{"id":"https://openalex.org/W4401870874","doi":"https://doi.org/10.1109/msp.2024.3384179","title":"Quaternion Neural Networks: A physics-incorporated intelligence framework","display_name":"Quaternion Neural Networks: A physics-incorporated intelligence framework","publication_year":2024,"publication_date":"2024-05-01","ids":{"openalex":"https://openalex.org/W4401870874","doi":"https://doi.org/10.1109/msp.2024.3384179"},"language":"en","primary_location":{"id":"doi:10.1109/msp.2024.3384179","is_oa":false,"landing_page_url":"https://doi.org/10.1109/msp.2024.3384179","pdf_url":null,"source":{"id":"https://openalex.org/S120977877","display_name":"IEEE Signal Processing Magazine","issn_l":"1053-5888","issn":["1053-5888","1558-0792"],"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 Signal Processing Magazine","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/A5075783559","display_name":"Akira Hirose","orcid":"https://orcid.org/0000-0002-6936-9733"},"institutions":[{"id":"https://openalex.org/I14396692","display_name":"Tokyo University of Information Sciences","ror":"https://ror.org/044bdx604","country_code":"JP","type":"education","lineage":["https://openalex.org/I14396692"]},{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Akira Hirose","raw_affiliation_strings":["Department of Electrical Engineering and Information Systems, University of Tokyo, Tokyo, Japan"],"raw_orcid":"https://orcid.org/0000-0002-6936-9733","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Information Systems, University of Tokyo, Tokyo, Japan","institution_ids":["https://openalex.org/I14396692","https://openalex.org/I74801974"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073741045","display_name":"Fang Shang","orcid":"https://orcid.org/0000-0003-0801-926X"},"institutions":[{"id":"https://openalex.org/I20529979","display_name":"University of Electro-Communications","ror":"https://ror.org/02x73b849","country_code":"JP","type":"education","lineage":["https://openalex.org/I20529979"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Fang Shang","raw_affiliation_strings":["Graduate School of Informatics and Engineering, University of Electro-Communications, Japan"],"raw_orcid":"https://orcid.org/0000-0003-0801-926X","affiliations":[{"raw_affiliation_string":"Graduate School of Informatics and Engineering, University of Electro-Communications, Japan","institution_ids":["https://openalex.org/I20529979"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101873118","display_name":"Yuta Otsuka","orcid":"https://orcid.org/0000-0002-7101-5838"},"institutions":[{"id":"https://openalex.org/I14396692","display_name":"Tokyo University of Information Sciences","ror":"https://ror.org/044bdx604","country_code":"JP","type":"education","lineage":["https://openalex.org/I14396692"]},{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yuta Otsuka","raw_affiliation_strings":["Department of Electrical Engineering and Information Systems, University of Tokyo, Tokyo, Japan"],"raw_orcid":"https://orcid.org/0000-0002-7101-5838","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Information Systems, University of Tokyo, Tokyo, Japan","institution_ids":["https://openalex.org/I14396692","https://openalex.org/I74801974"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080770673","display_name":"Ryo Natsuaki","orcid":"https://orcid.org/0000-0003-2291-4375"},"institutions":[{"id":"https://openalex.org/I14396692","display_name":"Tokyo University of Information Sciences","ror":"https://ror.org/044bdx604","country_code":"JP","type":"education","lineage":["https://openalex.org/I14396692"]},{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Ryo Natsuaki","raw_affiliation_strings":["Department of Electrical Engineering and Information Systems, University of Tokyo, Tokyo, Japan"],"raw_orcid":"https://orcid.org/0000-0003-2291-4375","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Information Systems, University of Tokyo, Tokyo, Japan","institution_ids":["https://openalex.org/I14396692","https://openalex.org/I74801974"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028705745","display_name":"Yuya Matsumoto","orcid":"https://orcid.org/0000-0002-6483-5854"},"institutions":[{"id":"https://openalex.org/I118347220","display_name":"NEC (Japan)","ror":"https://ror.org/04jndar25","country_code":"JP","type":"company","lineage":["https://openalex.org/I118347220"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yuya Matsumoto","raw_affiliation_strings":["Visual Intelligence Research Laboratories, NEC Corporation, Kawasaki, Japan"],"raw_orcid":"https://orcid.org/0000-0002-6483-5854","affiliations":[{"raw_affiliation_string":"Visual Intelligence Research Laboratories, NEC Corporation, Kawasaki, Japan","institution_ids":["https://openalex.org/I118347220"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078019076","display_name":"Naoto Usami","orcid":"https://orcid.org/0000-0001-5609-9781"},"institutions":[{"id":"https://openalex.org/I2800865746","display_name":"Japan Aerospace Exploration Agency","ror":"https://ror.org/059yhyy33","country_code":"JP","type":"facility","lineage":["https://openalex.org/I2800865746"]},{"id":"https://openalex.org/I4210136277","display_name":"Institute of Space and Astronautical