{"id":"https://openalex.org/W2902132144","doi":"https://doi.org/10.1109/icpr.2018.8546152","title":"Cayley- Klein Metric Learning with Shrinkage-Expansion Constraints","display_name":"Cayley- Klein Metric Learning with Shrinkage-Expansion Constraints","publication_year":2018,"publication_date":"2018-08-01","ids":{"openalex":"https://openalex.org/W2902132144","doi":"https://doi.org/10.1109/icpr.2018.8546152","mag":"2902132144"},"language":"en","primary_location":{"id":"doi:10.1109/icpr.2018.8546152","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icpr.2018.8546152","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 24th International Conference on Pattern Recognition (ICPR)","raw_type":"proceedings-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/A5036068443","display_name":"Yanhong Bi","orcid":null},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yanhong Bi","raw_affiliation_strings":["University of Chinese Academy of Sciences, Beijing, P.R. China"],"affiliations":[{"raw_affiliation_string":"University of Chinese Academy of Sciences, Beijing, P.R. China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064925158","display_name":"Bin Fan","orcid":"https://orcid.org/0000-0002-1155-467X"},"institutions":[{"id":"https://openalex.org/I4210112150","display_name":"Institute of Automation","ror":"https://ror.org/022c3hy66","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210112150"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bin Fan","raw_affiliation_strings":["National Laboratory of Pattern Recognition, Chinese Academy of Sciences, Beijing, P.R. China"],"affiliations":[{"raw_affiliation_string":"National Laboratory of Pattern Recognition, Chinese Academy of Sciences, Beijing, P.R. China","institution_ids":["https://openalex.org/I4210112150","https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101718805","display_name":"Fuchao Wu","orcid":"https://orcid.org/0000-0002-4365-4843"},"institutions":[{"id":"https://openalex.org/I4210112150","display_name":"Institute of Automation","ror":"https://ror.org/022c3hy66","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210112150"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fuchao Wu","raw_affiliation_strings":["National Laboratory of Pattern Recognition, Chinese Academy of Sciences, Beijing, P.R. China"],"affiliations":[{"raw_affiliation_string":"National Laboratory of Pattern Recognition, Chinese Academy of Sciences, Beijing, P.R. China","institution_ids":["https://openalex.org/I4210112150","https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5036068443"],"corresponding_institution_ids":["https://openalex.org/I4210165038"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1392775,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"42","issue":null,"first_page":"43","last_page":"48"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10627","display_name":"Advanced Image and Video Retrieval Techniques","score":0.9902999997138977,"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"}},"topics":[{"id":"https://openalex.org/T10627","display_name":"Advanced Image and Video Retrieval Techniques","score":0.9902999997138977,"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/T10057","display_name":"Face and Expression Recognition","score":0.9837999939918518,"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/T10331","display_name":"Video Surveillance and Tracking Methods","score":0.9789999723434448,"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/metric","display_name":"Metric (unit)","score":0.7465542554855347},{"id":"https://openalex.org/keywords/pairwise-comparison","display_name":"Pairwise comparison","score":0.7363439798355103},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.5859220623970032},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5401958227157593},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5380039215087891},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.45430877804756165},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.45258814096450806},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.4482472538948059},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3058473467826843},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30547958612442017},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.30355942249298096},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14143097400665283},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.10022097826004028},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09618622064590454}],"concepts":[{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.7465542554855347},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.7363439798355103},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.5859220623970032},