{"id":"https://openalex.org/W3176499146","doi":"https://doi.org/10.1142/s0217595921500330","title":"An Ordinal Weighted EDM Model for Nonmetric Multidimensional Scaling","display_name":"An Ordinal Weighted EDM Model for Nonmetric Multidimensional Scaling","publication_year":2021,"publication_date":"2021-06-28","ids":{"openalex":"https://openalex.org/W3176499146","doi":"https://doi.org/10.1142/s0217595921500330","mag":"3176499146"},"language":"en","primary_location":{"id":"doi:10.1142/s0217595921500330","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0217595921500330","pdf_url":null,"source":{"id":"https://openalex.org/S1254427","display_name":"Asia Pacific Journal of Operational Research","issn_l":"0217-5959","issn":["0217-5959","1793-7019"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asia-Pacific Journal of Operational Research","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/A5077587421","display_name":"Qingna Li","orcid":"https://orcid.org/0000-0002-1397-6200"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qing-Na Li","raw_affiliation_strings":["School of Mathematics and Statistics, Beijing Key Laboratory on MCAACI, Beijing, Institute of Technology, Beijing 100081, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Beijing Key Laboratory on MCAACI, Beijing, Institute of Technology, Beijing 100081, P. R. China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100458219","display_name":"Chi Zhang","orcid":"https://orcid.org/0000-0003-0034-843X"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chi Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P. R. China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015754562","display_name":"Mengzhi Cao","orcid":null},"institutions":[{"id":"https://openalex.org/I107077323","display_name":"Worcester Polytechnic Institute","ror":"https://ror.org/05ejpqr48","country_code":"US","type":"education","lineage":["https://openalex.org/I107077323"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mengzhi Cao","raw_affiliation_strings":["Data Science, Worcester Polytechnic Institute, Worcester 01609, USA"],"affiliations":[{"raw_affiliation_string":"Data Science, Worcester Polytechnic Institute, Worcester 01609, USA","institution_ids":["https://openalex.org/I107077323"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5077587421"],"corresponding_institution_ids":["https://openalex.org/I125839683"],"apc_list":null,"apc_paid":null,"fwci":0.1247,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.46462022,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"39","issue":"03","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10689","display_name":"Remote-Sensing Image Classification","score":0.994700014591217,"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"}},"topics":[{"id":"https://openalex.org/T10689","display_name":"Remote-Sensing Image Classification","score":0.994700014591217,"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"}},{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9740999937057495,"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/T13282","display_name":"Automated Road and Building Extraction","score":0.9631999731063843,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean Engineering"},"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/multidimensional-scaling","display_name":"Multidimensional scaling","score":0.7350703477859497},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.6997605562210083},{"id":"https://openalex.org/keywords/ordinal-data","display_name":"Ordinal data","score":0.6661993265151978},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5938096642494202},{"id":"https://openalex.org/keywords/ranking","display_name":"Ranking (information retrieval)","score":0.5899763703346252},{"id":"https://openalex.org/keywords/ordinal-regression","display_name":"Ordinal regression","score":0.571699321269989},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.5716271996498108},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.4998471736907959},{"id":"https://openalex.org/keywords/ordinal-scale","display_name":"Ordinal Scale","score":0.4852316379547119},{"id":"https://openalex.org/keywords/similarity","display_name":"Similarity (geometry)","score":0.47282207012176514},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.45289909839630127},{"id":"https://openalex.org/keywords/ordinal-optimization","display_name":"Ordinal optimization","score":0.43303412199020386},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.41196587681770325},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.41091787815093994},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37990936636924744},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.35033607482910156},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34368133544921875},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.25751394033432007},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.20391258597373962},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.19732755422592163},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08603206276893616}],"concepts":[{"id":"https://openalex.org/C91682802","wikidata":"https://www.wikidata.org/wiki/Q620538","display_name":"Multidimensional scaling","level":2,"score":0.7350703477859497},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.6997605562210083},{"id":"https://openalex.org/C85461838","wikidata":"https://www.wikidata.org/wiki/Q7100785","display_name":"Ordinal data","level":2,"score":0.6661993265151978},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5938096642494202},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.5899763703346252},{"id":"https://openalex.org/C110313322","wikidata":"https://www.wikidata.org/wiki/Q7100793","display_name":"Ordinal