{"id":"https://openalex.org/W4360993142","doi":"https://doi.org/10.1109/lsp.2023.3262059","title":"Improved Bilinear Pooling With Pseudo Square-Rooted Matrix","display_name":"Improved Bilinear Pooling With Pseudo Square-Rooted Matrix","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4360993142","doi":"https://doi.org/10.1109/lsp.2023.3262059"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2023.3262059","is_oa":true,"landing_page_url":"https://doi.org/10.1109/lsp.2023.3262059","pdf_url":"https://ieeexplore.ieee.org/ielx7/97/4358004/10081496.pdf","source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Signal Processing Letters","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://ieeexplore.ieee.org/ielx7/97/4358004/10081496.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102738560","display_name":"Sixiang Xu","orcid":"https://orcid.org/0000-0003-4561-0358"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Sixiang Xu","raw_affiliation_strings":["Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, International Research Center for Intelligent Perception and Computation, Joint International Research Laboratory of Intelligent Perception and Computation, School of Artificial Intelligence, Xidian University, Xi&#x0027;an, Shaanxi Province, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, International Research Center for Intelligent Perception and Computation, Joint International Research Laboratory of Intelligent Perception and Computation, School of Artificial Intelligence, Xidian University, Xi&#x0027;an, Shaanxi Province, China","institution_ids":["https://openalex.org/I149594827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025451778","display_name":"Damien Muselet","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Damien Muselet","raw_affiliation_strings":["Universit&#x00E9; de Lyon, UJM-Saint-Etienne, CNRS, Saint-Etienne, France"],"affiliations":[{"raw_affiliation_string":"Universit&#x00E9; de Lyon, UJM-Saint-Etienne, CNRS, Saint-Etienne, France","institution_ids":["https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041689611","display_name":"Alain Tr\u00e9meau","orcid":"https://orcid.org/0000-0003-2826-7519"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Alain Tr\u00e9meau","raw_affiliation_strings":["Universit&#x00E9; de Lyon, UJM-Saint-Etienne, CNRS, Saint-Etienne, France"],"affiliations":[{"raw_affiliation_string":"Universit&#x00E9; de Lyon, UJM-Saint-Etienne, CNRS, Saint-Etienne, France","institution_ids":["https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050630882","display_name":"Licheng Jiao","orcid":"https://orcid.org/0000-0003-3354-9617"},"institutions":[{"id":"https://openalex.org/I149594827","display_name":"Xidian University","ror":"https://ror.org/05s92vm98","country_code":"CN","type":"education","lineage":["https://openalex.org/I149594827"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Licheng Jiao","raw_affiliation_strings":["Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, International Research Center for Intelligent Perception and Computation, Joint International Research Laboratory of Intelligent Perception and Computation, School of Artificial Intelligence, Xidian University, Xi&#x0027;an, Shaanxi Province, China"],"affiliations":[{"raw_affiliation_string":"Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education, International Research Center for Intelligent Perception and Computation, Joint International Research Laboratory of Intelligent Perception and Computation, School of Artificial Intelligence, Xidian University, Xi&#x0027;an, Shaanxi Province, China","institution_ids":["https://openalex.org/I149594827"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5102738560"],"corresponding_institution_ids":["https://openalex.org/I149594827"],"apc_list":null,"apc_paid":null,"fwci":0.489,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.63386943,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"30","issue":null,"first_page":"423","last_page":"427"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10036","display_name":"Advanced Neural Network Applications","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/T10036","display_name":"Advanced Neural Network Applications","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/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9988999962806702,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/pooling","display_name":"Pooling","score":0.9058091640472412},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.7852899432182312},{"id":"https://openalex.org/keywords/normalization","display_name":"Normalization (sociology)","score":0.7307370901107788},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5952242016792297},{"id":"https://openalex.org/keywords/discriminative-model","display_name":"Discriminative model","score":0.5503531694412231},{"id":"https://openalex.org/keywords/square-root","display_name":"Square root","score":0.5350924730300903},{"id":"https://openalex.org/keywords/square-matrix","display_name":"Square matrix","score":0.5206360220909119},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4848233759403229},{"id":"https://openalex.org/keywords/convolutional-neural-network","display_name":"Convolutional neural network","score":0.4444253742694855},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.4401409327983856},{"id":"https://openalex.org/keywords/encode","display_name":"ENCODE","score":0.4361107051372528},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3666721284389496},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3040318191051483},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.19857728481292725},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.08097758889198303}],"concepts":[{"id":"https://openalex.org/C70437156","wikidata":"https://www.wikidata.org/wiki/Q7228652","display_name":"Pooling","level":2,"score":0.9058091640472412},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.7852899432182312},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.7307370901107788},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5952242016792297},{"id":"https://openalex.org/C97931131","wikidata":"https://www.wikidata.org/wiki/Q5282087","display_name":"Discriminative