboratory of Brain and Cognitive Science, Beijing, China","institution_ids":["https://openalex.org/I4210131870","https://openalex.org/I4391767814"]},{"raw_affiliation_string":"State Key Lab. of Brain & Cognitive Sci., Inst. of Psychol., Beijing, China","institution_ids":["https://openalex.org/I4210115644"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5066403927"],"corresponding_institution_ids":["https://openalex.org/I4210115644","https://openalex.org/I4210131870","https://openalex.org/I4391767814"],"apc_list":null,"apc_paid":null,"fwci":8.4025,"has_fulltext":false,"cited_by_count":71,"citation_normalized_percentile":{"value":0.9822608,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"23","issue":"2","first_page":"920","last_page":"930"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9988999962806702,"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":0.9988999962806702,"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/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.982699990272522,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.9821000099182129,"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/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.7655484676361084},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5402727723121643},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.510050356388092},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5057718753814697},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.49826717376708984},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.45378443598747253},{"id":"https://openalex.org/keywords/matrix-exponential","display_name":"Matrix exponential","score":0.4419851005077362},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4335687458515167},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4310641884803772},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4017430543899536},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.40152668952941895}],"concepts":[{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.7655484676361084},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5402727723121643},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.510050356388092},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5057718753814697},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.49826717376708984},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.45378443598747253},{"id":"https://openalex.org/C195906000","wikidata":"https://www.wikidata.org/wiki/Q1191722","display_name":"Matrix exponential","level":3,"score":0.4419851005077362},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4335687458515167},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4310641884803772},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4017430543899536},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.40152668952941895},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tip.2013.2297020","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2013.2297020","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"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 Image Processing","raw_type":"journal-article"},{"id":"pmid:26270928","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/26270928","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 image processing : a publication of the IEEE Signal Processing Society","raw_type":null},{"id":"pmh:oai:scholarbank.nus.edu.sg:10635/81870","is_oa":false,"landing_page_url":"http://scholarbank.nus.edu.sg/handle/10635/81870","pdf_url":null,"source":{"id":"https://openalex.org/S7407052290","display_name":"National University of Singapore","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scopus","raw_type":"Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.894.4214","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.894.4214","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://or.nsfc.gov.cn/bitstream/00001903-5/100053/1/1000009444406.pdf","raw_type":"text"},{"id":"pmh:oai:ir.psych.ac.cn:311026/14174","is_oa":true,"landing_page_url":"http://ir.psych.ac.cn/handle/311026/14174","pdf_url":null,"source":{"id":"https://openalex.org/S4377196583","display_name":"Institutional Repository of Institute of Psychology, Chinese Academy of Sciences (Institute of Psychology, Chinese Academy of Sciences)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210131870","host_organization_name":"Institute of Psychology, Chinese Academy of Sciences","host_organization_lineage":["https://openalex.org/I4210131870"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:ir.psych.ac.cn:311026/14174","is_oa":true,"landing_page_url":"http://ir.psych.ac.cn/handle/311026/14174","pdf_url":null,"source":{"id":"https://openalex.org/S4377196583","display_name":"Institutional