{"id":"https://openalex.org/W2973709366","doi":"https://doi.org/10.48550/arxiv.1909.10228","title":"Manifold Fitting under Unbounded Noise","display_name":"Manifold Fitting under Unbounded Noise","publication_year":2019,"publication_date":"2019-09-23","ids":{"openalex":"https://openalex.org/W2973709366","doi":"https://doi.org/10.48550/arxiv.1909.10228","mag":"2973709366"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1909.10228","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.10228","pdf_url":"https://arxiv.org/pdf/1909.10228","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1909.10228","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075757275","display_name":"Zhigang Yao","orcid":"https://orcid.org/0000-0001-5927-6958","observed_orcids":["https://orcid.org/0000-0001-5927-6958"]},"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":"Yao, Zhigang","raw_affiliation_strings":["Department of Statistics and Data Science National University of Singapore 21 Lower Kent Ridge Road Singapore 117546","National University of Singapore,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and Data Science National University of Singapore 21 Lower Kent Ridge Road Singapore 117546","institution_ids":["https://openalex.org/I165932596"]},{"raw_affiliation_string":"National University of Singapore,","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101798856","display_name":"Yuqing Xia","orcid":"https://orcid.org/0000-0002-3411-7210","observed_orcids":["https://orcid.org/0000-0002-3411-7210"]},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]},{"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","US"],"is_corresponding":false,"raw_author_name":"Xia, Yuqing","raw_affiliation_strings":["Center of Mathematical Sciences and Applications Harvard University 20 Garden Street Cambridge USA 02138","National University of Singapore,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center of Mathematical Sciences and Applications Harvard University 20 Garden Street Cambridge USA 02138","institution_ids":["https://openalex.org/I136199984"]},{"raw_affiliation_string":"National University of Singapore,","institution_ids":["https://openalex.org/I165932596"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.3285999894142151,"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"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.3285999894142151,"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"}},{"id":"https://openalex.org/T11871","display_name":"Advanced Statistical Methods and Models","score":0.10289999842643738,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.0892999991774559,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/high-dimensional-data","display_name":"high-dimensional data","score":0.6299999952316284},{"id":"https://openalex.org/keywords/convergence-bounds","display_name":"convergence bounds","score":0.4359999895095825}],"concepts":[{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.8089224100112915},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6393249034881592},{"id":"https://openalex.org/C169391604","wikidata":"https://www.wikidata.org/wiki/Q7604402","display_name":"Statistical manifold","level":5,"score":0.6075242161750793},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.601341187953949},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.5749639868736267},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.5454937815666199},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5074030756950378},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.47964221239089966},{"id":"https://openalex.org/C153120616","wikidata":"https://www.wikidata.org/wiki/Q17068315","display_name":"Manifold alignment","level":4,"score":0.4690592288970947},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4658810496330261},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.4522829055786133},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4040908217430115},{"id":"https://openalex.org/C151876577","wikidata":"https://www.wikidata.org/wiki/Q7049464","display_name":"Nonlinear dimensionality reduction","level":3,"score":0.31720107793807983},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27221477031707764},{"id":"https://openalex.org/C109546454","wikidata":"https://www.wikidata.org/wiki/Q3798604","display_name":"Information geometry","level":4,"score":0.257377564907074},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16107836365699768},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09277120232582092},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"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/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.0},{"id":"https://openalex.org/C12520029","wikidata":"https://www.wikidata.org/wiki/Q1147161","display_name":"Scalar