{"id":"https://openalex.org/W2003827862","doi":"https://doi.org/10.1137/13094918x","title":"Constrained Best Euclidean Distance Embedding on a Sphere: A Matrix Optimization Approach","display_name":"Constrained Best Euclidean Distance Embedding on a Sphere: A Matrix Optimization Approach","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2003827862","doi":"https://doi.org/10.1137/13094918x","mag":"2003827862"},"language":"en","primary_location":{"id":"doi:10.1137/13094918x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/13094918x","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"type":"article","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/A5111471089","display_name":"Shuanghua Bai","orcid":null},"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":"Shuanghua Bai","raw_affiliation_strings":["University of Southampton"],"affiliations":[{"raw_affiliation_string":"University of Southampton","institution_ids":["https://openalex.org/I43439940"]}]},{"author_position":"middle","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":false,"raw_author_name":"Huo-Duo Qi","raw_affiliation_strings":["University of Southampton"],"affiliations":[{"raw_affiliation_string":"University of Southampton","institution_ids":["https://openalex.org/I43439940"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071551240","display_name":"Naihua Xiu","orcid":"https://orcid.org/0000-0002-3129-2005"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Naihua Xiu","raw_affiliation_strings":["Department of Applied Mathematics, Beijing Jiaotong University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Beijing Jiaotong University, Beijing, China","institution_ids":["https://openalex.org/I21193070"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5111471089"],"corresponding_institution_ids":["https://openalex.org/I43439940"],"apc_list":null,"apc_paid":null,"fwci":0.92863211,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.76182401,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"25","issue":"1","first_page":"439","last_page":"467"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9976999759674072,"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9921000003814697,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7087991237640381},{"id":"https://openalex.org/keywords/euclidean-distance-matrix","display_name":"Euclidean distance matrix","score":0.5599991083145142},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.49828648567199707},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.49271419644355774},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4668740928173065},{"id":"https://openalex.org/keywords/euclidean-shortest-path","display_name":"Euclidean shortest path","score":0.4642743468284607},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4501608610153198},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.43828317523002625},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.43706172704696655},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.42702123522758484},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.4134436249732971},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33301734924316406},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.29364892840385437},{"id":"https://openalex.org/keywords/shortest-path-problem","display_name":"Shortest path problem","score":0.14753538370132446},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.11771214008331299}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7087991237640381},{"id":"https://openalex.org/C171558263","wikidata":"https://www.wikidata.org/wiki/Q5406122","display_name":"Euclidean distance matrix","level":3,"score":0.5599991083145142},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.49828648567199707},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.49271419644355774},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4668740928173065},{"id":"https://openalex.org/C170836113","wikidata":"https://www.wikidata.org/wiki/Q5406126","display_name":"Euclidean shortest path","level":5,"score":0.4642743468284607},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4501608610153198},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.43828317523002625},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.43706172704696655},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.42702123522758484},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.4134436249732971},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33301734924316406},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.29364892840385437},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.14753538370132446},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.11771214008331299},{"id":"https://openalex.org/C1465435","wikidata":"https://www.wikidata.org/wiki/Q2916352","display_name":"Longest