{"id":"https://openalex.org/W2944220395","doi":"https://doi.org/10.1145/3314203","title":"Variant Grassmann Manifolds","display_name":"Variant Grassmann Manifolds","publication_year":2019,"publication_date":"2019-04-30","ids":{"openalex":"https://openalex.org/W2944220395","doi":"https://doi.org/10.1145/3314203","mag":"2944220395"},"language":"en","primary_location":{"id":"doi:10.1145/3314203","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3314203","pdf_url":null,"source":{"id":"https://openalex.org/S41523882","display_name":"ACM Transactions on Knowledge Discovery from Data","issn_l":"1556-4681","issn":["1556-4681","1556-472X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Knowledge Discovery from Data","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/A5071064449","display_name":"Junyuan Hong","orcid":"https://orcid.org/0000-0002-5718-5187"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Junyuan Hong","raw_affiliation_strings":["University of Science and Technology of China, Anhui, China"],"affiliations":[{"raw_affiliation_string":"University of Science and Technology of China, Anhui, China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100341561","display_name":"Yang Li","orcid":"https://orcid.org/0000-0002-6259-8242"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yang Li","raw_affiliation_strings":["University of Science and Technology of China, Anhui, China"],"affiliations":[{"raw_affiliation_string":"University of Science and Technology of China, Anhui, China","institution_ids":["https://openalex.org/I126520041"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100605447","display_name":"Huanhuan Chen","orcid":"https://orcid.org/0000-0002-3918-384X"},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Huanhuan Chen","raw_affiliation_strings":["University of Science and Technology of China, Anhui, China"],"affiliations":[{"raw_affiliation_string":"University of Science and Technology of China, Anhui, China","institution_ids":["https://openalex.org/I126520041"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5071064449"],"corresponding_institution_ids":["https://openalex.org/I126520041"],"apc_list":null,"apc_paid":null,"fwci":1.3309,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.84439536,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"13","issue":"2","first_page":"1","last_page":"23"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10812","display_name":"Human Pose and Action Recognition","score":0.9997000098228455,"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/T10812","display_name":"Human Pose and Action Recognition","score":0.9997000098228455,"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":0.996399998664856,"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"}},{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.994700014591217,"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/linear-subspace","display_name":"Linear subspace","score":0.8240193128585815},{"id":"https://openalex.org/keywords/softmax-function","display_name":"Softmax function","score":0.7364176511764526},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.7209277153015137},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6580014824867249},{"id":"https://openalex.org/keywords/orthonormal-basis","display_name":"Orthonormal basis","score":0.6464713215827942},{"id":"https://openalex.org/keywords/grassmannian","display_name":"Grassmannian","score":0.6265776753425598},{"id":"https://openalex.org/keywords/manifold","display_name":"Manifold (fluid mechanics)","score":0.5437695980072021},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5410813689231873},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5059091448783875},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.47942060232162476},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4572993218898773},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.43196630477905273},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3451656401157379},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.25670915842056274},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.16570106148719788},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.13296321034431458},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13238874077796936}],"concepts":[{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.8240193128585815},{"id":"https://openalex.org/C188441871","wikidata":"https://www.wikidata.org/wiki/Q7554146","display_name":"Softmax function","level":3,"score":0.7364176511764526},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.7209277153015137},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6580014824867249},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.6464713215827942},{"id":"https://openalex.org/C162929932","wikidata":"https://www.wikidata.org/wiki/Q129638","display_name":"Grassmannian","level":2,"score":0.6265776753425598},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.5437695980072021},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5410813689231873},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5059091448783875},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.47942060232162476},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4572993218898773},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.43196630477905273},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3451656401157379},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.25670915842056274},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.16570106148719788},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.13296321034431458},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13238874077796936},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3314203","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3314203","pdf_url":null,"source":{"id":"https://openalex.org/S41523882","display_name":"ACM