{"id":"https://openalex.org/W2084809122","doi":"https://doi.org/10.1145/1553374.1553494","title":"Structure preserving embedding","display_name":"Structure preserving embedding","publication_year":2009,"publication_date":"2009-06-14","ids":{"openalex":"https://openalex.org/W2084809122","doi":"https://doi.org/10.1145/1553374.1553494","mag":"2084809122"},"language":"en","primary_location":{"id":"doi:10.1145/1553374.1553494","doi":"https://doi.org/10.1145/1553374.1553494","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1553374.1553494","pdf_url":null,"source":{"id":"https://openalex.org/S4306419644","display_name":"International Conference on Machine Learning","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 26th Annual International Conference on Machine Learning","raw_type":"proceedings-article"},"parent_works":[],"lineage":["https://openalex.org/W2084809122"],"child_works_count":0,"type":"conference-paper","is_traditional":true,"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":null,"display_name":"Blake Shaw","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Blake Shaw","raw_affiliation_strings":["Columbia University, New York, NY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Columbia University, New York, NY","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068077704","display_name":"Tony Jebara","orcid":"https://orcid.org/0000-0003-0314-3376","observed_orcids":["https://orcid.org/0000-0003-0314-3376"]},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tony Jebara","raw_affiliation_strings":["Columbia University, New York, NY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Columbia University, New York, NY","institution_ids":["https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I78577930"],"apc_list":null,"apc_paid":null,"fwci":9.5139,"has_fulltext":false,"cited_by_count":203,"citation_normalized_percentile":{"value":0.98776364,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"937","last_page":"944"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.415800005197525,"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/T11273","display_name":"Advanced Graph Neural Networks","score":0.415800005197525,"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":0.3801000118255615,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.14270000159740448,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/network-embedding","display_name":"graph embedding","score":0.9980000257492065},{"id":"https://openalex.org/keywords/low-dimensional-embedding","display_name":"low-dimensional embedding","score":0.6990000009536743},{"id":"https://openalex.org/keywords/topology-preservation","display_name":"topology preservation","score":0.6690000295639038},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"semidefinite programming","score":0.9229999780654907},{"id":"https://openalex.org/keywords/k-nearest-neighbors","display_name":"k-nearest neighbors","score":0.6579999923706055},{"id":"https://openalex.org/keywords/network-visualization","display_name":"network visualization","score":0.8529999852180481},{"id":"https://openalex.org/keywords/graph-compression","display_name":"graph compression","score":0.7250000238418579},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"dimensionality reduction","score":0.906000018119812},{"id":"https://openalex.org/keywords/spectral-embedding","display_name":"spectral embedding","score":0.8090000152587891},{"id":"https://openalex.org/keywords/laplacian-eigenmaps","display_name":"Laplacian eigenmaps","score":0.9869999885559082}],"concepts":[{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.71793532371521},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.5879819393157959},{"id":"https://openalex.org/C75564084","wikidata":"https://www.wikidata.org/wiki/Q5597085","display_name":"Graph embedding","level":3,"score":0.5726886987686157},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5432118773460388},{"id":"https://openalex.org/C81081738","wikidata":"https://www.wikidata.org/wiki/Q55542","display_name":"Lossless compression","level":3,"score":0.5014359951019287},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.4439709484577179},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4249197244644165},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.41252344846725464},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3837195634841919},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3305678367614746},{"id":"https://openalex.org/C78548338","wikidata":"https://www.wikidata.org/wiki/Q2493","display_name":"Data