{"id":"https://openalex.org/W2160124221","doi":"https://doi.org/10.1109/tsmcb.2011.2170564","title":"A Note on Octonionic Support Vector Regression","display_name":"A Note on Octonionic Support Vector Regression","publication_year":2011,"publication_date":"2011-11-17","ids":{"openalex":"https://openalex.org/W2160124221","doi":"https://doi.org/10.1109/tsmcb.2011.2170564","mag":"2160124221","pmid":"https://pubmed.ncbi.nlm.nih.gov/22106150"},"language":"en","primary_location":{"id":"doi:10.1109/tsmcb.2011.2170564","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmcb.2011.2170564","pdf_url":null,"source":{"id":"https://openalex.org/S4210170378","display_name":"IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics)","issn_l":"1083-4419","issn":["1083-4419","1941-0492"],"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 Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics)","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://figshare.com/articles/journal_contribution/A_note_on_octonionic_support_vector_regression/20816404","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":"The 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":"A. Shilton","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, The University of Melbourne, Melbourne, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, The University of Melbourne, Melbourne, Australia","institution_ids":["https://openalex.org/I165779595"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087639822","display_name":"Daniel Lai","orcid":"https://orcid.org/0000-0003-3459-7709"},"institutions":[{"id":"https://openalex.org/I71270174","display_name":"Victoria University","ror":"https://ror.org/04j757h98","country_code":"AU","type":"education","lineage":["https://openalex.org/I71270174"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"D. T. H. Lai","raw_affiliation_strings":["School of Engineering and Science, Victoria University, Melbourne, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering and Science, Victoria University, Melbourne, Australia","institution_ids":["https://openalex.org/I71270174"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091461783","display_name":"Braveena K. Santhiranayagam","orcid":null},"institutions":[{"id":"https://openalex.org/I71270174","display_name":"Victoria University","ror":"https://ror.org/04j757h98","country_code":"AU","type":"education","lineage":["https://openalex.org/I71270174"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"B. K. Santhiranayagam","raw_affiliation_strings":["School of Sport and Exercise Science, Victoria University, Melbourne, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Sport and Exercise Science, Victoria University, Melbourne, Australia","institution_ids":["https://openalex.org/I71270174"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080554686","display_name":"Marimuthu Palaniswami","orcid":"https://orcid.org/0000-0002-3635-4252"},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"The 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":"M. Palaniswami","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, The University of Melbourne, Melbourne, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, The University of Melbourne, Melbourne, Australia","institution_ids":["https://openalex.org/I165779595"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1623,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.77220544,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"42","issue":"3","first_page":"950","last_page":"955"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9728000164031982,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13261","display_name":"Elasticity and Wave Propagation","score":0.9563999772071838,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/support-vector-machine","display_name":"Support vector machine","score":0.715560257434845},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6311346292495728},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5403345823287964},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.524332582950592},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5122072100639343},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.485419362783432},{"id":"https://openalex.org/keywords/feature","display_name":"Feature (linguistics)","score":0.476953387260437},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4660326838493347},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39922183752059937},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3859180808067322},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3669915199279785},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10123294591903687},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.06455031037330627}],"concepts":[{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.715560257434845},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6311346292495728},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5403345823287964},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.524332582950592},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5122072100639343},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.485419362783432},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.476953387260437},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4660326838493347},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39922183752059937},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3859180808067322},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3669915199279785},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10123294591903687},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.06455031037330627},{"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003661","descriptor_name":"Decision