Transactions on Knowledge Discovery from Data","issn_l":"1556-4681","issn":["1556-4681","1556-472X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Knowledge Discovery from Data","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.5299999713897705}],"awards":[{"id":"https://openalex.org/G8125077543","display_name":null,"funder_award_id":"91846111 and 91746209","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8805597337","display_name":null,"funder_award_id":"2017YFC0804003","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W1583837637","https://openalex.org/W1627755346","https://openalex.org/W1804110266","https://openalex.org/W1922045146","https://openalex.org/W1922659888","https://openalex.org/W1966521860","https://openalex.org/W1973532874","https://openalex.org/W1984798172","https://openalex.org/W1995113806","https://openalex.org/W2008765809","https://openalex.org/W2008824967","https://openalex.org/W2023927582","https://openalex.org/W2037756434","https://openalex.org/W2045512849","https://openalex.org/W2062950526","https://openalex.org/W2066986622","https://openalex.org/W2073139398","https://openalex.org/W2075295044","https://openalex.org/W2078885226","https://openalex.org/W2085735683","https://openalex.org/W2096418885","https://openalex.org/W2104867159","https://openalex.org/W2113592754","https://openalex.org/W2114296159","https://openalex.org/W2126017757","https://openalex.org/W2138451337","https://openalex.org/W2142040002","https://openalex.org/W2143004591","https://openalex.org/W2143267104","https://openalex.org/W2144380653","https://openalex.org/W2145546283","https://openalex.org/W2149338181","https://openalex.org/W2158542502","https://openalex.org/W2169251375","https://openalex.org/W2182587296","https://openalex.org/W2221226740","https://openalex.org/W2233545183","https://openalex.org/W2250968750","https://openalex.org/W2268980625","https://openalex.org/W2297328716","https://openalex.org/W2531563875","https://openalex.org/W2560018085","https://openalex.org/W2584419447","https://openalex.org/W2604863233","https://openalex.org/W2780602937","https://openalex.org/W2785577567","https://openalex.org/W2912155302","https://openalex.org/W3102475017","https://openalex.org/W4205293427"],"related_works":["https://openalex.org/W2949616856","https://openalex.org/W1804640662","https://openalex.org/W2146523743","https://openalex.org/W2287336960","https://openalex.org/W2963346868","https://openalex.org/W2074005788","https://openalex.org/W3159603713","https://openalex.org/W112369303","https://openalex.org/W2057238507","https://openalex.org/W4293570198"],"abstract_inverted_index":{"In":[0,35],"classification":[1,161],"tasks,":[2],"classifiers":[3,166],"trained":[4],"with":[5,14,175],"finite":[6],"examples":[7,29],"might":[8],"generalize":[9],"poorly":[10],"to":[11,32,114,128,173],"new":[12],"data":[13,20,42,97],"unknown":[15],"variance.":[16],"For":[17],"this":[18,36],"issue,":[19],"augmentation":[21,43],"is":[22,83,141],"a":[23,71,115,132,176],"successful":[24],"solution":[25],"where":[26,51],"numerous":[27],"artificial":[28],"are":[30,54],"added":[31],"training":[33],"sets.":[34],"article,":[37],"we":[38,105],"focus":[39],"on":[40,135],"the":[41,46,92,136,144],"for":[44],"improving":[45],"accuracy":[47],"of":[48,94,138,157],"action":[49,52,121],"recognition,":[50],"videos":[53],"modeled":[55],"by":[56],"linear":[57,64],"dynamical":[58],"systems":[59],"and":[60,153,159],"approximately":[61],"represented":[62],"as":[63,79,123],"subspaces.":[65],"These":[66],"subspace":[67,139],"representations":[68],"lie":[69],"in":[70],"non-Euclidean":[72],"space,":[73],"named":[74],"Grassmann":[75,110,125],"manifold,":[76],"containing":[77],"points":[78,126],"orthonormal":[80],"matrixes.":[81],"It":[82],"our":[84],"concern":[85],"that":[86,163],"poor":[87],"generalization":[88],"may":[89],"result":[90],"from":[91,99],"variance":[93],"manifolds":[95,111],"when":[96],"come":[98],"different":[100,124],"sources":[101],"or":[102],"classes.":[103],"Thus,":[104],"introduce":[106],"infinitely":[107],"many":[108],"variant":[109],"(VGM)":[112],"subject":[113],"known":[116],"distribution,":[117],"then":[118],"represent":[119],"each":[120],"video":[122],"leading":[127],"augmented":[129],"representations.":[130],"Furthermore,":[131],"prior":[133],"based":[134],"stability":[137],"bases":[140],"introduced,":[142],"so":[143],"manifold":[145],"distribution":[146],"can":[147],"be":[148],"adaptively":[149],"determined,":[150],"balancing":[151],"discrimination":[152],"representation.":[154],"Experimental":[155],"results":[156],"multi-class":[158],"multi-source":[160],"show":[162],"VGM":[164],"softmax":[165],"achieve":[167],"lower":[168],"test":[169],"error":[170],"rates":[171],"compared":[172],"methods":[174],"single":[177],"manifold.":[178]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":6}],"updated_date":"2026-04-03T22:45:19.894376","created_date":"2025-10-10T00:00:00"}