{"id":"https://openalex.org/W2297593803","doi":"https://doi.org/10.1109/tsp.2016.2645517","title":"Laplacian Eigenmaps From Sparse, Noisy Similarity Measurements","display_name":"Laplacian Eigenmaps From Sparse, Noisy Similarity Measurements","publication_year":2016,"publication_date":"2016-12-28","ids":{"openalex":"https://openalex.org/W2297593803","doi":"https://doi.org/10.1109/tsp.2016.2645517","mag":"2297593803"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2016.2645517","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2016.2645517","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1603.03972","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112870105","display_name":"Keith Levin","orcid":null},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Keith Levin","raw_affiliation_strings":["Department of Computer Science, Johns Hopkins University, Baltimore, MD, USA","Department of Applied Mathematics and Statistics and the Human Language Technologies Center of Excellence, Johns Hopkins University, Baltimore, MD, 21218 USA","Department of Computer Science, Johns Hopkins University, Baltimore, MD, 21218 USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Johns Hopkins University, Baltimore, MD, USA","institution_ids":["https://openalex.org/I145311948"]},{"raw_affiliation_string":"Department of Applied Mathematics and Statistics and the Human Language Technologies Center of Excellence, Johns Hopkins University, Baltimore, MD, 21218 USA","institution_ids":["https://openalex.org/I145311948"]},{"raw_affiliation_string":"Department of Computer Science, Johns Hopkins University, Baltimore, MD, 21218 USA","institution_ids":["https://openalex.org/I145311948"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014425850","display_name":"Vince Lyzinski","orcid":"https://orcid.org/0000-0001-5594-8956"},"institutions":[{"id":"https://openalex.org/I6059380","display_name":"University of Baltimore","ror":"https://ror.org/024gw2733","country_code":"US","type":"education","lineage":["https://openalex.org/I6059380"]},{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]},{"id":"https://openalex.org/I2799853436","display_name":"Johns Hopkins Medicine","ror":"https://ror.org/037zgn354","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I2799853436"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vince Lyzinski","raw_affiliation_strings":["Department of Applied Mathematics and Statistics and the Human Language Technologies Center of Excellence, Johns Hopkins University, Baltimore, MD, USA","Department of Computer Science, Johns Hopkins University, Baltimore, MD, 21218 USA","Department of Applied Mathematics and Statistics and the Human Language Technologies Center of Excellence, Johns Hopkins University, Baltimore, MD, 21218 USA"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Statistics and the Human Language Technologies Center of Excellence, Johns Hopkins University, Baltimore, MD, USA","institution_ids":["https://openalex.org/I145311948","https://openalex.org/I2799853436","https://openalex.org/I6059380"]},{"raw_affiliation_string":"Department of Computer Science, Johns Hopkins University, Baltimore, MD, 21218 USA","institution_ids":["https://openalex.org/I145311948"]},{"raw_affiliation_string":"Department of Applied Mathematics and Statistics and the Human Language Technologies Center of Excellence, Johns Hopkins University, Baltimore, MD, 21218 USA","institution_ids":["https://openalex.org/I145311948"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5112870105"],"corresponding_institution_ids":["https://openalex.org/I145311948"],"apc_list":null,"apc_paid":null,"fwci":2.6662,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.91776136,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"65","issue":"8","first_page":"1988","last_page":"2003"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9995999932289124,"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/T10320","display_name":"Neural Networks and Applications","score":0.9995999932289124,"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":0.9986000061035156,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.9975000023841858,"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/isomap","display_name":"Isomap","score":0.8942471742630005},{"id":"https://openalex.org/keywords/nonlinear-dimensionality-reduction","display_name":"Nonlinear dimensionality reduction","score":0.7736149430274963},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"Dimensionality