{"id":"https://openalex.org/W1895508850","doi":"https://doi.org/10.1109/cvpr.2015.7298847","title":"Beyond Mahalanobis metric: Cayley-Klein metric learning","display_name":"Beyond Mahalanobis metric: Cayley-Klein metric learning","publication_year":2015,"publication_date":"2015-06-01","ids":{"openalex":"https://openalex.org/W1895508850","doi":"https://doi.org/10.1109/cvpr.2015.7298847","mag":"1895508850"},"language":"en","primary_location":{"id":"doi:10.1109/cvpr.2015.7298847","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2015.7298847","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)","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/I4210094879","display_name":"Shandong Institute of Automation","ror":"https://ror.org/00qdtba35","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210094879","https://openalex.org/I4210142748"]},{"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":true,"raw_author_name":"Yanhong Bi","raw_affiliation_strings":["Institute of Automation, Chinese Academy of Sciences, Beijing, China","Institute of Automation Chinese Academy of Sciences, Beijing, 100190, CHINA"],"affiliations":[{"raw_affiliation_string":"Institute of Automation, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210094879","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Institute of Automation Chinese Academy of Sciences, Beijing, 100190, CHINA","institution_ids":[]}]},{"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/I4210094879","display_name":"Shandong Institute of Automation","ror":"https://ror.org/00qdtba35","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210094879","https://openalex.org/I4210142748"]},{"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":["Institute of Automation, Chinese Academy of Sciences, Beijing, China","Institute of Automation Chinese Academy of Sciences, Beijing, 100190, CHINA"],"affiliations":[{"raw_affiliation_string":"Institute of Automation, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210094879","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Institute of Automation Chinese Academy of Sciences, Beijing, 100190, CHINA","institution_ids":[]}]},{"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/I4210094879","display_name":"Shandong Institute of Automation","ror":"https://ror.org/00qdtba35","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210094879","https://openalex.org/I4210142748"]},{"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":["Institute of Automation, Chinese Academy of Sciences, Beijing, China","Institute of Automation Chinese Academy of Sciences, Beijing, 100190, CHINA"],"affiliations":[{"raw_affiliation_string":"Institute of Automation, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210094879","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Institute of Automation Chinese Academy of Sciences, Beijing, 100190, CHINA","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5036068443"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210094879"],"apc_list":null,"apc_paid":null,"fwci":1.8718,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.90216231,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"2339","last_page":"2347"},"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":0.951200008392334,"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":0.951200008392334,"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/mahalanobis-distance","display_name":"Mahalanobis distance","score":0.8714414238929749},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.7585530281066895},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6224969625473022},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.6076838374137878},{"id":"https://openalex.org/keywords/convex-metric-space","display_name":"Convex metric space","score":0.5656507015228271},{"id":"https://openalex.org/keywords/equivalence-of-metrics","display_name":"Equivalence of metrics","score":0.5599948763847351},{"id":"https://openalex.org/keywords/injective-metric-space","display_name":"Injective metric space","score":0.4583120048046112},{"id":"https://openalex.org/keywords/fisher-information-metric","display_name":"Fisher information metric","score":0.44633281230926514},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.43760475516319275},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.4324500262737274},{"id":"https://openalex.org/keywords/metric-differential","display_name":"Metric differential","score":0.4315982460975647},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4206997752189636},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.40145865082740784},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3635389804840088},{"id":"https://openalex.org/keywords/intrinsic-metric","display_name":"Intrinsic metric","score":0.34998953342437744},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32428494095802307},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3015492260456085},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12097316980361938},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11069250106811523},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09265142679214478}],"concepts":[{"id":"https://openalex.org/C1921717","wikidata":"https://www.wikidata.org/wiki/Q1334846","display_name":"Mahalanobis