path problem","level":4,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/13094918x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/13094918x","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:eprints.soton.ac.uk:372356","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":null,"sustainable_development_goals":[],"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"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W84056083","https://openalex.org/W1480708938","https://openalex.org/W1543573801","https://openalex.org/W1551360398","https://openalex.org/W1553702074","https://openalex.org/W1582520000","https://openalex.org/W1601741115","https://openalex.org/W1856811566","https://openalex.org/W1964922595","https://openalex.org/W1980610004","https://openalex.org/W1984910745","https://openalex.org/W1986929032","https://openalex.org/W1990908167","https://openalex.org/W1992688650","https://openalex.org/W1993613781","https://openalex.org/W1999597013","https://openalex.org/W2000389722","https://openalex.org/W2003250847","https://openalex.org/W2007304358","https://openalex.org/W2009216547","https://openalex.org/W2014548643","https://openalex.org/W2037261607","https://openalex.org/W2037402401","https://openalex.org/W2056854783","https://openalex.org/W2057069782","https://openalex.org/W2061629994","https://openalex.org/W2061681393","https://openalex.org/W2077260542","https://openalex.org/W2077482036","https://openalex.org/W2086953401","https://openalex.org/W2087087428","https://openalex.org/W2099799470","https://openalex.org/W2104481149","https://openalex.org/W2127930751","https://openalex.org/W2128762995","https://openalex.org/W2144002138","https://openalex.org/W2150386905","https://openalex.org/W2154228232","https://openalex.org/W2158043848","https://openalex.org/W2158604542","https://openalex.org/W2163392119","https://openalex.org/W2164002139","https://openalex.org/W2165289170","https://openalex.org/W2169065610","https://openalex.org/W2320533836","https://openalex.org/W2327230547","https://openalex.org/W2913066018","https://openalex.org/W2953018250","https://openalex.org/W2962771824","https://openalex.org/W3046579346","https://openalex.org/W4230800447","https://openalex.org/W4236113971"],"related_works":["https://openalex.org/W3037672488","https://openalex.org/W2947897749","https://openalex.org/W2364679747","https://openalex.org/W2318206461","https://openalex.org/W2610477248","https://openalex.org/W2003250847","https://openalex.org/W2095047739","https://openalex.org/W5644033","https://openalex.org/W2029691756","https://openalex.org/W1493422928"],"abstract_inverted_index":{"The":[0,33],"problem":[1,81,88,164],"of":[2,8,43,121,129,147],"data":[3,19,45],"representation":[4,35],"on":[5,46],"a":[6,40,47,90,102],"sphere":[7,48],"unknown":[9],"radius":[10],"arises":[11],"from":[12,138],"various":[13,152],"disciplines":[14],"such":[15],"as":[16,49,51,82],"Statistics":[17],"(spatial":[18],"representation),":[20],"Psychology":[21],"(constrained":[22],"multidimensional":[23,141],"scaling),":[24],"and":[25,30,62,118],"Computer":[26],"Science":[27],"(machine":[28],"learning":[29],"pattern":[31],"recognition).":[32],"best":[34],"often":[36],"needs":[37],"to":[38,52,71,143,160],"minimize":[39],"distance":[41,56,64,85],"function":[42],"the":[44,72,80,119,126,130,139,145,148,161],"well":[50],"satisfy":[53],"some":[54,135],"Euclidean":[55,63,84],"constraints.":[57,153],"It":[58],"is":[59],"those":[60],"spherical":[61,140],"constraints":[65],"that":[66,100,124],"present":[67,156],"an":[68,83,97,157],"enormous":[69],"challenge":[70],"existing":[73],"algorithms.":[74],"In":[75],"this":[76],"paper,":[77],"we":[78],"reformulate":[79],"matrix":[86],"optimization":[87],"with":[89],"low":[91],"rank":[92],"constraint.":[93],"We":[94,111,133,154],"then":[95],"propose":[96],"iterative":[98],"algorithm":[99,149],"uses":[101],"quadratically":[103],"convergent":[104],"Newton-CG":[105],"method":[106],"at":[107],"its":[108],"each":[109],"step.":[110],"study":[112],"fundamental":[113],"issues":[114],"including":[115],"constraint":[116],"nondegeneracy":[117],"nonsingularity":[120],"generalized":[122],"Jacobian":[123],"ensure":[125],"quadratic":[127],"convergence":[128],"Newton":[131],"method.":[132],"use":[134],"classic":[136],"examples":[137],"scaling":[142],"demonstrate":[144],"flexibility":[146],"in":[150],"incorporating":[151],"also":[155],"interesting":[158],"application":[159],"circle":[162],"fitting":[163]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":5},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}