{"id":"https://openalex.org/W2112175875","doi":"https://doi.org/10.1109/ijcnn.2007.4371081","title":"Quaternionic and complex-valued Support Vector Regression for Equalization and Function Approximation","display_name":"Quaternionic and complex-valued Support Vector Regression for Equalization and Function Approximation","publication_year":2007,"publication_date":"2007-08-01","ids":{"openalex":"https://openalex.org/W2112175875","doi":"https://doi.org/10.1109/ijcnn.2007.4371081","mag":"2112175875"},"language":"en","primary_location":{"id":"doi:10.1109/ijcnn.2007.4371081","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2007.4371081","pdf_url":null,"source":{"id":"https://openalex.org/S4210195743","display_name":"IEEE International Conference on Neural Networks/IEEE ... International Conference on Neural Networks","issn_l":"1098-7576","issn":["1098-7576","1558-3902"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 International Joint Conference on Neural Networks","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/11343/34668","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062759273","display_name":"Alistair Shilton","orcid":"https://orcid.org/0000-0002-0849-3271"},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Alistair Shilton","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, University of Melbourne, Melbourne, Australia","Melbourne Univ., Melbourne#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, University of Melbourne, Melbourne, Australia","institution_ids":["https://openalex.org/I165779595"]},{"raw_affiliation_string":"Melbourne Univ., Melbourne#TAB#","institution_ids":["https://openalex.org/I165779595"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087639822","display_name":"Daniel Lai","orcid":"https://orcid.org/0000-0003-3459-7709"},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Daniel T. H. Lai","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, University of Melbourne, Melbourne, Australia","Melbourne Univ., Melbourne#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, University of Melbourne, Melbourne, Australia","institution_ids":["https://openalex.org/I165779595"]},{"raw_affiliation_string":"Melbourne Univ., Melbourne#TAB#","institution_ids":["https://openalex.org/I165779595"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5062759273"],"corresponding_institution_ids":["https://openalex.org/I165779595"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.22408484,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"920","last_page":"925"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9980999827384949,"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/T10320","display_name":"Neural Networks and Applications","score":0.9980999827384949,"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/T11447","display_name":"Blind Source Separation Techniques","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/quaternion","display_name":"Quaternion","score":0.8246549367904663},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.705541729927063},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5552576780319214},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5061535239219666},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.503828227519989},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5012660026550293},{"id":"https://openalex.org/keywords/regression-analysis","display_name":"Regression analysis","score":0.4456876218318939},{"id":"https://openalex.org/keywords/equalization","display_name":"Equalization (audio)","score":0.43637365102767944},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.43563398718833923},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.43556880950927734},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4225912094116211},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39120742678642273},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3888029456138611},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3527999520301819},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3434714078903198},{"id":"https://openalex.org/keywords/channel","display_name":"Channel (broadcasting)","score":0.33795952796936035},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.30234503746032715},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.1856812834739685},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.17434397339820862},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12837067246437073},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.09046250581741333},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07933461666107178}],"concepts":[{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.8246549367904663},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.705541729927063},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5552576780319214},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5061535239219666},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.503828227519989},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5012660026550293},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.4456876218318939},{"id":"https://openalex.org/C75755367","wikidata":"https://www.wikidata.org/wiki/Q104531076","display_name":"Equalization (audio)","level":3,"score":0.43637365102767944},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.43563398718833923},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.43556880950927734},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4225912094116211},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39120742678642273},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3888029456138611},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3527999520301819},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3434714078903198},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.33795952796936035},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.30234503746032715},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.1856812834739685},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.17434397339820862},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12837067246437073},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.09046250581741333},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07933461666107178},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1109/ijcnn.2007.4371081","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2007.4371081","pdf_url":null,"source":{"id":"https://openalex.org/S4210195743","display_name":"IEEE