{"id":"https://openalex.org/W2035990705","doi":"https://doi.org/10.1145/1102351.1102450","title":"Analysis and extension of spectral methods for nonlinear dimensionality reduction","display_name":"Analysis and extension of spectral methods for nonlinear dimensionality reduction","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2035990705","doi":"https://doi.org/10.1145/1102351.1102450","mag":"2035990705"},"language":"en","primary_location":{"id":"doi:10.1145/1102351.1102450","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1102351.1102450","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 22nd international conference on Machine learning - ICML '05","raw_type":"proceedings-article"},"type":"conference-paper","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/A5101544732","display_name":"Fei Sha","orcid":"https://orcid.org/0000-0002-9382-0010"},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fei Sha","raw_affiliation_strings":["University of Pennsylvania, Philadelphia, PA","Univ. of Pennsylvania, Philadelphia, PA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Pennsylvania, Philadelphia, PA","institution_ids":["https://openalex.org/I79576946"]},{"raw_affiliation_string":"Univ. of Pennsylvania, Philadelphia, PA","institution_ids":["https://openalex.org/I79576946"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103354854","display_name":"Lawrence K. Saul","orcid":null},"institutions":[{"id":"https://openalex.org/I79576946","display_name":"University of Pennsylvania","ror":"https://ror.org/00b30xv10","country_code":"US","type":"education","lineage":["https://openalex.org/I79576946"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lawrence K. Saul","raw_affiliation_strings":["University of Pennsylvania, Philadelphia, PA","Univ. of Pennsylvania, Philadelphia, PA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Pennsylvania, Philadelphia, PA","institution_ids":["https://openalex.org/I79576946"]},{"raw_affiliation_string":"Univ. of Pennsylvania, Philadelphia, PA","institution_ids":["https://openalex.org/I79576946"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I79576946"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":107,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"784","last_page":"791"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9979000091552734,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9979000091552734,"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"}},{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9909999966621399,"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":0.9815000295639038,"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/semidefinite-embedding","display_name":"Semidefinite embedding","score":0.9035590887069702},{"id":"https://openalex.org/keywords/nonlinear-dimensionality-reduction","display_name":"Nonlinear dimensionality reduction","score":0.7697699069976807},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.7585934400558472},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.7510608434677124},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.7113476991653442},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.6125857830047607},{"id":"https://openalex.org/keywords/data-point","display_name":"Data point","score":0.6109062433242798},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6054869890213013},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5487292408943176},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.527686357498169},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.38868939876556396},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37467584013938904},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.349259614944458},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3403657078742981},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3131415843963623}],"concepts":[{"id":"https://openalex.org/C206818286","wikidata":"https://www.wikidata.org/wiki/Q7449403","display_name":"Semidefinite embedding","level":4,"score":0.9035590887069702},{"id":"https://openalex.org/C151876577","wikidata":"https://www.wikidata.org/wiki/Q7049464","display_name":"Nonlinear dimensionality reduction","level":3,"score":0.7697699069976807},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.7585934400558472},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.7510608434677124},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.7113476991653442},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.6125857830047607},{"id":"https://openalex.org/C21080849","wikidata":"https://www.wikidata.org/wiki/Q13611879","display_name":"Data point","level":2,"score":0.6109062433242798},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6054869890213013},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5487292408943176},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.527686357498169},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.38868939876556396},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37467584013938904},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.349259614944458},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3403657078742981},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3131415843963623},{"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/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.0},{"id":"https://openalex.org/C65148998","wikidata":"https://www.wikidata.org/wiki/Q7268373","display_name":"Quadratically constrained quadratic program","level":3,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/1102351.1102450","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1102351.1102450","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 22nd international conference on Machine learning - ICML '05","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.80.2009","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.80.2009","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://imls.engr.oregonstate.edu/www/htdocs/proceedings/icml2005/papers/099_AnalysisExtension_ShaSaul.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":12,"referenced_works":["https://openalex.org/W108019484","https://openalex.org/W1578099820","https://openalex.org/W1792341371","https://openalex.org/W2001141328","https://openalex.org/W2053186076","https://openalex.org/W2097308346","https://openalex.org/W2112148214","https://openalex.org/W2150627493","https://openalex.org/W2156287497","https://openalex.org/W2156838815","https://openalex.org/W2912522929","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2385886188","https://openalex.org/W2288891047","https://openalex.org/W2524928742","https://openalex.org/W2362452378","https://openalex.org/W2353517195","https://openalex.org/W3166939022","https://openalex.org/W1727084346","https://openalex.org/W2544939111","https://openalex.org/W2364156185","https://openalex.org/W2035990705"],"abstract_inverted_index":{"Many":[0],"unsupervised":[1],"algorithms":[2,27],"for":[3],"nonlinear":[4],"dimensionality":[5],"reduction,":[6],"such":[7,46],"as":[8,47],"locally":[9],"linear":[10],"embedding":[11,62,72],"(LLE)":[12],"and":[13],"Laplacian":[14,82],"eigenmaps,":[15],"are":[16,38],"derived":[17,74],"from":[18,75],"the":[19,76,99,115,126],"spectral":[20],"decompositions":[21],"of":[22,79,98,101,114,128],"sparse":[23],"matrices.":[24],"While":[25],"these":[26],"aim":[28],"to":[29,42,57],"preserve":[30,43],"certain":[31],"proximity":[32],"relations":[33],"on":[34,121],"average,":[35],"their":[36],"embeddings":[37],"not":[39],"explicitly":[40],"designed":[41],"local":[44],"features":[45],"distances":[48],"or":[49],"angles.":[50],"In":[51],"this":[52],"paper,":[53],"we":[54],"show":[55],"how":[56],"construct":[58],"a":[59],"low":[60],"dimensional":[61],"that":[63],"maximally":[64],"preserves":[65],"angles":[66],"between":[67],"nearby":[68],"data":[69,102,123],"points.":[70,103],"The":[71,104],"is":[73,96],"bottom":[77],"eigenvectors":[78],"LLE":[80],"and/or":[81],"eigenmaps":[83],"by":[84,107],"solving":[85],"an":[86,112],"additional":[87],"(but":[88],"small)":[89],"problem":[90],"in":[91],"semidefinite":[92,108],"programming,":[93],"whose":[94],"size":[95],"independent":[97],"number":[100],"solution":[105],"obtained":[106],"programming":[109],"also":[110],"yields":[111],"estimate":[113],"data's":[116],"intrinsic":[117],"dimensionality.":[118],"Experimental":[119],"results":[120],"several":[122],"sets":[124],"demonstrate":[125],"merits":[127],"our":[129],"approach.":[130]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":6}],"updated_date":"2026-07-19T07:52:34.831488","created_date":"2025-10-10T00:00:00"}