distance","level":2,"score":0.8714414238929749},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.7585530281066895},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6224969625473022},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.6076838374137878},{"id":"https://openalex.org/C196613150","wikidata":"https://www.wikidata.org/wiki/Q3966092","display_name":"Convex metric space","level":3,"score":0.5656507015228271},{"id":"https://openalex.org/C191226916","wikidata":"https://www.wikidata.org/wiki/Q5384710","display_name":"Equivalence of metrics","level":4,"score":0.5599948763847351},{"id":"https://openalex.org/C177547787","wikidata":"https://www.wikidata.org/wiki/Q6034319","display_name":"Injective metric space","level":3,"score":0.4583120048046112},{"id":"https://openalex.org/C127104897","wikidata":"https://www.wikidata.org/wiki/Q5454858","display_name":"Fisher information metric","level":4,"score":0.44633281230926514},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.43760475516319275},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.4324500262737274},{"id":"https://openalex.org/C146562557","wikidata":"https://www.wikidata.org/wiki/Q1925669","display_name":"Metric differential","level":5,"score":0.4315982460975647},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4206997752189636},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.40145865082740784},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3635389804840088},{"id":"https://openalex.org/C41261874","wikidata":"https://www.wikidata.org/wiki/Q3855712","display_name":"Intrinsic metric","level":4,"score":0.34998953342437744},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32428494095802307},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3015492260456085},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12097316980361938},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11069250106811523},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09265142679214478},{"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:10.1109/cvpr.2015.7298847","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cvpr.2015.7298847","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.1032.6639","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1032.6639","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cv-foundation.org/openaccess/content_cvpr_2015/papers/Bi_Beyond_Mahalanobis_Metric_2015_CVPR_paper.pdf","raw_type":"text"}],"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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W1532499126","https://openalex.org/W1544007523","https://openalex.org/W1546430343","https://openalex.org/W1566135517","https://openalex.org/W1620759536","https://openalex.org/W2032942379","https://openalex.org/W2048110836","https://openalex.org/W2072184377","https://openalex.org/W2076434944","https://openalex.org/W2083621124","https://openalex.org/W2091632079","https://openalex.org/W2100799972","https://openalex.org/W2106053110","https://openalex.org/W2111286903","https://openalex.org/W2111654153","https://openalex.org/W2114217318","https://openalex.org/W2117154949","https://openalex.org/W2118393783","https://openalex.org/W2122111042","https://openalex.org/W2125044442","https://openalex.org/W2129156852","https://openalex.org/W2129476886","https://openalex.org/W2140376886","https://openalex.org/W2144935315","https://openalex.org/W2145773134","https://openalex.org/W2150470820","https://openalex.org/W2158320292","https://openalex.org/W2164031334","https://openalex.org/W2169495281","https://openalex.org/W2294130536","https://openalex.org/W2536626143","https://openalex.org/W3099514962","https://openalex.org/W3144613155","https://openalex.org/W4211105492","https://openalex.org/W4250857377","https://openalex.org/W6631637103","https://openalex.org/W6632543029","https://openalex.org/W6632558652","https://openalex.org/W6636582384","https://openalex.org/W6675751002","https://openalex.org/W6676794045","https://openalex.org/W6677328822","https://openalex.org/W6677884823","https://openalex.org/W6678848024","https://openalex.org/W6680832709","https://openalex.org/W6680962578","https://openalex.org/W6681440187","https://openalex.org/W6682131137"],"related_works":["https://openalex.org/W2947185879","https://openalex.org/W4363675004","https://openalex.org/W2987243377","https://openalex.org/W2048731283","https://openalex.org/W4255883801","https://openalex.org/W2398868469","https://openalex.org/W2565930412","https://openalex.org/W2995145105","https://openalex.org/W2389830804","https://openalex.org/W2095137273"],"abstract_inverted_index":{"Cayley-Klein":[0,68,73,78,87,97],"metric":[1,7,26,52,61,69,74,79,88,98],"is":[2,47],"a":[3,24,48],"kind":[4],"of":[5,50,67,86,95],"non-Euclidean":[6,44],"suitable":[8],"for":[9],"projective":[10],"space.":[11],"In":[12],"this":[13],"paper,":[14],"we":[15,63],"introduce":[16],"it":[17,46],"into":[18],"the":[19,31,84,93],"computer":[20],"vision":[21],"community":[22],"as":[23,58],"powerful":[25],"and":[27,76,92],"an":[28],"alternative":[29],"to":[30],"widely":[32],"studied":[33],"Mahalanobis":[34,51,60,90],"metric.":[35],"We":[36],"show":[37],"that":[38],"besides":[39],"its":[40],"good":[41],"characteristic":[42],"in":[43,53],"space,":[45],"generalization":[49],"some":[54],"specific":[55],"cases.":[56],"Furthermore,":[57],"many":[59],"learning,":[62],"give":[64],"two":[65],"kinds":[66],"learning":[70,75,99],"methods:":[71],"MMC":[72],"LMNN":[77],"learning.":[80],"Experiments":[81],"have":[82],"shown":[83],"superiority":[85],"over":[89],"ones":[91],"effectiveness":[94],"our":[96],"methods.":[100]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
