{"id":"https://openalex.org/W2963244596","doi":"https://doi.org/10.1007/s10107-016-1090-7","title":"Convex optimization learning of faithful Euclidean distance representations in nonlinear dimensionality reduction","display_name":"Convex optimization learning of faithful Euclidean distance representations in nonlinear dimensionality reduction","publication_year":2016,"publication_date":"2016-11-11","ids":{"openalex":"https://openalex.org/W2963244596","doi":"https://doi.org/10.1007/s10107-016-1090-7","mag":"2963244596"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-016-1090-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-016-1090-7","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10107-016-1090-7.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs10107-016-1090-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057244957","display_name":"Chao Ding","orcid":"https://orcid.org/0000-0002-4228-6700"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chao Ding","raw_affiliation_strings":["Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, People\u2019s Republic of China","Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, People\u2019s Republic of China","institution_ids":["https://openalex.org/I19820366"]},{"raw_affiliation_string":"Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing, People's Republic of China","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112621269","display_name":"Houduo Qi","orcid":"https://orcid.org/0000-0003-3481-4814"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Hou-Duo Qi","raw_affiliation_strings":["School of Mathematics, University of Southampton, Southampton, SO17 1BJ, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Southampton, Southampton, SO17 1BJ, UK","institution_ids":["https://openalex.org/I43439940"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5112621269"],"corresponding_institution_ids":["https://openalex.org/I43439940"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":2.9257,"has_fulltext":true,"cited_by_count":24,"citation_normalized_percentile":{"value":0.90353519,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"164","issue":"1-2","first_page":"341","last_page":"381"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9951000213623047,"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/T10689","display_name":"Remote-Sensing Image Classification","score":0.978600025177002,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7313663363456726},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5448517799377441},{"id":"https://openalex.org/keywords/matrix-completion","display_name":"Matrix completion","score":0.4874434769153595},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.467266708612442},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.4600536525249481},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.4402271807193756},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4244334399700165},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.42373859882354736},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4126676917076111},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3786534070968628},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3658672571182251},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.3531680703163147},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.31996017694473267}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7313663363456726},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5448517799377441},{"id":"https://openalex.org/C2778459887","wikidata":"https://www.wikidata.org/wiki/Q6787865","display_name":"Matrix completion","level":3,"score":0.4874434769153595},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.467266708612442},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.4600536525249481},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.4402271807193756},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4244334399700165},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.42373859882354736},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4126676917076111},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3786534070968628},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3658672571182251},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3531680703163147},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.31996017694473267},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10107-016-1090-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-016-1090-7","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10107-016-1090-7.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:eprints.soton.ac.uk:391500","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401019","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1007/s10107-016-1090-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-016-1090-7","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs10107-016-1090-7.