model","level":2,"score":0.5503531694412231},{"id":"https://openalex.org/C11577676","wikidata":"https://www.wikidata.org/wiki/Q134237","display_name":"Square root","level":2,"score":0.5350924730300903},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.5206360220909119},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4848233759403229},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.4444253742694855},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.4401409327983856},{"id":"https://openalex.org/C66746571","wikidata":"https://www.wikidata.org/wiki/Q1134833","display_name":"ENCODE","level":3,"score":0.4361107051372528},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3666721284389496},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3040318191051483},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.19857728481292725},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.08097758889198303},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C19165224","wikidata":"https://www.wikidata.org/wiki/Q23404","display_name":"Anthropology","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/lsp.2023.3262059","is_oa":true,"landing_page_url":"https://doi.org/10.1109/lsp.2023.3262059","pdf_url":"https://ieeexplore.ieee.org/ielx7/97/4358004/10081496.pdf","source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Signal Processing Letters","raw_type":"journal-article"},{"id":"pmh:oai:HAL:ujm-04799251v1","is_oa":true,"landing_page_url":"https://ujm.hal.science/ujm-04799251","pdf_url":"https://ujm.hal.science/ujm-04799251v1/document","source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Signal Processing Letters, 2023, 30, pp.423-427. &#x27E8;10.1109/LSP.2023.3262059&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"doi:10.1109/lsp.2023.3262059","is_oa":true,"landing_page_url":"https://doi.org/10.1109/lsp.2023.3262059","pdf_url":"https://ieeexplore.ieee.org/ielx7/97/4358004/10081496.pdf","source":{"id":"https://openalex.org/S120629676","display_name":"IEEE Signal Processing Letters","issn_l":"1070-9908","issn":["1070-9908","1558-2361"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Signal Processing Letters","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6451932392","display_name":null,"funder_award_id":"XJSJ23084","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4360993142.pdf","grobid_xml":"https://content.openalex.org/works/W4360993142.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W1797268635","https://openalex.org/W1846799578","https://openalex.org/W2104657103","https://openalex.org/W2112759033","https://openalex.org/W2117539524","https://openalex.org/W2138011018","https://openalex.org/W2170653751","https://openalex.org/W2194775991","https://openalex.org/W2204257188","https://openalex.org/W2475287302","https://openalex.org/W2554320282","https://openalex.org/W2731821979","https://openalex.org/W2740620254","https://openalex.org/W2752965000","https://openalex.org/W2888453526","https://openalex.org/W2936614765","https://openalex.org/W2949041290","https://openalex.org/W2962761264","https://openalex.org/W2963015611","https://openalex.org/W2963066927","https://openalex.org/W2963150162","https://openalex.org/W2963383024","https://openalex.org/W2964350570","https://openalex.org/W3175668602","https://openalex.org/W4224949201","https://openalex.org/W6638319203","https://openalex.org/W6638677478","https://openalex.org/W6683590716","https://openalex.org/W6763569150","https://openalex.org/W6803916128"],"related_works":["https://openalex.org/W2950524887","https://openalex.org/W2883502031","https://openalex.org/W2261271299","https://openalex.org/W4280638452","https://openalex.org/W4285020665","https://openalex.org/W2963066927","https://openalex.org/W3160506688","https://openalex.org/W3111811104","https://openalex.org/W4380083739","https://openalex.org/W2964944724"],"abstract_inverted_index":{"Bilinear":[0,47],"pooling":[1,40],"is":[2],"a":[3,13,18,24,109,116,132,139],"feature":[4,161],"aggregation":[5],"step":[6],"applied":[7],"after":[8],"the":[9,54,67,128,150],"convolutional":[10],"layers":[11],"of":[12,20,56,69],"deep":[14],"network":[15],"and":[16,50,86,141],"encodes":[17],"matrix":[19,119,130,162],"local":[21],"features":[22],"into":[23,83,138],"fixed-size":[25],"bilinear":[26,143],"representation.":[27,144],"It":[28],"improves":[29],"performance":[30,178],"in":[31,100],"many":[32],"image":[33,171],"classification":[34,172,177],"tasks.":[35],"Since":[36],"its":[37],"emergence,":[38],"this":[39,98,101],"has":[41,60,155],"seen":[42],"two":[43,58,156],"major":[44],"improvements:":[45],"Compact":[46],"Pooling":[48],"(CBP)":[49],"square-root":[51,111],"normalization.":[52],"Recently,":[53],"combination":[55,74],"these":[57],"elements":[59],"been":[61],"widely":[62],"studied.":[63],"However,":[64],"due":[65],"to":[66,105,114,135,147],"lack":[68],"good":[70],"normalization":[71,112,151],"solutions,":[72],"existing":[73,93],"approaches":[75],"showed":[76],"less":[77,87,181],"efficiency":[78],"when":[79,89],"they":[80,90],"are":[81],"plugged":[82],"different":[84,165],"networks":[85],"compatibility":[88],"work":[91],"with":[92],"CBP":[94,133],"techniques.":[95],"To":[96],"solve":[97],"problem,":[99],"paper,":[102],"we":[103],"propose":[104],"apply":[106],"Newton":[107],"iterations,":[108],"fast":[110],"method,":[113],"produce":[115],"new":[117,129],"normalized":[118,142],"called":[120],"<italic":[121],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[122],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">pseudo":[123],"square-rooted":[124],"matrix</i>":[125],".":[126],"Subsequently,":[127],"allows":[131],"technique":[134],"encode":[136],"itself":[137],"compact":[140],"In":[145],"order":[146],"further":[148],"accelerate":[149],"process,":[152],"our":[153],"approach":[154],"variants":[157],"which":[158],"can":[159],"handle":[160],"extracted":[163],"by":[164],"networks.":[166],"Tested":[167],"on":[168],"three":[169],"fine-grained":[170],"datasets,":[173],"it":[174],"provides":[175],"competitive":[176],"while":[179],"consuming":[180],"computational":[182],"time":[183],"than":[184],"other":[185],"prior":[186],"works.":[187]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1}],"updated_date":"2026-03-13T16:22:10.518609","created_date":"2025-10-10T00:00:00"}