Repository of Institute of Psychology, Chinese Academy of Sciences (Institute of Psychology, Chinese Academy of Sciences)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210131870","host_organization_name":"Institute of Psychology, Chinese Academy of Sciences","host_organization_lineage":["https://openalex.org/I4210131870"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.699999988079071,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320309321","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W1481933820","https://openalex.org/W1502638562","https://openalex.org/W1974097586","https://openalex.org/W1985809919","https://openalex.org/W2009743150","https://openalex.org/W2022463363","https://openalex.org/W2025341678","https://openalex.org/W2028573862","https://openalex.org/W2038697827","https://openalex.org/W2050343246","https://openalex.org/W2052214166","https://openalex.org/W2054271410","https://openalex.org/W2067136705","https://openalex.org/W2070127246","https://openalex.org/W2079780979","https://openalex.org/W2088900896","https://openalex.org/W2093402979","https://openalex.org/W2098949973","https://openalex.org/W2099173991","https://openalex.org/W2106565812","https://openalex.org/W2116551122","https://openalex.org/W2117553576","https://openalex.org/W2121647436","https://openalex.org/W2123180320","https://openalex.org/W2132822263","https://openalex.org/W2133893370","https://openalex.org/W2138451337","https://openalex.org/W2142216712","https://openalex.org/W2143103810","https://openalex.org/W2146820706","https://openalex.org/W2152758153","https://openalex.org/W2156718197","https://openalex.org/W2163647352","https://openalex.org/W2167144347","https://openalex.org/W2171347282","https://openalex.org/W2171849959","https://openalex.org/W2204756796","https://openalex.org/W2612972698","https://openalex.org/W3148981562","https://openalex.org/W4237723258","https://openalex.org/W4285719527","https://openalex.org/W6630114213","https://openalex.org/W6674716897","https://openalex.org/W6674787683","https://openalex.org/W6682755970","https://openalex.org/W6687890955","https://openalex.org/W7034449035"],"related_works":["https://openalex.org/W2487162673","https://openalex.org/W2942366970","https://openalex.org/W1968265719","https://openalex.org/W2994280181","https://openalex.org/W4317660424","https://openalex.org/W4382762952","https://openalex.org/W2067382432","https://openalex.org/W1969390712","https://openalex.org/W2589376966","https://openalex.org/W1970439644"],"abstract_inverted_index":{"As":[0],"a":[1,8,71],"general":[2,72],"framework,":[3,79,132],"Laplacian":[4,141],"embedding,":[5],"based":[6],"on":[7,157],"pairwise":[9],"similarity":[10,94],"matrix,":[11,95],"infers":[12],"low":[13],"dimensional":[14,18],"representations":[15],"from":[16,24],"high":[17],"data.":[19],"However,":[20],"it":[21],"generally":[22],"suffers":[23],"three":[25],"issues:":[26],"1)":[27],"algorithmic":[28],"performance":[29],"is":[30,98,122],"sensitive":[31],"to":[32,137],"the":[33,38,41,51,78,80,88,92,110,116,158,163,170,177],"size":[34,46],"of":[35,105,115,119],"neighbors;":[36],"2)":[37],"algorithm":[39,52],"encounters":[40],"well":[42,175],"known":[43],"small":[44,54,127],"sample":[45],"(SSS)":[47],"problem;":[48],"and":[49,69,96,151,162],"3)":[50],"de-emphasizes":[53],"distance":[55,128],"pairs.":[56,129],"To":[57],"address":[58,176],"these":[59],"issues,":[60],"here":[61],"we":[62,133],"propose":[63],"exponential":[64,68,82,107,120,136],"embedding":[65,121,142],"using":[66],"matrix":[67,81,106,135],"provide":[70],"framework":[73,173],"for":[74],"dimensionality":[75],"reduction.":[76],"In":[77],"can":[83,174],"be":[84],"roughly":[85],"interpreted":[86],"by":[87],"random":[89],"walk":[90],"over":[91],"feature":[93],"thus":[97],"more":[99,123],"robust.":[100],"The":[101,113],"positive":[102],"definite":[103],"property":[104],"deals":[108],"with":[109],"SSS":[111],"problem.":[112],"behavior":[114],"decay":[117],"function":[118],"significant":[124],"in":[125],"emphasizing":[126],"Under":[130],"this":[131],"apply":[134],"extend":[138],"many":[139],"popular":[140],"algorithms,":[143],"e.g.,":[144],"locality":[145],"preserving":[146],"projections,":[147,150],"unsupervised":[148],"discriminant":[149],"marginal":[152],"fisher":[153],"analysis.":[154],"Experiments":[155],"conducted":[156],"synthesized":[159],"data,":[160],"UCI,":[161],"Georgia":[164],"Tech":[165],"face":[166],"database":[167],"show":[168],"that":[169],"proposed":[171],"new":[172],"issues":[178],"mentioned":[179],"above.":[180]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":13},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":5}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