International Conference on Neural Networks/IEEE ... International Conference on Neural Networks","issn_l":"1098-7576","issn":["1098-7576","1558-3902"],"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 International Joint Conference on Neural Networks","raw_type":"proceedings-article"},{"id":"pmh:oai:jupiter.its.unimelb.edu.au:11343/34668","is_oa":true,"landing_page_url":"http://hdl.handle.net/11343/34668","pdf_url":"http://hdl.handle.net/11343/34668","source":{"id":"https://openalex.org/S4377196259","display_name":"Minerva Access (University of Melbourne)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I165779595","host_organization_name":"The University of Melbourne","host_organization_lineage":["https://openalex.org/I165779595"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"The 2007 International Joint Conference on Neural Networks","raw_type":"Conference Paper"},{"id":"pmh:oai:eprints.vu.edu.au:35940","is_oa":false,"landing_page_url":"https://vuir.vu.edu.au/35940/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400215","display_name":"Victoria University Research Repository (Victoria University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I41156924","host_organization_name":"Victoria University of Wellington","host_organization_lineage":["https://openalex.org/I41156924"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.563.789","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.563.789","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.eng.unimelb.edu.au/shiltona/publications/ijcnn07.pdf","raw_type":"text"},{"id":"pmh:oai:dro.deakin.edu.au:DU:30125935","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401102","display_name":"Own your potential (DEAKIN)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149704539","host_organization_name":"Deakin University","host_organization_lineage":["https://openalex.org/I149704539"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference Paper"},{"id":"pmh:oai:figshare.com:article/20816374","is_oa":true,"landing_page_url":"https://figshare.com/articles/conference_contribution/Quaternionic_and_complex-valued_support_vector_regression_for_equalization_and_function_approximation/20816374","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:jupiter.its.unimelb.edu.au:11343/34668","is_oa":true,"landing_page_url":"http://hdl.handle.net/11343/34668","pdf_url":"http://hdl.handle.net/11343/34668","source":{"id":"https://openalex.org/S4377196259","display_name":"Minerva Access (University of Melbourne)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I165779595","host_organization_name":"The University of Melbourne","host_organization_lineage":["https://openalex.org/I165779595"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"The 2007 International Joint Conference on Neural Networks","raw_type":"Conference Paper"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2112175875.pdf","grobid_xml":"https://content.openalex.org/works/W2112175875.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1480215172","https://openalex.org/W1527786550","https://openalex.org/W1540110494","https://openalex.org/W1588628884","https://openalex.org/W1593361846","https://openalex.org/W1964357740","https://openalex.org/W2014158063","https://openalex.org/W2093609627","https://openalex.org/W2104128541","https://openalex.org/W2119821739","https://openalex.org/W2123019231","https://openalex.org/W2123374346","https://openalex.org/W2123737232","https://openalex.org/W2137226992","https://openalex.org/W2164096571","https://openalex.org/W2293578641","https://openalex.org/W2304818820","https://openalex.org/W2588559030","https://openalex.org/W4229748564","https://openalex.org/W4239510810","https://openalex.org/W4251652949","https://openalex.org/W6641163509","https://openalex.org/W6675374405","https://openalex.org/W6680532697","https://openalex.org/W6683915272","https://openalex.org/W6698060391","https://openalex.org/W6733252325"],"related_works":["https://openalex.org/W3127350447","https://openalex.org/W3108700312","https://openalex.org/W2887325221","https://openalex.org/W4225472102","https://openalex.org/W2382948573","https://openalex.org/W2184550115","https://openalex.org/W4289828965","https://openalex.org/W2391028436","https://openalex.org/W4385643989","https://openalex.org/W2368484960"],"abstract_inverted_index":{"Support":[0],"vector":[1,14],"regressors":[2],"(SVRs)":[3],"are":[4],"a":[5],"class":[6],"of":[7,45,84,93,144,161,169],"nonlinear":[8],"regressor":[9],"inspired":[10],"by":[11,165],"Vapnik's":[12],"support":[13],"(SV)":[15],"method":[16,86,103,115],"for":[17],"pattern":[18],"classification.":[19],"The":[20],"standard":[21,101],"SVR":[22,102],"has":[23],"been":[24,74],"successfully":[25],"applied":[26,125],"to":[27,48,76,87,106],"real":[28],"number":[29],"regression":[30,108],"problems":[31],"such":[32],"as":[33,121,136],"financial":[34],"prediction":[35],"and":[36,55,79,90,112],"weather":[37],"forecasting.":[38],"However":[39],"in":[40,109,126,137,147],"some":[41],"applications":[42],"the":[43,46,82,97,100,122,127,142,145,148,154,158,167],"domain":[44],"function":[47,124],"be":[49,52,77],"estimated":[50],"may":[51],"more":[53],"naturally":[54],"efficiently":[56],"expressed":[57],"using":[58],"complex":[59,88,110],"numbers":[60,89,111],"(eg.":[61,66],"communications":[62,170],"channels)":[63],"or":[64],"quaternions":[65,91],"3-dimensional":[67],"geometrical":[68],"problems).":[69],"Since":[70],"SVRs":[71],"have":[72],"previously":[73],"proven":[75],"efficient":[78],"accurate":[80],"regressors,":[81],"extension":[83],"this":[85,162],"is":[92,104,130,134,141,151],"great":[94],"interest.":[95],"In":[96],"present":[98],"paper":[99],"extended":[105],"cover":[107],"quaternions.":[113],"Our":[114],"differs":[116],"from":[117],"existing":[118],"approaches":[119],"in-so-far":[120],"cost":[123],"output":[128,149],"space":[129],"rotationally":[131],"invariant,":[132],"which":[133,150],"important":[135],"most":[138],"cases":[139],"it":[140],"magnitude":[143],"error":[146],"important,":[152],"not":[153],"angle.":[155],"We":[156],"demonstrate":[157],"practical":[159],"usefulness":[160],"new":[163],"formulation":[164],"considering":[166],"problem":[168],"channel":[171],"equalization.":[172]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}