{"id":"https://openalex.org/W4226245241","doi":"https://doi.org/10.1109/access.2022.3170712","title":"Dictionary Learning of Symmetric Positive Definite Data Based on Riemannian Manifold Tangent Spaces and Local Homeomorphism","display_name":"Dictionary Learning of Symmetric Positive Definite Data Based on Riemannian Manifold Tangent Spaces and Local Homeomorphism","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4226245241","doi":"https://doi.org/10.1109/access.2022.3170712"},"language":"en","primary_location":{"id":"doi:10.1109/access.2022.3170712","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2022.3170712","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/9668973/09763529.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/9668973/09763529.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002614753","display_name":"Hui He","orcid":"https://orcid.org/0000-0002-9830-1076"},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hui He","raw_affiliation_strings":["School of Electronics and Information Technology, Sun Yat-Sen University, Guangzhou, China"],"affiliations":[{"raw_affiliation_string":"School of Electronics and Information Technology, Sun Yat-Sen University, Guangzhou, China","institution_ids":["https://openalex.org/I157773358"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001120037","display_name":"Shuyu Liu","orcid":"https://orcid.org/0000-0002-0230-1400"},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shuyu Liu","raw_affiliation_strings":["Public Experimental Teaching Center, Sun Yat-sen University, Guangzhou, China"],"affiliations":[{"raw_affiliation_string":"Public Experimental Teaching Center, Sun Yat-sen University, Guangzhou, China","institution_ids":["https://openalex.org/I157773358"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077902355","display_name":"Zhengming Ma","orcid":"https://orcid.org/0000-0001-6553-1070"},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhengming Ma","raw_affiliation_strings":["School of Electronics and Information Technology, Sun Yat-Sen University, Guangzhou, China"],"affiliations":[{"raw_affiliation_string":"School of Electronics and Information Technology, Sun Yat-Sen University, Guangzhou, China","institution_ids":["https://openalex.org/I157773358"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070732947","display_name":"Weijia Feng","orcid":"https://orcid.org/0000-0003-2362-1304"},"institutions":[{"id":"https://openalex.org/I4210136246","display_name":"China Telecom (China)","ror":"https://ror.org/03jgnzt20","country_code":"CN","type":"company","lineage":["https://openalex.org/I4210136246"]},{"id":"https://openalex.org/I4387153335","display_name":"China Telecom","ror":"https://ror.org/05p67dv18","country_code":null,"type":"company","lineage":["https://openalex.org/I4387153335"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weijia Feng","raw_affiliation_strings":["China Telecom Cloud Technology Company Ltd., Guangzhou, China"],"affiliations":[{"raw_affiliation_string":"China Telecom Cloud Technology Company Ltd., Guangzhou, China","institution_ids":["https://openalex.org/I4210136246","https://openalex.org/I4387153335"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5002614753"],"corresponding_institution_ids":["https://openalex.org/I157773358"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03148628,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"10","issue":null,"first_page":"46114","last_page":"46127"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9944999814033508,"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/T10057","display_name":"Face and Expression Recognition","score":0.9944999814033508,"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":0.9889000058174133,"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/T12740","display_name":"Gait Recognition and Analysis","score":0.9812999963760376,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/reproducing-kernel-hilbert-space","display_name":"Reproducing kernel Hilbert space","score":0.7818388938903809},{"id":"https://openalex.org/keywords/tangent-space","display_name":"Tangent space","score":0.726426362991333},{"id":"https://openalex.org/keywords/riemannian-manifold","display_name":"Riemannian manifold","score":0.6251898407936096},{"id":"https://openalex.org/keywords/tangent-vector","display_name":"Tangent vector","score":0.617069661617279},{"id":"https://openalex.org/keywords/hilbert-manifold","display_name":"Hilbert manifold","score":0.5881699323654175},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.55134516954422},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5280795097351074},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.5158792734146118},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.5142049789428711},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5067699551582336},{"id":"https://openalex.org/keywords/parallelizable-manifold","display_name":"Parallelizable manifold","score":0.49950742721557617},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.4828636944293976},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4214969575405121},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.39485931396484375},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3584074378013611},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.346707820892334},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3402445316314697},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2382526993751526},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11098074913024902}],"concepts":[{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.7818388938903809},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.726426362991333},{"id":"https://openalex.org/C2779593128","wikidata":"https://www.wikidata.org/wiki/Q632814","display_name":"Riemannian manifold","level":2,"score":0.6251898407936096},{"id":"https://openalex.org/C47890412","wikidata":"https://www.wikidata.org/wiki/Q1179296","display_name":"Tangent vector","level":3,"score":0.617069661617279},{"id":"https://openalex.org/C147493315","wikidata":"https://www.wikidata.org/wiki/Q3554824","display_name":"Hilbert manifold","level":3,"score":0.5881699323654175},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.55134516954422},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5280795097351074},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.5158792734146118},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5142049789428711},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5067699551582336},{"id":"https://openalex.org/C148047603","wikidata":"https://www.wikidata.org/wiki/Q1014612","display_name":"Parallelizable manifold","level":2,"score":0.49950742721557617},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.4828636944293976},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4214969575405121},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.39485931396484375},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3584074378013611},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.346707820892334},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3402445316314697},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2382526993751526},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11098074913024902},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2022.3170712","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2022.3170712","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/9668973/09763529.