curvature","level":3,"score":0.0},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:1909.10228","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.10228","pdf_url":"https://arxiv.org/pdf/1909.10228","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},{"id":"doi:10.48550/arxiv.1909.10228","doi":"https://doi.org/10.48550/arxiv.1909.10228","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1909.10228","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1909.10228","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.10228","pdf_url":"https://arxiv.org/pdf/1909.10228","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4070917339","display_name":null,"funder_award_id":"Tier 1","funder_id":"https://openalex.org/F4320320698","funder_display_name":"National University of Singapore"}],"funders":[{"id":"https://openalex.org/F4320309622","display_name":"Harvard University","ror":"https://ror.org/03vek6s52"},{"id":"https://openalex.org/F4320320698","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49"},{"id":"https://openalex.org/F4320322724","display_name":"Ministry of Education, India","ror":"https://ror.org/048xjjh50"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W434012021","https://openalex.org/W1593775104","https://openalex.org/W1969447312","https://openalex.org/W2002437266","https://openalex.org/W2053186076","https://openalex.org/W2058214587","https://openalex.org/W2077776048","https://openalex.org/W2096496077","https://openalex.org/W2097308346","https://openalex.org/W2098049350","https://openalex.org/W2123921160","https://openalex.org/W2129657231","https://openalex.org/W2138675231","https://openalex.org/W2157878484","https://openalex.org/W2166325531","https://openalex.org/W2173520492","https://openalex.org/W2808636150","https://openalex.org/W2962914462","https://openalex.org/W2963991860","https://openalex.org/W3092670835","https://openalex.org/W3102292222","https://openalex.org/W3105264615"],"related_works":["https://openalex.org/W4366399421","https://openalex.org/W3160230076","https://openalex.org/W7221000807","https://openalex.org/W6910559249","https://openalex.org/W2950117264","https://openalex.org/W4390040832","https://openalex.org/W7124424057","https://openalex.org/W1490656300","https://openalex.org/W2953387140","https://openalex.org/W7100174260"],"abstract_inverted_index":{"There":[0],"has":[1],"been":[2],"an":[3,44],"emerging":[4],"trend":[5],"in":[6,164,167],"non-Euclidean":[7],"statistical":[8],"analysis":[9],"of":[10,34,169,173,184,195,212],"aiming":[11],"to":[12,32,145,203,226],"recover":[13],"a":[14,19,83,98,114],"low":[15],"dimensional":[16,24],"structure,":[17],"namely":[18],"manifold,":[20,138],"underlying":[21,137,180],"the":[22,27,30,49,66,71,77,86,91,101,107,120,128,132,136,142,147,151,154,170,174,177,185,193,210],"high":[23,165],"data.":[25],"Recovering":[26],"manifold":[28,46,99,122,187,218],"requires":[29],"noise":[31,72,78,155],"be":[33,95],"certain":[35],"concentration.":[36],"Existing":[37],"methods":[38,62],"address":[39],"this":[40,110],"problem":[41],"by":[42,118,125,150,191],"constructing":[43],"approximated":[45],"based":[47],"on":[48,135],"tangent":[50,87,103,129],"space":[51,88,104],"estimation":[52,89],"at":[53,90,131,141],"each":[54],"sample":[55,143],"point.":[56],"Although":[57],"theoretical":[58,162,206],"convergence":[59,163],"for":[60],"these":[61],"is":[63,73,79,82,123,156,188,224],"guaranteed,":[64],"either":[65],"samples":[67,93],"are":[68,201],"noiseless":[69],"or":[70],"bounded.":[74],"However,":[75],"if":[76],"unbounded,":[80,157],"which":[81,119],"common":[84],"scenario,":[85],"noisy":[92],"will":[94],"blurred.":[96],"Fitting":[97],"from":[100],"blurred":[102],"might":[105],"increase":[106],"inaccuracy.":[108],"In":[109],"paper,":[111],"we":[112],"introduce":[113],"new":[115,159],"manifold-fitting":[116],"method,":[117],"output":[121],"constructed":[124],"directly":[126],"estimating":[127],"spaces":[130],"projected":[133],"points":[134],"rather":[139],"than":[140],"points,":[144],"decrease":[146],"error":[148],"caused":[149],"noise.":[152],"Assuming":[153],"our":[158,205,213,222],"method":[160,214,223],"provides":[161],"probability,":[166],"terms":[168],"upper":[171],"bound":[172],"distance":[175],"between":[176],"estimated":[178,186],"and":[179,208],"manifold.":[181],"The":[182],"smoothness":[183],"also":[189],"evaluated":[190],"bounding":[192],"supremum":[194],"twice":[196],"difference":[197],"above.":[198],"Numerical":[199],"simulations":[200],"provided":[202],"validate":[204],"findings":[207],"demonstrate":[209],"advantages":[211],"over":[215],"other":[216],"relevant":[217],"fitting":[219],"methods.":[220],"Finally,":[221],"applied":[225],"real":[227],"data":[228],"examples.":[229]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2019-09-26T00:00:00"}
