{"id":"https://openalex.org/W2162971057","doi":"https://doi.org/10.1109/iccv.2007.4409096","title":"Laplacian PCA and Its Applications","display_name":"Laplacian PCA and Its Applications","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2162971057","doi":"https://doi.org/10.1109/iccv.2007.4409096","mag":"2162971057"},"language":"en","primary_location":{"id":"doi:10.1109/iccv.2007.4409096","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iccv.2007.4409096","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 IEEE 11th International Conference on Computer Vision","raw_type":"proceedings-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/A5101911374","display_name":"Deli Zhao","orcid":"https://orcid.org/0000-0002-8838-578X"},"institutions":[{"id":"https://openalex.org/I4210113369","display_name":"Microsoft Research Asia (China)","ror":"https://ror.org/0300m5276","country_code":"CN","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210113369"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Deli Zhao","raw_affiliation_strings":["Visual Computing Group, Microsoft Research Asia, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Visual Computing Group, Microsoft Research Asia, Beijing, China","institution_ids":["https://openalex.org/I4210113369"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016399094","display_name":"Zhouchen Lin","orcid":"https://orcid.org/0000-0003-1493-7569"},"institutions":[{"id":"https://openalex.org/I4210113369","display_name":"Microsoft Research Asia (China)","ror":"https://ror.org/0300m5276","country_code":"CN","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210113369"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhouchen Lin","raw_affiliation_strings":["Visual Computing Group, Microsoft Research Asia, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Visual Computing Group, Microsoft Research Asia, Beijing, China","institution_ids":["https://openalex.org/I4210113369"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110380387","display_name":"Xiaoou Tang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210113369","display_name":"Microsoft Research Asia (China)","ror":"https://ror.org/0300m5276","country_code":"CN","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210113369"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoou Tang","raw_affiliation_strings":["Visual Computing Group, Microsoft Research Asia, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Visual Computing Group, Microsoft Research Asia, Beijing, China","institution_ids":["https://openalex.org/I4210113369"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101911374"],"corresponding_institution_ids":["https://openalex.org/I4210113369"],"apc_list":null,"apc_paid":null,"fwci":4.6028,"has_fulltext":false,"cited_by_count":52,"citation_normalized_percentile":{"value":0.9517099,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9994000196456909,"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":0.9994000196456909,"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/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9976999759674072,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9925000071525574,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/principal-component-analysis","display_name":"Principal component analysis","score":0.7768764495849609},{"id":"https://openalex.org/keywords/nonlinear-dimensionality-reduction","display_name":"Nonlinear dimensionality reduction","score":0.7585616111755371},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.6850345134735107},{"id":"https://openalex.org/keywords/kernel-principal-component-analysis","display_name":"Kernel principal component analysis","score":0.5947471261024475},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.5387668609619141},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.537161111831665},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5247288346290588},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.49507132172584534},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.4895256459712982},{"id":"https://openalex.org/keywords/isomap","display_name":"Isomap","score":0.4571495056152344},{"id":"https://openalex.org/keywords/facial-recognition-system","display_name":"Facial recognition system","score":0.4556288421154022},{"id":"https://openalex.org/keywords/tangent-space","display_name":"Tangent space","score":0.45543748140335083},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.43531912565231323},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43130722641944885},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.4157765507698059},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.17583337426185608},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1564238965511322},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12474557757377625},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.11048975586891174}],"concepts":[{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.7768764495849609},{"id":"https://openalex.org/C151876577","wikidata":"https://www.wikidata.org/wiki/Q7049464","display_name":"Nonlinear dimensionality reduction","level":3,"score":0.7585616111755371},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.6850345134735107},{"id":"https://openalex.org/C182335926","wikidata":"https://www.wikidata.org/wiki/Q17093020","display_name":"Kernel principal component