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:c56474e36ea843afb57e8f6d6c7173fc","is_oa":true,"landing_page_url":"https://doaj.org/article/c56474e36ea843afb57e8f6d6c7173fc","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 10, Pp 46114-46127 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2022.3170712","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2022.3170712","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/9668973/09763529.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1121271761","display_name":null,"funder_award_id":"Program","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1231421488","display_name":null,"funder_award_id":"under","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G37568934","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5939423041","display_name":null,"funder_award_id":"Technology","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7719176616","display_name":null,"funder_award_id":"61773022","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":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4226245241.pdf","grobid_xml":"https://content.openalex.org/works/W4226245241.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W92310073","https://openalex.org/W191001584","https://openalex.org/W585133165","https://openalex.org/W1508406818","https://openalex.org/W1515954165","https://openalex.org/W1591717461","https://openalex.org/W1606263802","https://openalex.org/W1964321627","https://openalex.org/W1983496390","https://openalex.org/W2004996467","https://openalex.org/W2006793117","https://openalex.org/W2025805530","https://openalex.org/W2070262181","https://openalex.org/W2092535060","https://openalex.org/W2103096501","https://openalex.org/W2116836863","https://openalex.org/W2122378993","https://openalex.org/W2125389556","https://openalex.org/W2140245639","https://openalex.org/W2148029428","https://openalex.org/W2165797462","https://openalex.org/W2167164761","https://openalex.org/W2242953327","https://openalex.org/W2315814222","https://openalex.org/W2321395385","https://openalex.org/W2600467585","https://openalex.org/W2797867454","https://openalex.org/W2897484797","https://openalex.org/W2959706953","https://openalex.org/W2962905348","https://openalex.org/W2964009357","https://openalex.org/W2972522811","https://openalex.org/W3014226319"],"related_works":["https://openalex.org/W2361271799","https://openalex.org/W1598317013","https://openalex.org/W4249328994","https://openalex.org/W3019892541","https://openalex.org/W1985723153","https://openalex.org/W3135467630","https://openalex.org/W3009871337","https://openalex.org/W2379038002","https://openalex.org/W2948326635","https://openalex.org/W4226245241"],"abstract_inverted_index":{"Symmetric":[0],"Positive":[1],"Definite":[2],"(SPD)":[3],"data":[4,13,18,233,252,265,301],"are":[5,14,272],"increasingly":[6],"prevalent":[7],"in":[8,64,230],"dictionary":[9,27,69,85,256,269,302],"learning":[10,28,70,86,115,138,303],"recently.":[11],"SPD":[12,35,76,89,251,264,300],"the":[15,65,68,95,160,164,171,177,181,185,190,193,198,201,219,231,235,240,261,285],"typical":[16],"non-Euclidean":[17,140],"and":[19,176,253,266],"cannot":[20,30],"constitute":[21],"a":[22,60,83,106,132,148,151,204,244,296],"Euclidean":[23,61,111,119],"space.":[24],"Therefore,":[25],"many":[26],"algorithms":[29,116],"be":[31,72,122,228],"directly":[32,73,123],"adopted":[33],"on":[34,75,94,105,118,150,163,279],"data.":[36,77,141],"Reproducing":[37],"Kernel":[38],"Hilbert":[39,56,108],"Spaces":[40],"(RKHS)":[41],"is":[42,53,92,103],"now":[43],"commonly":[44],"used":[45,74],"to":[46,71,125,197,227],"deal":[47],"with":[48,180],"this":[49,79],"problem.":[50],"However,":[51],"RKHS":[52,220],"an":[54,155,210],"infinite-dimensional":[55],"space,":[57,62,109,112],"rather":[58],"than":[59],"resulting":[63],"inability":[66],"of":[67,129,139,170,192,200,247,263],"In":[78,238],"paper,":[80],"we":[81],"propose":[82],"novel":[84],"algorithm":[87,242,287],"for":[88,136],"data,":[90],"which":[91],"based":[93,104],"Riemannian":[96,152,165],"Manifold":[97],"Tangent":[98],"Space":[99],"(RMTS).":[100],"Since":[101],"RMTS":[102,130,144,255,268],"finite-dimensional":[107],"i.e.,":[110],"most":[113],"machine":[114,137],"developed":[117],"space":[120],"can":[121],"applied":[124],"RMTS.":[126],"The":[127,142],"introduction":[128],"provides":[131],"better":[133],"mathematical":[134],"platform":[135],"proposed":[143,241,286],"method":[145,221],"first":[146],"selects":[147],"point":[149],"manifold":[153,166],"as":[154,215,273,275],"anchor":[156,178,186],"point.":[157,187],"It":[158],"transforms":[159],"other":[161],"points":[162,175],"into":[167],"tangent":[168,182,194,207],"vectors":[169,183,208],"geodesics":[172],"between":[173,250],"these":[174],"point,":[179],"at":[184],"We":[188],"set":[189],"length":[191,199],"vector":[195],"equal":[196],"geodesic.":[202],"As":[203],"result,":[205],"such":[206,214],"have":[209],"explicit":[211],"geometric":[212,225],"meaning,":[213],"direction":[216],"information,":[217],"while":[218],"may":[222],"cause":[223],"some":[224],"meaning":[226],"lost":[229],"original":[232],"during":[234],"mapping":[236],"process.":[237],"addition,":[239],"adds":[243],"regular":[245],"term":[246],"local":[248],"homomorphism":[249],"its":[254,267],"coding":[257,270],"coefficients,":[258],"so":[259],"that":[260,284],"similarity":[262],"coefficients":[271],"close":[274],"possible.":[276],"Experimental":[277],"results":[278],"four":[280],"public":[281],"datasets":[282],"demonstrate":[283],"significantly":[288],"outperforms":[289],"five":[290],"state-of-the-art":[291],"algorithms.":[292],"This":[293],"work":[294],"opens":[295],"new":[297],"pathway":[298],"towards":[299],"methods.":[304]},"counts_by_year":[],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}