compression","level":2,"score":0.20807045698165894},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1990211308002472},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.18546637892723083}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/1553374.1553494","doi":"https://doi.org/10.1145/1553374.1553494","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1553374.1553494","pdf_url":null,"source":{"id":"https://openalex.org/S4306419644","display_name":"International Conference on Machine Learning","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 26th Annual International Conference on Machine Learning","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.149.7500","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.149.7500","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.mcgill.ca/~icml2009/papers/418.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.161.451","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.161.451","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.columbia.edu/~jebara/papers/spe-icml09.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1552347772","https://openalex.org/W1578099820","https://openalex.org/W1651008648","https://openalex.org/W1966139704","https://openalex.org/W2001141328","https://openalex.org/W2020632401","https://openalex.org/W2035981651","https://openalex.org/W2053186076","https://openalex.org/W2092423930","https://openalex.org/W2097308346","https://openalex.org/W2102664288","https://openalex.org/W2143075842","https://openalex.org/W2150675045","https://openalex.org/W2152284345","https://openalex.org/W3120740533","https://openalex.org/W4251607247","https://openalex.org/W6834473044"],"related_works":["https://openalex.org/W7097929234","https://openalex.org/W2156660313","https://openalex.org/W4205348060","https://openalex.org/W3034831228","https://openalex.org/W2950397852","https://openalex.org/W4282934215","https://openalex.org/W2801961705","https://openalex.org/W3004343251","https://openalex.org/W7057736963","https://openalex.org/W7099048319"],"abstract_inverted_index":{"Structure":[0],"Preserving":[1],"Embedding":[2],"(SPE)":[3],"is":[4,17,30,59],"an":[5],"algorithm":[6],"for":[7],"embedding":[8,16,89,129],"graphs":[9,138],"in":[10,114],"Euclidean":[11],"space":[12],"such":[13,36,126],"that":[14,65,135],"the":[15,21,26,43,46,51,54,80,84,101],"low-dimensional":[18],"and":[19,99,118,130,139],"preserves":[20],"global":[22],"topological":[23],"properties":[24],"of":[25,45,53,75,83,116,121,163],"input":[27,47,85],"graph.":[28,86],"Topology":[29],"preserved":[31],"if":[32],"a":[33,62,67,73,147],"connectivity":[34,81],"algorithm,":[35],"as":[37,61,127],"k-nearest":[38],"neighbors,":[39],"can":[40,104,141],"easily":[41],"recover":[42],"edges":[44],"graph":[48,88],"from":[49],"only":[50,146],"coordinates":[52],"nodes":[55],"after":[56],"embedding.":[57],"SPE":[58,110],"formulated":[60],"semidefinite":[63],"program":[64],"learns":[66],"low-rank":[68],"kernel":[69],"matrix":[70],"constrained":[71],"by":[72],"set":[74],"linear":[76],"inequalities":[77],"which":[78],"captures":[79],"structure":[82,94,152],"Traditional":[87],"algorithms":[90,158],"do":[91],"not":[92],"preserve":[93],"according":[95],"to":[96],"our":[97],"definition,":[98],"thus":[100],"resulting":[102],"visualizations":[103],"be":[105,142],"misleading":[106],"or":[107],"less":[108],"informative.":[109],"provides":[111],"significant":[112],"improvements":[113],"terms":[115],"visualization":[117],"lossless":[119],"compression":[120],"graphs,":[122],"outperforming":[123],"popular":[124],"methods":[125],"spectral":[128],"Laplacian":[131],"eigen-maps.":[132],"We":[133],"find":[134],"many":[136],"classical":[137],"networks":[140],"properly":[143],"embedded":[144],"using":[145],"few":[148],"dimensions.":[149],"Furthermore,":[150],"introducing":[151],"preserving":[153],"constraints":[154],"into":[155],"dimensionality":[156],"reduction":[157],"produces":[159],"more":[160],"accurate":[161],"representations":[162],"high-dimensional":[164],"data.":[165]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":16},{"year":2020,"cited_by_count":15},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":19},{"year":2017,"cited_by_count":15},{"year":2016,"cited_by_count":13},{"year":2015,"cited_by_count":17},{"year":2014,"cited_by_count":15},{"year":2013,"cited_by_count":11},{"year":2012,"cited_by_count":9}],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2016-06-24T00:00:00"}