analysis","level":4,"score":0.5947471261024475},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.5387668609619141},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.537161111831665},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5247288346290588},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.49507132172584534},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.4895256459712982},{"id":"https://openalex.org/C2778626561","wikidata":"https://www.wikidata.org/wiki/Q6086067","display_name":"Isomap","level":4,"score":0.4571495056152344},{"id":"https://openalex.org/C31510193","wikidata":"https://www.wikidata.org/wiki/Q1192553","display_name":"Facial recognition system","level":3,"score":0.4556288421154022},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.45543748140335083},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.43531912565231323},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43130722641944885},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.4157765507698059},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.17583337426185608},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1564238965511322},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12474557757377625},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.11048975586891174},{"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/iccv.2007.4409096","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iccv.2007.4409096","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 IEEE 11th International Conference on Computer Vision","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.187.7779","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.187.7779","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://research.microsoft.com/en-us/people/zhoulin/Publications/2007-ICCV-LPCA.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W56210758","https://openalex.org/W411712352","https://openalex.org/W1480376833","https://openalex.org/W1502435410","https://openalex.org/W1531189931","https://openalex.org/W1949248870","https://openalex.org/W1969766704","https://openalex.org/W2001141328","https://openalex.org/W2012352340","https://openalex.org/W2053186076","https://openalex.org/W2077776048","https://openalex.org/W2093238900","https://openalex.org/W2097308346","https://openalex.org/W2098263160","https://openalex.org/W2112148214","https://openalex.org/W2117553576","https://openalex.org/W2121647436","https://openalex.org/W2122992400","https://openalex.org/W2129890539","https://openalex.org/W2137659841","https://openalex.org/W2138451337","https://openalex.org/W2139850885","https://openalex.org/W2140095548","https://openalex.org/W2140151376","https://openalex.org/W2145309677","https://openalex.org/W2146610201","https://openalex.org/W2149481809","https://openalex.org/W2152826865","https://openalex.org/W2156838815","https://openalex.org/W2160126058","https://openalex.org/W2163808566","https://openalex.org/W2164931791","https://openalex.org/W2167144347","https://openalex.org/W2177347332","https://openalex.org/W2798909945","https://openalex.org/W3099514962","https://openalex.org/W3148981562","https://openalex.org/W4232449688","https://openalex.org/W4402546660","https://openalex.org/W6614282263","https://openalex.org/W6631681266","https://openalex.org/W6640499739","https://openalex.org/W6674677300","https://openalex.org/W6676938131","https://openalex.org/W6678764298","https://openalex.org/W6680905637","https://openalex.org/W6750968397"],"related_works":["https://openalex.org/W2375574759","https://openalex.org/W3124275785","https://openalex.org/W4287375746","https://openalex.org/W1562785334","https://openalex.org/W2375518579","https://openalex.org/W2161951361","https://openalex.org/W2914688691","https://openalex.org/W1541753963","https://openalex.org/W2153105632","https://openalex.org/W1521522576"],"abstract_inverted_index":{"Dimensionality":[0],"reduction":[1],"plays":[2],"a":[3,35],"fundamental":[4],"role":[5],"in":[6],"data":[7],"processing,":[8],"for":[9],"which":[10,28,140],"principal":[11,111],"component":[12],"analysis":[13],"(PCA)":[14],"is":[15,29,74,159],"widely":[16],"used.":[17],"In":[18,45],"this":[19],"paper,":[20],"we":[21],"develop":[22],"the":[23,30,42,48,52,59,65,77,96,102,109,118,135,162],"Laplacian":[24],"PCA":[25,33,155,158],"(LPCA)":[26],"algorithm":[27,73],"extension":[31],"of":[32,50,80,99,113,121,137,144,152],"to":[34,47,107,123,154],"more":[36],"general":[37],"form":[38],"by":[39,55,134,148,161],"locally":[40,81],"optimizing":[41],"weighted":[43],"scatter.":[44],"addition":[46],"simplicity":[49],"PCA,":[51],"benefits":[53],"brought":[54],"LPCA":[56,72,122,153],"are":[57,141],"twofold:":[58],"strong":[60],"robustness":[61],"against":[62],"noise":[63],"and":[64,156,172],"weak":[66],"metric-dependence":[67],"on":[68,76,95,164],"sample":[69],"spaces.":[70],"The":[71,150],"based":[75],"global":[78],"alignment":[79,88,136],"Gaussian":[82],"or":[83],"linear":[84,142],"subspaces":[85],"via":[86],"an":[87],"technique":[89],"borrowed":[90],"from":[91],"manifold":[92,124,173],"learning.":[93,125],"Based":[94],"coding":[97],"length":[98],"local":[100,110],"samples,":[101],"weights":[103],"can":[104,131],"be":[105,132],"determined":[106],"capture":[108],"structure":[112],"data.":[114],"We":[115],"also":[116],"give":[117],"exemplary":[119],"application":[120],"Manifold":[126],"unfolding":[127],"(non-linear":[128],"dimensionality":[129],"reduction)":[130],"performed":[133],"tangential":[138],"maps":[139],"transformations":[143],"tangent":[145],"coordinates":[146],"approximated":[147],"LPCA.":[149],"superiority":[151],"kernel":[157],"verified":[160],"experiments":[163],"face":[165,170],"recognition":[166],"(FRGC":[167],"version":[168],"2":[169],"database)":[171],"(Scherk":[174],"surface)":[175],"unfolding.":[176]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":6},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