reduction","score":0.6679815053939819},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.6522788405418396},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.6360403299331665},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.5702738165855408},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5588652491569519},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5201632976531982},{"id":"https://openalex.org/keywords/data-point","display_name":"Data point","score":0.49767783284187317},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.478464812040329},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.44216835498809814},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42636638879776},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.4232103228569031},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4164823293685913},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.07898837327957153}],"concepts":[{"id":"https://openalex.org/C2778626561","wikidata":"https://www.wikidata.org/wiki/Q6086067","display_name":"Isomap","level":4,"score":0.8942471742630005},{"id":"https://openalex.org/C151876577","wikidata":"https://www.wikidata.org/wiki/Q7049464","display_name":"Nonlinear dimensionality reduction","level":3,"score":0.7736149430274963},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.6679815053939819},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6522788405418396},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.6360403299331665},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.5702738165855408},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5588652491569519},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5201632976531982},{"id":"https://openalex.org/C21080849","wikidata":"https://www.wikidata.org/wiki/Q13611879","display_name":"Data point","level":2,"score":0.49767783284187317},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.478464812040329},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.44216835498809814},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42636638879776},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.4232103228569031},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4164823293685913},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.07898837327957153},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tsp.2016.2645517","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2016.2645517","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"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 Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1603.03972","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1603.03972","pdf_url":"https://arxiv.org/pdf/1603.03972","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1603.03972","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1603.03972","pdf_url":"https://arxiv.org/pdf/1603.03972","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"score":0.4399999976158142,"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4"}],"awards":[{"id":"https://openalex.org/G3990529561","display_name":null,"funder_award_id":"FA8750-12-2-0303","funder_id":"https://openalex.org/F4320338294","funder_display_name":"Air Force Research Laboratory"}],"funders":[{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320338294","display_name":"Air Force Research Laboratory","ror":"https://ror.org/02e2egq70"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":101,"referenced_works":["https://openalex.org/W568673721","https://openalex.org/W635122248","https://openalex.org/W857387926","https://openalex.org/W1490549637","https://openalex.org/W1530239281","https://openalex.org/W1577418252","https://openalex.org/W1578099820","https://openalex.org/W1612031067","https://openalex.org/W1640765157","https://openalex.org/W1789701990","https://openalex.org/W1894984256","https://openalex.org/W1927438844","https://openalex.org/W1967184357","https://openalex.org/W1970377488","https://openalex.org/W1973207991","https://openalex.org/W1973836644","https://openalex.org/W1977361006","https://openalex.org/W1996023858","https://openalex.org/W2000977215","https://openalex.org/W2001141328","https://openalex.org/W2002240881","https://openalex.org/W2011832962","https://openalex.org/W2021145763","https://openalex.org/W2025341678","https://openalex.org/W2044433757","https://openalex.org/W2047071281","https://openalex.org/W2047109555","https://openalex.org/W2053186076","https://openalex.org/W2057469720","https://openalex.org/W2059652594","https://openalex.org/W2094433168","https://openalex.org/W2096746450","https://openalex.org/W2097308346","https://openalex.org/W2099111195","https://