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.7099999785423279,"id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G1261773691","display_name":null,"funder_award_id":"EP/K007645/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1561470135","display_name":"Large-Scale Optimization on Euclidean Distance Matrices","funder_award_id":"EP/K007645/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5891674479","display_name":"\u57fa\u4e8e\u77e9\u9635\u4f18\u5316\u6a21\u578b\u7684\u793e\u4ea4\u7f51\u7edc\u5206\u6790\u7814\u7a76\u53ca\u5176\u5e94\u7528","funder_award_id":"11671387","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2963244596.pdf","grobid_xml":"https://content.openalex.org/works/W2963244596.grobid-xml"},"referenced_works_count":70,"referenced_works":["https://openalex.org/W55941057","https://openalex.org/W142207546","https://openalex.org/W340056678","https://openalex.org/W340244495","https://openalex.org/W390146837","https://openalex.org/W648260396","https://openalex.org/W950821216","https://openalex.org/W1546851689","https://openalex.org/W1552347772","https://openalex.org/W1573579329","https://openalex.org/W1966303152","https://openalex.org/W1975172027","https://openalex.org/W1977959082","https://openalex.org/W1993744672","https://openalex.org/W1994593142","https://openalex.org/W1999597013","https://openalex.org/W1999913571","https://openalex.org/W2001141328","https://openalex.org/W2009271970","https://openalex.org/W2029213856","https://openalex.org/W2047071281","https://openalex.org/W2052104835","https://openalex.org/W2061681393","https://openalex.org/W2061901927","https://openalex.org/W2072840758","https://openalex.org/W2083412275","https://openalex.org/W2088715239","https://openalex.org/W2093499918","https://openalex.org/W2095534914","https://openalex.org/W2104780023","https://openalex.org/W2107411554","https://openalex.org/W2111297856","https://openalex.org/W2117920736","https://openalex.org/W2118550318","https://openalex.org/W2120872934","https://openalex.org/W2134332047","https://openalex.org/W2142153450","https://openalex.org/W2146281661","https://openalex.org/W2148606196","https://openalex.org/W2152284345","https://openalex.org/W2157656721","https://openalex.org/W2166163936","https://openalex.org/W2183587030","https://openalex.org/W2324151815","https://openalex.org/W2327230547","https://openalex.org/W2376603351","https://openalex.org/W2495084345","https://openalex.org/W2611328865","https://openalex.org/W2616032753","https://openalex.org/W2798707604","https://openalex.org/W2905110430","https://openalex.org/W2952477160","https://openalex.org/W2962769133","https://openalex.org/W2962771824","https://openalex.org/W2962986187","https://openalex.org/W2965497096","https://openalex.org/W3013880646","https://openalex.org/W3098045837","https://openalex.org/W3098807808","https://openalex.org/W3104501706","https://openalex.org/W3125671026","https://openalex.org/W3144881883","https://openalex.org/W3160079335","https://openalex.org/W4205622916","https://openalex.org/W4234292554","https://openalex.org/W4247571494","https://openalex.org/W4254491045","https://openalex.org/W4255333822","https://openalex.org/W4301425558","https://openalex.org/W4312512934"],"related_works":["https://openalex.org/W2912837894","https://openalex.org/W3153752017","https://openalex.org/W4324118942","https://openalex.org/W2913057782","https://openalex.org/W2734993473","https://openalex.org/W2185064329","https://openalex.org/W2187229407","https://openalex.org/W2059909660","https://openalex.org/W3030201206","https://openalex.org/W4302394465"],"abstract_inverted_index":{"Classical":[0],"multidimensional":[1],"scaling":[2],"only":[3],"works":[4],"well":[5],"when":[6,91,138],"the":[7,77,80,92,119,139,142,148,173,195,208],"noisy":[8],"distances":[9,22],"observed":[10],"in":[11,23,89],"a":[12,24,104,114,132,153,158,182],"high":[13,58,136,201],"dimensional":[14,26],"space":[15],"can":[16,177,197],"be":[17,178],"faithfully":[18],"represented":[19],"by":[20,181],"Euclidean":[21,109],"low":[25],"space.":[27],"Advanced":[28],"models":[29,53],"such":[30,47],"as":[31],"Maximum":[32],"Variance":[33],"Unfolding":[34],"(MVU)":[35],"and":[36,126,167],"Minimum":[37],"Volume":[38],"Embedding":[39],"(MVE)":[40],"use":[41],"Semi-Definite":[42],"Programming":[43],"(SDP)":[44],"to":[45,157,213],"reconstruct":[46],"faithful":[48],"representations.":[49],"While":[50],"those":[51],"SDP":[52,209],"are":[54,87,95],"capable":[55],"of":[56,79,108,135,141,150,152,189,200],"producing":[57],"quality":[59,78,202],"configuration":[60],"numerically,":[61],"they":[62,86],"suffer":[63],"two":[64],"major":[65],"drawbacks.":[66],"One":[67],"is":[68,84,146],"that":[69,85,128,194,207],"there":[70],"exist":[71],"no":[72],"theoretically":[73],"guaranteed":[74],"bounds":[75],"on":[76,203],"configuration.":[81],"The":[82],"other":[83],"slow":[88],"computation":[90],"data":[93,205],"points":[94,206],"beyond":[96],"moderate":[97],"size.":[98],"In":[99],"this":[100],"paper,":[101],"we":[102],"propose":[103],"convex":[105,174],"optimization":[106,175],"model":[107,122,130,176,196],"distance":[110],"matrices.":[111],"We":[112],"establish":[113],"non-asymptotic":[115],"error":[116],"bound":[117],"for":[118],"random":[120],"graph":[121],"with":[123],"sub-Gaussian":[124],"noise,":[125],"prove":[127],"our":[129],"produces":[131],"matrix":[133,155],"estimator":[134],"accuracy":[137],"order":[140],"uniform":[143],"sample":[144],"size":[145],"roughly":[147],"degree":[149],"freedom":[151],"low-rank":[154],"up":[156],"logarithmic":[159],"factor.":[160],"Our":[161],"results":[162],"partially":[163],"explain":[164],"why":[165],"MVU":[166],"MVE":[168],"often":[169],"work":[170],"well.":[171],"Moreover,":[172],"efficiently":[179],"solved":[180],"recently":[183],"proposed":[184],"3-block":[185],"alternating":[186],"direction":[187],"method":[188],"multipliers.":[190],"Numerical":[191],"experiments":[192],"show":[193],"produce":[198],"configurations":[199],"large":[204],"approach":[210],"would":[211],"struggle":[212],"cope":[214],"with.":[215]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