Science","ror":"https://ror.org/034gcgw60","country_code":"JP","type":"facility","lineage":["https://openalex.org/I2800865746","https://openalex.org/I4210136277"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Naoto Usami","raw_affiliation_strings":["Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency (JAXA), Sagamihara, Japan"],"raw_orcid":"https://orcid.org/0000-0001-5609-9781","affiliations":[{"raw_affiliation_string":"Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency (JAXA), Sagamihara, Japan","institution_ids":["https://openalex.org/I2800865746","https://openalex.org/I4210136277"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073435041","display_name":"Yicheng Song","orcid":"https://orcid.org/0000-0002-2612-4859"},"institutions":[{"id":"https://openalex.org/I14396692","display_name":"Tokyo University of Information Sciences","ror":"https://ror.org/044bdx604","country_code":"JP","type":"education","lineage":["https://openalex.org/I14396692"]},{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yicheng Song","raw_affiliation_strings":["Department of Electrical Engineering and Information Systems, University of Tokyo, Tokyo, Japan"],"raw_orcid":"https://orcid.org/0000-0002-2612-4859","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Information Systems, University of Tokyo, Tokyo, Japan","institution_ids":["https://openalex.org/I14396692","https://openalex.org/I74801974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100711883","display_name":"Haotian Chen","orcid":"https://orcid.org/0000-0003-2388-2299"},"institutions":[{"id":"https://openalex.org/I14396692","display_name":"Tokyo University of Information Sciences","ror":"https://ror.org/044bdx604","country_code":"JP","type":"education","lineage":["https://openalex.org/I14396692"]},{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Haotian Chen","raw_affiliation_strings":["Department of Electrical Engineering and Information Systems, University of Tokyo, Tokyo, Japan"],"raw_orcid":"https://orcid.org/0000-0003-2388-2299","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Information Systems, University of Tokyo, Tokyo, Japan","institution_ids":["https://openalex.org/I14396692","https://openalex.org/I74801974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5075783559"],"corresponding_institution_ids":["https://openalex.org/I14396692","https://openalex.org/I74801974"],"apc_list":null,"apc_paid":null,"fwci":6.6227,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.97193691,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"41","issue":"3","first_page":"88","last_page":"100"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9919999837875366,"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"}},{"id":"https://openalex.org/T13114","display_name":"Image Processing Techniques and Applications","score":0.9692999720573425,"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/hypercomplex-number","display_name":"Hypercomplex number","score":0.97846519947052},{"id":"https://openalex.org/keywords/quaternion","display_name":"Quaternion","score":0.9163186550140381},{"id":"https://openalex.org/keywords/signal-processing","display_name":"Signal processing","score":0.6333256363868713},{"id":"https://openalex.org/keywords/image-processing","display_name":"Image processing","score":0.5871677398681641},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5463422536849976},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5183007121086121},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.49436283111572266},{"id":"https://openalex.org/keywords/signal","display_name":"SIGNAL (programming language)","score":0.43632155656814575},{"id":"https://openalex.org/keywords/multidimensional-signal-processing","display_name":"Multidimensional signal processing","score":0.4134387671947479},{"id":"https://openalex.org/keywords/computer-vision","display_name":"Computer vision","score":0.3994913101196289},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.38619768619537354},{"id":"https://openalex.org/keywords/digital-signal-processing","display_name":"Digital signal processing","score":0.31353986263275146},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2746024429798126},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.09983223676681519}],"concepts":[{"id":"https://openalex.org/C203249530","wikidata":"https://www.wikidata.org/wiki/Q837414","display_name":"Hypercomplex number","level":3,"score":0.97846519947052},{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.9163186550140381},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.6333256363868713},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.5871677398681641},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5463422536849976},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5183007121086121},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.49436283111572266},{"id":"https://openalex.org/C2779843651","wikidata":"https://www.wikidata.org/wiki/Q7390335","display_name":"SIGNAL (programming language)","level":2,"score":0.43632155656814575},{"id":"https://openalex.org/C501101116","wikidata":"https://www.wikidata.org/wiki/Q18378116","display_name":"Multidimensional signal processing","level":4,"score":0.4134387671947479},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.3994913101196289},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.38619768619537354},{"id":"https://openalex.org/C84462506","wikidata":"https://www.wikidata.org/wiki/Q173142","display_name":"Digital