Support Techniques","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003661","descriptor_name":"Decision Support Techniques","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D003661","descriptor_name":"Decision Support Techniques","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D010363","descriptor_name":"Pattern Recognition, Automated","qualifier_ui":"Q000379","qualifier_name":"methods","is_major_topic":false},{"descriptor_ui":"D012044","descriptor_name":"Regression Analysis","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012044","descriptor_name":"Regression Analysis","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012044","descriptor_name":"Regression Analysis","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D015233","descriptor_name":"Models, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D015233","descriptor_name":"Models, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D015233","descriptor_name":"Models, Statistical","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":5,"locations":[{"id":"doi:10.1109/tsmcb.2011.2170564","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsmcb.2011.2170564","pdf_url":null,"source":{"id":"https://openalex.org/S4210170378","display_name":"IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics)","issn_l":"1083-4419","issn":["1083-4419","1941-0492"],"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 Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics)","raw_type":"journal-article"},{"id":"pmid:22106150","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/22106150","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 systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society","raw_type":null},{"id":"pmh:oai:eprints.vu.edu.au:7634","is_oa":false,"landing_page_url":"https://vuir.vu.edu.au/7634/","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":"Article"},{"id":"pmh:oai:dro.deakin.edu.au:DU:30112735","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":"Journal Article"},{"id":"pmh:oai:figshare.com:article/20816404","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/A_note_on_octonionic_support_vector_regression/20816404","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":null,"raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:figshare.com:article/20816404","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/A_note_on_octonionic_support_vector_regression/20816404","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":null,"raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W178039687","https://openalex.org/W641490683","https://openalex.org/W1496317909","https://openalex.org/W1502069036","https://openalex.org/W1587294646","https://openalex.org/W1593361846","https://openalex.org/W1598507070","https://openalex.org/W1629404328","https://openalex.org/W2002206292","https://openalex.org/W2005641898","https://openalex.org/W2035227519","https://openalex.org/W2048681918","https://openalex.org/W2091210372","https://openalex.org/W2097334502","https://openalex.org/W2110506616","https://openalex.org/W2119040979","https://openalex.org/W2123374346","https://openalex.org/W2138469121","https://openalex.org/W2160664600","https://openalex.org/W2296319761","https://openalex.org/W2588559030","https://openalex.org/W4250589301","https://openalex.org/W4285719527","https://openalex.org/W4301501800","https://openalex.org/W4312960235","https://openalex.org/W6636766739"],"related_works":["https://openalex.org/W2090763504","https://openalex.org/W148178222","https://openalex.org/W2104657898","https://openalex.org/W1948992892","https://openalex.org/W1886884218","https://openalex.org/W1910826599","https://openalex.org/W2012353789","https://openalex.org/W2530420969","https://openalex.org/W2051187167","https://openalex.org/W1980100242"],"abstract_inverted_index":{"This":[0],"note":[1],"presents":[2],"an":[3,53,102],"analysis":[4,105],"of":[5,9,24,52,65,79,86,114],"the":[6,10,25,39,49,57,87,92,96,115,119,123],"octonionic":[7,97],"form":[8,27],"division":[11],"algebraic":[12],"support":[13],"vector":[14],"regressor":[15],"(SVR)":[16],"first":[17],"introduced":[18],"by":[19],"Shilton":[20],"A":[21],"detailed":[22],"derivation":[23],"dual":[26],"is":[28,36,45,70,99,110],"given,":[29],"and":[30,107,122],"three":[31],"conditions":[32],"under":[33],"which":[34],"it":[35],"analogous":[37],"to":[38,83,101,112],"quaternionic":[40],"case":[41,51],"are":[42],"exhibited.":[43],"It":[44],"shown":[46],"that,":[47],"in":[48,72,91],"general":[50,93],"octonionic-valued":[54],"feature":[55],"map,":[56],"usual":[58],"\"kernel":[59],"trick\"":[60],"breaks":[61],"down.":[62],"The":[63],"cause":[64],"this":[66],"(and":[67],"its":[68,108],"interpretation)":[69],"discussed":[71],"some":[73],"detail,":[74],"along":[75],"with":[76],"potential":[77],"ways":[78],"extending":[80],"kernel":[81],"methods":[82],"take":[84],"advantage":[85],"distinct":[88],"features":[89],"present":[90],"case.":[94],"Finally,":[95],"SVR":[98],"applied":[100],"example":[103],"gait":[104],"problem,":[106],"performance":[109],"compared":[111],"that":[113],"least":[116],"squares":[117],"SVR,":[118,121],"Clifford":[120],"multidimensional":[124],"SVR.":[125]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
