{"id":"https://openalex.org/W4313449746","doi":"https://doi.org/10.1109/tip.2022.3229616","title":"Quaternion Scalar and Vector Norm Decomposition: Quaternion PCA for Color Face Recognition","display_name":"Quaternion Scalar and Vector Norm Decomposition: Quaternion PCA for Color Face Recognition","publication_year":2022,"publication_date":"2022-12-20","ids":{"openalex":"https://openalex.org/W4313449746","doi":"https://doi.org/10.1109/tip.2022.3229616","pmid":"https://pubmed.ncbi.nlm.nih.gov/37015432"},"language":"en","primary_location":{"id":"doi:10.1109/tip.2022.3229616","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2022.3229616","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Image Processing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5041447631","display_name":"Wankai Liu","orcid":"https://orcid.org/0000-0003-4391-8068"},"institutions":[{"id":"https://openalex.org/I59483232","display_name":"Shandong University of Finance and Economics","ror":"https://ror.org/02e2nnq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I59483232"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wankai Liu","raw_affiliation_strings":["School of Statistics and Mathematics, Shandong University of Finance and Economics, Jinan, China"],"raw_orcid":"https://orcid.org/0000-0003-4391-8068","affiliations":[{"raw_affiliation_string":"School of Statistics and Mathematics, Shandong University of Finance and Economics, Jinan, China","institution_ids":["https://openalex.org/I59483232"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016962594","display_name":"Kit Ian Kou","orcid":"https://orcid.org/0000-0003-1924-9087"},"institutions":[{"id":"https://openalex.org/I204512498","display_name":"University of Macau","ror":"https://ror.org/01r4q9n85","country_code":"MO","type":"education","lineage":["https://openalex.org/I204512498"]}],"countries":["MO"],"is_corresponding":false,"raw_author_name":"Kit Ian Kou","raw_affiliation_strings":["Faculty of Science and Technology, University of Macau, Macau, China"],"raw_orcid":"https://orcid.org/0000-0003-1924-9087","affiliations":[{"raw_affiliation_string":"Faculty of Science and Technology, University of Macau, Macau, China","institution_ids":["https://openalex.org/I204512498"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010571667","display_name":"Jifei Miao","orcid":"https://orcid.org/0000-0001-5663-8749"},"institutions":[{"id":"https://openalex.org/I189210763","display_name":"Yunnan University","ror":"https://ror.org/0040axw97","country_code":"CN","type":"education","lineage":["https://openalex.org/I189210763"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jifei Miao","raw_affiliation_strings":["School of Mathematics and Statistics, Yunnan University, Kunming, China"],"raw_orcid":"https://orcid.org/0000-0001-5663-8749","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Yunnan University, Kunming, China","institution_ids":["https://openalex.org/I189210763"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102279417","display_name":"Zhenfeng Cai","orcid":null},"institutions":[{"id":"https://openalex.org/I74525822","display_name":"Hubei University of Technology","ror":"https://ror.org/02d3fj342","country_code":"CN","type":"education","lineage":["https://openalex.org/I74525822"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhenfeng Cai","raw_affiliation_strings":["Faculty of Science, Hubei University of Technology, Wuhan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Science, Hubei University of Technology, Wuhan, China","institution_ids":["https://openalex.org/I74525822"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3808,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.88400038,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"32","issue":null,"first_page":"446","last_page":"457"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9991000294685364,"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":0.9991000294685364,"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":0.9965999722480774,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/quaternion","display_name":"Quaternion","score":0.8857742547988892},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5714214444160461},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5605294108390808},{"id":"https://openalex.org/keywords/principal-component-analysis","display_name":"Principal component analysis","score":0.512155294418335},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.47892698645591736},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.45260539650917053},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.45169445872306824},{"id":"https://openalex.org/keywords/color-image","display_name":"Color image","score":0.42696499824523926},{"id":"https://openalex.org/keywords/facial-recognition-system","display_name":"Facial recognition system","score":0.41933977603912354},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4004395604133606},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.39049673080444336},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3549899458885193},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.3535105884075165},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3243054151535034},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.13508200645446777}],"concepts":[{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.8857742547988892},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5714214444160461},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5605294108390808},{"id":"https://openalex.org/C27438332","wikidata":"https://www.wikidata.org/wiki/Q2873","display_name":"Principal component