signal processing","level":2,"score":0.31353986263275146},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2746024429798126},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.09983223676681519},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C9390403","wikidata":"https://www.wikidata.org/wiki/Q3966","display_name":"Computer hardware","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/msp.2024.3384179","is_oa":false,"landing_page_url":"https://doi.org/10.1109/msp.2024.3384179","pdf_url":null,"source":{"id":"https://openalex.org/S120977877","display_name":"IEEE Signal Processing Magazine","issn_l":"1053-5888","issn":["1053-5888","1558-0792"],"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 Signal Processing Magazine","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G439518252","display_name":null,"funder_award_id":"18H04105","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8056864775","display_name":null,"funder_award_id":"23H00487","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W386692692","https://openalex.org/W1575685434","https://openalex.org/W1576577473","https://openalex.org/W1700035086","https://openalex.org/W1976792405","https://openalex.org/W1989757000","https://openalex.org/W1992233064","https://openalex.org/W2009565519","https://openalex.org/W2043978450","https://openalex.org/W2047515252","https://openalex.org/W2088630956","https://openalex.org/W2097446478","https://openalex.org/W2099057098","https://openalex.org/W2141150222","https://openalex.org/W2143572124","https://openalex.org/W2146069630","https://openalex.org/W2165019472","https://openalex.org/W2247736297","https://openalex.org/W2488580825","https://openalex.org/W2548430983","https://openalex.org/W2550009815","https://openalex.org/W2559324447","https://openalex.org/W2595106450","https://openalex.org/W2607714468","https://openalex.org/W2722385933","https://openalex.org/W2754361766","https://openalex.org/W2793189836","https://openalex.org/W2804850629","https://openalex.org/W2887258823","https://openalex.org/W2894977338","https://openalex.org/W2899764986","https://openalex.org/W2900556069","https://openalex.org/W2964871970","https://openalex.org/W2984197517","https://openalex.org/W3000085358","https://openalex.org/W3016589748","https://openalex.org/W3031158439","https://openalex.org/W3138659895","https://openalex.org/W3153078573","https://openalex.org/W3209698659","https://openalex.org/W4206771519","https://openalex.org/W4225890596","https://openalex.org/W4241214195","https://openalex.org/W4250972035","https://openalex.org/W4285158293","https://openalex.org/W4383752791","https://openalex.org/W4383899494","https://openalex.org/W4385672002","https://openalex.org/W4387803054","https://openalex.org/W4387803056","https://openalex.org/W6601634529","https://openalex.org/W6613271927","https://openalex.org/W6633656704","https://openalex.org/W6637501666"],"related_works":["https://openalex.org/W2916518000","https://openalex.org/W2916498667","https://openalex.org/W2917906954","https://openalex.org/W2572893131","https://openalex.org/W2917330019","https://openalex.org/W4210925376","https://openalex.org/W4399665812","https://openalex.org/W4401871031","https://openalex.org/W4210376836","https://openalex.org/W3193411882"],"abstract_inverted_index":{"Why":[0],"quaternions":[1,8,46],"in":[2,9,59,79],"neural":[3],"networks":[4],"(NNs)?":[5],"Are":[6],"there":[7],"the":[10,34,56,68,135],"human":[11,139,147],"brain?":[12],"\u201cNo\u201d":[13],"may":[14],"be":[15],"an":[16],"ordinary":[17],"answer.":[18],"However,":[19],"quaternion":[20],"NNs":[21,43,107],"(QNNs)":[22],"are":[23,103],"a":[24,104,114,126,138],"powerful":[25],"framework":[26,115],"that":[27,108],"strongly":[28],"connects":[29],"artificial":[30,89],"intelligence":[31],"(AI)":[32],"and":[33,47,51,93,131,145],"real":[35,146],"world.":[36],"In":[37],"this":[38],"article,":[39],"we":[40,65],"deal":[41],"with":[42,120],"based":[44],"on":[45,76,88],"describe":[48],"their":[49,60,77],"basics":[50],"features.":[52],"We":[53,74],"also":[54],"detail":[55],"underlying":[57],"ideas":[58],"engineering":[61],"applications,":[62],"especially":[63,111],"when":[64],"adaptively":[66],"process":[67],"polarization":[69],"information":[70],"of":[71,106,129,137],"electromagnetic":[72],"waves.":[73],"focus":[75],"role":[78],"remote":[80],"sensing,":[81],"such":[82],"as":[83,96,98],"Earth":[84],"observation":[85],"radar":[86],"mounted":[87],"satellites":[90],"or":[91],"aircraft":[92],"underground":[94],"radar,":[95],"well":[97],"mobile":[99],"communication.":[100],"There,":[101],"QNNs":[102],"class":[105],"know":[109],"physics,":[110],"polarization,":[112],"composing":[113],"by":[116],"fusing":[117],"measurement":[118,130],"physics":[119],"adaptive-processing":[121],"mathematics.":[122],"This":[123],"fusion":[124],"realizes":[125],"seamless":[127],"integration":[128],"intelligence,":[132],"contributing":[133],"to":[134],"construction":[136],"society":[140],"having":[141],"harmony":[142],"between":[143],"AI":[144],"lives.":[148]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":13},{"year":2024,"cited_by_count":3}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2024-08-26T00:00:00"}