regression","level":2,"score":0.571699321269989},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.5716271996498108},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.4998471736907959},{"id":"https://openalex.org/C2909711754","wikidata":"https://www.wikidata.org/wiki/Q7100785","display_name":"Ordinal Scale","level":2,"score":0.4852316379547119},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.47282207012176514},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.45289909839630127},{"id":"https://openalex.org/C81386100","wikidata":"https://www.wikidata.org/wiki/Q7100792","display_name":"Ordinal optimization","level":3,"score":0.43303412199020386},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.41196587681770325},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.41091787815093994},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37990936636924744},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.35033607482910156},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34368133544921875},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.25751394033432007},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.20391258597373962},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.19732755422592163},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08603206276893616},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0217595921500330","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0217595921500330","pdf_url":null,"source":{"id":"https://openalex.org/S1254427","display_name":"Asia Pacific Journal of Operational Research","issn_l":"0217-5959","issn":["0217-5959","1793-7019"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asia-Pacific Journal of Operational Research","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:wsi:apjorx:v:39:y:2022:i:03:n:s0217595921500330","is_oa":false,"landing_page_url":"http://www.worldscientific.com/doi/abs/10.1142/S0217595921500330","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3734132368","display_name":null,"funder_award_id":"12071032","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W91728630","https://openalex.org/W1480382098","https://openalex.org/W1485321296","https://openalex.org/W1657174467","https://openalex.org/W1970503897","https://openalex.org/W1973192023","https://openalex.org/W1981036287","https://openalex.org/W1990908167","https://openalex.org/W1993436046","https://openalex.org/W1998167411","https://openalex.org/W2003677307","https://openalex.org/W2007304358","https://openalex.org/W2037402401","https://openalex.org/W2041814638","https://openalex.org/W2061681393","https://openalex.org/W2145505545","https://openalex.org/W2152825437","https://openalex.org/W2169371330","https://openalex.org/W2322097777","https://openalex.org/W2327230547","https://openalex.org/W2465368474","https://openalex.org/W2621372483","https://openalex.org/W2784477471","https://openalex.org/W2809824420","https://openalex.org/W2935924221","https://openalex.org/W2953018250","https://openalex.org/W3017769143","https://openalex.org/W3105700407","https://openalex.org/W4205622916","https://openalex.org/W4249142012","https://openalex.org/W4251142838","https://openalex.org/W4255902166","https://openalex.org/W4256550993"],"related_works":["https://openalex.org/W3021328243","https://openalex.org/W2051517726","https://openalex.org/W66181126","https://openalex.org/W2093964375","https://openalex.org/W2166716405","https://openalex.org/W2023060082","https://openalex.org/W2506242593","https://openalex.org/W4236508908","https://openalex.org/W27744225","https://openalex.org/W3092459516"],"abstract_inverted_index":{"Multidimensional":[0],"scaling":[1,50],"(MDS)":[2],"is":[3,41,52,70,150],"to":[4,54,71,144,151],"recover":[5],"a":[6,136],"set":[7],"of":[8,13,38,62,68,76,89,123,127,183],"points":[9],"by":[10,59],"making":[11],"use":[12,61],"noised":[14],"pairwise":[15],"Euclidean":[16,23,108],"distances.":[17],"In":[18,33,100],"some":[19],"situations,":[20],"the":[21,36,39,63,73,124,132,153,160,181,184,188],"observed":[22],"distances":[24,40,80],"may":[25],"contain":[26],"large":[27,74,125],"errors":[28],"or":[29],"even":[30],"missing":[31],"values.":[32],"such":[34],"cases,":[35],"order":[37],"far":[42],"more":[43],"important":[44],"than":[45],"their":[46],"magnitude.":[47],"Non-metric":[48],"multidimensional":[49],"(NMDS)":[51],"then":[53,140],"deal":[55],"with":[56],"this":[57,86,101],"problem":[58,156],"taking":[60],"ordinal":[64,77,106,117,128,133],"information.":[65],"The":[66,147,178],"challenge":[67],"NMDS":[69,158],"tackle":[72,131],"number":[75,126],"constraints":[78,129,134],"on":[79,168],"(for":[81],"[Formula:":[82,90],"see":[83,91],"text]":[84],"points,":[85],"will":[87,94],"be":[88],"text]),":[92],"which":[93],"slow":[95],"down":[96],"existing":[97,189],"numerical":[98,166],"algorithms.":[99],"paper,":[102],"we":[103,120],"propose":[104],"an":[105,116],"weighted":[107,118],"distance":[109],"matrix":[110],"model":[111,143],"for":[112],"NMDS.":[113],"By":[114],"designing":[115],"matrix,":[119],"get":[121],"rid":[122],"and":[130,175],"in":[135,159],"soft":[137],"way.":[138],"We":[139,163],"apply":[141],"our":[142],"image":[145,154],"ranking.":[146],"key":[148],"insight":[149],"view":[152],"ranking":[155],"as":[157],"kernel":[161],"space.":[162],"conduct":[164],"extensive":[165],"test":[167],"two":[169],"state-of-the-art":[170],"datasets:":[171],"FG-NET":[172],"aging":[173],"dataset":[174],"MSRA-MM":[176],"dataset.":[177],"results":[179],"show":[180],"improvement":[182],"proposed":[185],"approach":[186],"over":[187],"methods.":[190]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}