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5401958227157593},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5380039215087891},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.45430877804756165},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.45258814096450806},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.4482472538948059},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3058473467826843},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30547958612442017},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.30355942249298096},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14143097400665283},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.10022097826004028},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09618622064590454},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/icpr.2018.8546152","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icpr.2018.8546152","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 24th International Conference on Pattern Recognition (ICPR)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"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":42,"referenced_works":["https://openalex.org/W80869136","https://openalex.org/W162695192","https://openalex.org/W1487156568","https://openalex.org/W1496314943","https://openalex.org/W1546430343","https://openalex.org/W1566135517","https://openalex.org/W1895508850","https://openalex.org/W2005118650","https://openalex.org/W2048110836","https://openalex.org/W2065041032","https://openalex.org/W2083621124","https://openalex.org/W2106053110","https://openalex.org/W2111286903","https://openalex.org/W2111654153","https://openalex.org/W2117154949","https://openalex.org/W2118393783","https://openalex.org/W2122111042","https://openalex.org/W2125044442","https://openalex.org/W2129156852","https://openalex.org/W2151565710","https://openalex.org/W2151624282","https://openalex.org/W2151873133","https://openalex.org/W2169495281","https://openalex.org/W2294130536","https://openalex.org/W2536626143","https://openalex.org/W2757661336","https://openalex.org/W2767809328","https://openalex.org/W2950690897","https://openalex.org/W3144613155","https://openalex.org/W4211105492","https://openalex.org/W6606639828","https://openalex.org/W6628939056","https://openalex.org/W6629770831","https://openalex.org/W6632543029","https://openalex.org/W6639527392","https://openalex.org/W6675751002","https://openalex.org/W6676794045","https://openalex.org/W6677328822","https://openalex.org/W6677884823","https://openalex.org/W6678848024","https://openalex.org/W6682462792","https://openalex.org/W6682811751"],"related_works":["https://openalex.org/W2487162673","https://openalex.org/W2793211469","https://openalex.org/W2949152769","https://openalex.org/W4372354731","https://openalex.org/W2562400057","https://openalex.org/W1692008701","https://openalex.org/W2597588799","https://openalex.org/W4360593462","https://openalex.org/W2894446834","https://openalex.org/W4297851895"],"abstract_inverted_index":{"Cayley-Klein":[0,32,127,161],"metric":[1,8,18,33,128,143,162],"is":[2,138],"a":[3,70,77,87,92,104,113,125],"specific":[4],"kind":[5],"of":[6,57,69,86,103,115],"non-Euclidean":[7],"in":[9,141],"projective":[10],"space.":[11],"Recently,":[12],"it":[13],"has":[14],"been":[15],"introduced":[16],"into":[17],"learning":[19,34,129,142,163],"with":[20,25,36,132,146],"encouraging":[21],"performance":[22,157],"when":[23,52],"dealing":[24],"computer":[26],"vision":[27],"tasks.":[28],"However,":[29],"the":[30,53,65,82,99,159],"original":[31,160],"methods":[35],"conventional":[37],"pairwise":[38,135],"and":[39,81],"triplet-wise":[40],"constraints,":[41,47],"which":[42],"are":[43],"fixed":[44,78,93],"bound":[45],"based":[46],"may":[48],"not":[49],"perform":[50],"well":[51],"intra-and":[54],"inter-class":[55],"variations":[56],"data":[58,145],"distribution":[59],"become":[60],"complex.":[61],"Pairwise":[62],"constraints":[63,97],"restrict":[64,98],"distance":[66,83,100],"between":[67,84,101,112],"samples":[68,85,102,116],"similar":[71,105],"pair":[72,89,106,114],"to":[73,107],"be":[74,108],"lower":[75,94],"than":[76,91,110,158],"upper":[79],"bound,":[80],"dissimilar":[88],"higher":[90],"bound.":[95],"Triplet-wise":[96],"smaller":[109],"that":[111,153],"from":[117,144],"different":[118],"classes.":[119],"In":[120],"this":[121],"paper,":[122],"we":[123],"propose":[124],"novel":[126],"method":[130],"(CKseML)":[131],"adaptive":[133],"shrinkage-expansion":[134],"constraints.":[136],"CKseML":[137,154],"very":[139],"effective":[140],"complex":[147],"distributions.":[148],"Our":[149],"experimental":[150],"results":[151],"demonstrate":[152],"achieves":[155],"better":[156],"methods.":[164]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}