analysis","level":2,"score":0.512155294418335},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.47892698645591736},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.45260539650917053},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.45169445872306824},{"id":"https://openalex.org/C142616399","wikidata":"https://www.wikidata.org/wiki/Q5148604","display_name":"Color image","level":4,"score":0.42696499824523926},{"id":"https://openalex.org/C31510193","wikidata":"https://www.wikidata.org/wiki/Q1192553","display_name":"Facial recognition system","level":3,"score":0.41933977603912354},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4004395604133606},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.39049673080444336},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3549899458885193},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.3535105884075165},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3243054151535034},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.13508200645446777},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tip.2022.3229616","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tip.2022.3229616","pdf_url":null,"source":{"id":"https://openalex.org/S4210173141","display_name":"IEEE Transactions on Image Processing","issn_l":"1057-7149","issn":["1057-7149","1941-0042"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Image Processing","raw_type":"journal-article"},{"id":"pmid:37015432","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37015432","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on image processing : a publication of the IEEE Signal Processing Society","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1686750431","display_name":null,"funder_award_id":"ZR2021MA038","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G3361674047","display_name":null,"funder_award_id":"BSQD2019052","funder_id":"https://openalex.org/F4320321604","funder_display_name":"Hubei University of Technology"},{"id":"https://openalex.org/G862335472","display_name":null,"funder_award_id":"MYRG2022-00108-FST","funder_id":"https://openalex.org/F4320322841","funder_display_name":"Universidade de Macau"}],"funders":[{"id":"https://openalex.org/F4320321604","display_name":"Hubei University of Technology","ror":"https://ror.org/02d3fj342"},{"id":"https://openalex.org/F4320322841","display_name":"Universidade de Macau","ror":"https://ror.org/01r4q9n85"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1494757229","https://openalex.org/W1568554062","https://openalex.org/W1572131552","https://openalex.org/W1577889082","https://openalex.org/W1803059841","https://openalex.org/W1958349209","https://openalex.org/W1965914766","https://openalex.org/W1968539442","https://openalex.org/W1972673941","https://openalex.org/W1984188356","https://openalex.org/W1985287506","https://openalex.org/W1997011019","https://openalex.org/W2033419168","https://openalex.org/W2033772417","https://openalex.org/W2038502217","https://openalex.org/W2042333532","https://openalex.org/W2058558325","https://openalex.org/W2069165391","https://openalex.org/W2077926306","https://openalex.org/W2089468765","https://openalex.org/W2090550497","https://openalex.org/W2098693229","https://openalex.org/W2102544846","https://openalex.org/W2112828793","https://openalex.org/W2121713720","https://openalex.org/W2129812935","https://openalex.org/W2132467081","https://openalex.org/W2134309331","https://openalex.org/W2162831671","https://openalex.org/W2280409827","https://openalex.org/W2348144522","https://openalex.org/W2618534374","https://openalex.org/W2900378035","https://openalex.org/W2911935942","https://openalex.org/W2974585710","https://openalex.org/W3036076234","https://openalex.org/W3099931851","https://openalex.org/W4205712406"],"related_works":["https://openalex.org/W3127350447","https://openalex.org/W3108700312","https://openalex.org/W2887325221","https://openalex.org/W4225472102","https://openalex.org/W2382948573","https://openalex.org/W2465700534","https://openalex.org/W2388958958","https://openalex.org/W3019147359","https://openalex.org/W3003926144","https://openalex.org/W2809889952"],"abstract_inverted_index":{"This":[0,69],"paper":[1],"proposes":[2],"a":[3,56,65,107,113],"decomposition":[4,11],"called":[5],"quaternion":[6,23,83,108,120],"scalar":[7,100],"and":[8,152],"vector":[9,104,139],"norm":[10,24,141],"(QSVND)":[12],"for":[13,82,125,163],"approximation":[14],"problems":[15,75],"in":[16,77,86],"color":[17,87,114,126,164],"image":[18,88],"processing.":[19,89],"Different":[20],"from":[21],"traditional":[22],"approximations":[25],"that":[26],"are":[27],"always":[28],"the":[29,39,42,52,62,98,103,134,145,157,160],"single":[30],"objective":[31],"models":[32],"(SOM),":[33],"QSVND":[34,118],"is":[35,48,91,109],"adopted":[36],"to":[37,50,93,111,119],"transform":[38],"SOM":[40],"into":[41,64],"bi-objective":[43],"model":[44],"(BOM).":[45],"Furthermore,":[46],"regularization":[47],"used":[49,110],"solve":[51],"BOM":[53,63],"problem":[54],"as":[55],"common":[57],"scalarization":[58],"method,":[59],"which":[60,130],"converts":[61],"more":[66],"reasonable":[67],"SOM.":[68],"can":[70,131],"handle":[71],"over-fitting":[72],"or":[73],"under-fitting":[74,137],"neglected":[76],"this":[78],"kind":[79],"of":[80,106,136,138,159],"research":[81],"representation":[84],"(QR)":[85],"That":[90],"how":[92],"treat":[94],"redundancy":[95],"caused":[96],"by":[97],"extra":[99],"part":[101,105,140],"when":[102],"represent":[112],"pixel.":[115],"We":[116],"apply":[117],"principal":[121],"component":[122],"analysis":[123],"(QPCA)":[124],"face":[127],"recognition":[128],"(FR),":[129],"deal":[132],"with":[133,144],"phenomenon":[135],"approximation.":[142],"Comparisons":[143],"competing":[146],"approaches":[147],"on":[148],"AR,":[149],"FERET,":[150],"FEI,":[151],"KDEF&AKDEF":[153],"databases":[154],"consistently":[155],"show":[156],"superiority":[158],"proposed":[161],"approach":[162],"FR.":[165]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}