{"id":"https://openalex.org/W2160888808","doi":"https://doi.org/10.1109/tpami.2015.2408358","title":"Difference Subspace and Its Generalization for Subspace-Based Methods","display_name":"Difference Subspace and Its Generalization for Subspace-Based Methods","publication_year":2015,"publication_date":"2015-03-03","ids":{"openalex":"https://openalex.org/W2160888808","doi":"https://doi.org/10.1109/tpami.2015.2408358","mag":"2160888808","pmid":"https://pubmed.ncbi.nlm.nih.gov/26440259"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2015.2408358","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2015.2408358","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Pattern Analysis and Machine Intelligence","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/A5101567870","display_name":"Kazuhiro Fukui","orcid":"https://orcid.org/0000-0002-4201-1096"},"institutions":[{"id":"https://openalex.org/I146399215","display_name":"University of Tsukuba","ror":"https://ror.org/02956yf07","country_code":"JP","type":"education","lineage":["https://openalex.org/I146399215"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kazuhiro Fukui","raw_affiliation_strings":["Department of Computer Science, University of Tsukuba, Tsukuba, Japan"],"raw_orcid":"https://orcid.org/0000-0002-4201-1096","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Tsukuba, Tsukuba, Japan","institution_ids":["https://openalex.org/I146399215"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054834085","display_name":"Atsuto Maki","orcid":"https://orcid.org/0000-0002-4266-6746"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Atsuto Maki","raw_affiliation_strings":["School of Computer Science and Communication, KTH Royal Institute of Technology, Stockholm, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science and Communication, KTH Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.8571,"has_fulltext":false,"cited_by_count":87,"citation_normalized_percentile":{"value":0.95758044,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"37","issue":"11","first_page":"2164","last_page":"2177"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9994999766349792,"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":0.9994999766349792,"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/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.9884999990463257,"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/T10689","display_name":"Remote-Sensing Image Classification","score":0.9840999841690063,"subfield":{"id":"https://openalex.org/subfields/2214","display_name":"Media Technology"},"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/linear-subspace","display_name":"Linear subspace","score":0.8926876783370972},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.8818524479866028},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.7035373449325562},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6226713061332703},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.6208192110061646},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5962205529212952},{"id":"https://openalex.org/keywords/random-subspace-method","display_name":"Random subspace method","score":0.5922180414199829},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5769153833389282},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.5363152623176575},{"id":"https://openalex.org/keywords/cognitive-neuroscience-of-visual-object-recognition","display_name":"Cognitive neuroscience of visual object recognition","score":0.4623813033103943},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.43722644448280334},{"id":"https://openalex.org/keywords/object","display_name":"Object (grammar)","score":0.43543165922164917},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.428190678358078},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40226441621780396},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.3246030807495117},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.29126447439193726},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.13570061326026917},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.0822979211807251},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06361150741577148}],"concepts":[{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.8926876783370972},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.8818524479866028},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.7035373449325562},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6226713061332703},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.6208192110061646},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5962205529212952},{"id":"https://openalex.org/C106135958","wikidata":"https://www.wikidata.org/wiki/Q7291993","display_name":"Random subspace method","level":3,"score":0.5922180414199829},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5769153833389282},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.5363152623176575},{"id":"https://openalex.org/C64876066","wikidata":"https://www.wikidata.org/wiki/Q5141226","display_name":"Cognitive neuroscience of visual object recognition","level":3,"score":0.4623813033103943},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.43722644448280334},{"id":"https://openalex.org/C2781238097","wikidata":"https://www.wikidata.org/wiki/Q175026","display_name":"Object (grammar)","level":2,"score":0.43543165922164917},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.428190678358078},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40226441621780396},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.3246030807495117},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29126447439193726},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.13570061326026917},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0822979211807251},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06361150741577148}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tpami.2015.2408358","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2015.2408358","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","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 Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:26440259","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/26440259","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 pattern analysis and machine intelligence","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322509","display_name":"Kungliga Tekniska H\u00f6gskolan","ror":"https://ror.org/026vcq606"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W8105021","https://openalex.org/W1480487340","https://openalex.org/W1506013575","https://openalex.org/W1514458971","https://openalex.org/W1514876195","https://openalex.org/W1550919879","https://openalex.org/W1556074820","https://openalex.org/W1564660545","https://openalex.org/W1591413801","https://openalex.org/W1680583314","https://openalex.org/W1820849028","https://openalex.org/W2025341678","https://openalex.org/W2030328665","https://openalex.org/W2038621421","https://openalex.org/W2059173330","https://openalex.org/W2061360900","https://openalex.org/W2098693229","https://openalex.org/W2101837180","https://openalex.org/W2109885856","https://openalex.org/W2111601379","https://openalex.org/W2117138194","https://openalex.org/W2121647436","https://openalex.org/W2122738838","https://openalex.org/W2123921160","https://openalex.org/W2125874614","https://openalex.org/W2126017757","https://openalex.org/W2129812935","https://openalex.org/W2135346934","https://openalex.org/W2135510656","https://openalex.org/W2140095548","https://openalex.org/W2149338181","https://openalex.org/W2150600350","https://openalex.org/W2157500953","https://openalex.org/W2161347185","https://openalex.org/W2165916500","https://openalex.org/W2171692249","https://openalex.org/W2171849959","https://openalex.org/W2912990735","https://openalex.org/W6633171750","https://openalex.org/W6635390280","https://openalex.org/W6674764012","https://openalex.org/W6677833576"],"related_works":["https://openalex.org/W2896134808","https://openalex.org/W3172436493","https://openalex.org/W4287164812","https://openalex.org/W2007593166","https://openalex.org/W2957492749","https://openalex.org/W1887135636","https://openalex.org/W2386063599","https://openalex.org/W1975884855","https://openalex.org/W2094490861","https://openalex.org/W1603777065"],"abstract_inverted_index":{"Subspace-based":[0],"methods":[1,124],"are":[2,155],"known":[3],"to":[4,93,109,125,138],"provide":[5],"a":[6,25,37,64,75,134,159,182,203],"practical":[7],"solution":[8],"for":[9,28,99],"image":[10,254],"set-based":[11],"object":[12,51,217],"recognition.":[13],"Based":[14],"on":[15,226,241,256],"the":[16,33,40,60,94,104,150,169,175,194,250,257,263],"insight":[17],"that":[18],"local":[19],"shape":[20,87,166,188,224,269],"differences":[21,167,189,210],"between":[22,43,68,78,161,168,190,211],"objects":[23,233],"offer":[24],"sensitive":[26],"cue":[27],"recognition,":[29],"this":[30,108,153],"paper":[31,154],"addresses":[32],"problem":[34],"of":[35,50,54,74,106,117,152,177,187,196,231,239,271],"extracting":[36,209],"subspace":[38,62,97,110,113,201],"representing":[39],"difference":[41,61,76,96],"components":[42],"class":[44,163],"subspaces":[45,70,164],"generated":[46],"from":[47],"each":[48,55],"set":[49],"images":[52,230],"independently":[53],"other.":[56],"We":[57,89,220],"first":[58],"introduce":[59],"(DS),":[63],"novel":[65],"geometric":[66],"concept":[67],"two":[69,79,162,170],"as":[71,156,234,236],"an":[72,178,197],"extension":[73],"vector":[77,180,199],"vectors,":[80],"and":[81,102,111,129,192,214,228,262,267],"describe":[82],"its":[83],"effectiveness":[84],"in":[85,115,145,252],"analyzing":[86],"differences.":[88],"then":[90],"generalize":[91],"it":[92],"generalized":[95],"(GDS)":[98],"multi-class":[100],"subspaces,":[101,213],"show":[103],"benefit":[105],"applying":[107],"mutual":[112],"methods,":[114],"terms":[116],"recognition":[118,218],"capability.":[119],"Furthermore,":[120],"we":[121,248],"extend":[122],"these":[123],"kernel":[126,130,136],"DS":[127],"(KDS)":[128],"GDS":[131],"(KGDS)":[132],"by":[133],"nonlinear":[135],"mapping":[137],"deal":[139],"with":[140,244],"cases":[141],"involving":[142],"larger":[143],"changes":[144],"viewing":[146],"direction.":[147],"In":[148],"summary,":[149],"contributions":[151],"follows:":[157],"1)":[158],"DS/KDS":[160,183],"characterizes":[165],"respectively":[171],"corresponding":[172],"objects,":[173,191],"2)":[174],"projection":[176,195],"input":[179,198],"onto":[181,202],"realizes":[184],"selective":[185],"visualization":[186],"3)":[193],"or":[200],"GDS/KGDS":[204],"is":[205],"extremely":[206],"effective":[207],"at":[208],"multiple":[212],"therefore":[215],"improves":[216],"performance.":[219],"demonstrate":[221],"validity":[222],"through":[223],"analysis":[225],"synthetic":[227],"real":[229],"3D":[232],"well":[235],"extensive":[237],"comparison":[238],"performance":[240,251],"classification":[242,255,270],"tests":[243],"several":[245],"related":[246],"methods;":[247],"study":[249],"face":[253,259],"Yale":[258],"database":[260],"B+":[261],"CMU":[264],"Multi-PIE":[265],"database,":[266],"hand":[268],"multi-view":[272],"images.":[273]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}