openalex.org/W2100221277","https://openalex.org/W2100235303","https://openalex.org/W2102158416","https://openalex.org/W2104290444","https://openalex.org/W2107411554","https://openalex.org/W2112545207","https://openalex.org/W2118563516","https://openalex.org/W2125947724","https://openalex.org/W2128160875","https://openalex.org/W2130502756","https://openalex.org/W2132914434","https://openalex.org/W2137557016","https://openalex.org/W2137570937","https://openalex.org/W2142153450","https://openalex.org/W2145962650","https://openalex.org/W2149532724","https://openalex.org/W2154249783","https://openalex.org/W2156838815","https://openalex.org/W2157444450","https://openalex.org/W2158121106","https://openalex.org/W2168029744","https://openalex.org/W2176446742","https://openalex.org/W2294984095","https://openalex.org/W2326712857","https://openalex.org/W2407151108","https://openalex.org/W2464534118","https://openalex.org/W2478708596","https://openalex.org/W2611328865","https://openalex.org/W2756989319","https://openalex.org/W2798707604","https://openalex.org/W2951166730","https://openalex.org/W2962681781","https://openalex.org/W2962740067","https://openalex.org/W2963664118","https://openalex.org/W2964017521","https://openalex.org/W2997701990","https://openalex.org/W3022413497","https://openalex.org/W3033414884","https://openalex.org/W3098045837","https://openalex.org/W3099514962","https://openalex.org/W3099839986","https://openalex.org/W3101749733","https://openalex.org/W3101788906","https://openalex.org/W3101919829","https://openalex.org/W3104227803","https://openalex.org/W3148981562","https://openalex.org/W3160079335","https://openalex.org/W4213367101","https://openalex.org/W4235169531","https://openalex.org/W4237723258","https://openalex.org/W4243880374","https://openalex.org/W4249297864","https://openalex.org/W4251297447","https://openalex.org/W4254645981","https://openalex.org/W4255333822","https://openalex.org/W6620392953","https://openalex.org/W6623753063","https://openalex.org/W6636565117","https://openalex.org/W6639704161","https://openalex.org/W6675424377","https://openalex.org/W6675747103","https://openalex.org/W6679446029","https://openalex.org/W6680634009","https://openalex.org/W6683161245","https://openalex.org/W6697018953","https://openalex.org/W6714100551","https://openalex.org/W6834473044"],"related_works":["https://openalex.org/W2123981743","https://openalex.org/W2162490024","https://openalex.org/W2153105632","https://openalex.org/W1989880160","https://openalex.org/W2065819987","https://openalex.org/W2140492997","https://openalex.org/W2094462140","https://openalex.org/W2623252221","https://openalex.org/W1504224003","https://openalex.org/W625055723"],"abstract_inverted_index":{"Manifold":[0],"learning":[1],"and":[2,10,44,54,72,86,97,137,151],"dimensionality":[3],"reduction":[4],"techniques":[5],"are":[6,26],"ubiquitous":[7],"in":[8],"science":[9],"engineering,":[11],"but":[12],"can":[13,101,126],"be":[14],"computationally":[15],"expensive":[16,27],"procedures":[17],"when":[18,24,78],"applied":[19],"to":[20,28,37,109],"large":[21],"datasets":[22],"or":[23],"similarities":[25],"compute.":[29],"To":[30],"date,":[31],"little":[32],"work":[33],"has":[34],"been":[35],"done":[36],"investigate":[38],"the":[39,45,75,110,116,133],"tradeoff":[40],"between":[41],"computational":[42],"resources":[43],"quality":[46],"of":[47,57,135,143],"learned":[48],"representations.":[49],"We":[50],"present":[51],"both":[52],"theoretical":[53,90],"experimental":[55],"explorations":[56],"this":[58,79,128],"question.":[59],"In":[60],"particular,":[61],"we":[62,100,131],"consider":[63],"Laplacian":[64,111,140],"eigenmaps":[65,112,141],"embeddings":[66,76,142],"based":[67,114],"on":[68,115,139],"a":[69,106,158],"kernel":[70,80,118],"matrix,":[71],"explore":[73,132],"how":[74,124],"behave":[77],"matrix":[81],"is":[82],"corrupted":[83],"by":[84],"occlusion":[85,98,138],"noise.":[87],"Our":[88,120],"main":[89],"result":[91],"shows":[92],"that":[93],"under":[94],"modest":[95],"noise":[96,136],"assumptions,":[99],"(with":[102],"high":[103],"probability)":[104],"recover":[105],"good":[107],"approximation":[108],"embedding":[113],"uncorrupted":[117],"matrix.":[119],"results":[121],"also":[122],"show":[123],"regularization":[125],"aid":[127],"approximation.":[129],"Experimentally,":[130],"effects":[134],"two":[144],"real-world":[145],"datasets,":[146],"one":[147,152],"from":[148,153],"speech":[149],"processing":[150],"neuroscience,":[154],"as":[155,157],"well":[156],"synthetic":[159],"dataset.":[160]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
