{"id":"https://openalex.org/W1551479102","doi":"https://doi.org/10.1109/lsp.2015.2457294","title":"Design of Positive-Definite Quaternion Kernels","display_name":"Design of Positive-Definite Quaternion Kernels","publication_year":2015,"publication_date":"2015-07-16","ids":{"openalex":"https://openalex.org/W1551479102","doi":"https://doi.org/10.1109/lsp.2015.2457294","mag":"1551479102"},"language":"en","primary_location":{"id":"doi:10.1109/lsp.2015.2457294","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2015.2457294","pdf_url":null,"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":null,"license_id":null,"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":"green","oa_url":"https://www.repository.cam.ac.uk/handle/1810/248995","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020822083","display_name":"Felipe Tobar","orcid":"https://orcid.org/0000-0003-2486-3583"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Felipe Tobar","raw_affiliation_strings":["Department of Engineering, University of Cambridge, UK","Department of Engineering, University of Cambridge,,UK"],"affiliations":[{"raw_affiliation_string":"Department of Engineering, University of Cambridge, UK","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"Department of Engineering, University of Cambridge,,UK","institution_ids":["https://openalex.org/I241749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103001848","display_name":"Danilo P. Mandic","orcid":"https://orcid.org/0000-0001-8432-3963"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Danilo P. Mandic","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Imperial College London, UK","Department of Electrical and Electronic Engineering, Imperial College, London, Uk"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Imperial College London, UK","institution_ids":["https://openalex.org/I47508984"]},{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Imperial College, London, Uk","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5020822083"],"corresponding_institution_ids":["https://openalex.org/I241749"],"apc_list":null,"apc_paid":null,"fwci":0.2894,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.52995233,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"22","issue":"11","first_page":"2117","last_page":"2121"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10860","display_name":"Speech and Audio Processing","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T10860","display_name":"Speech and Audio Processing","score":0.9993000030517578,"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/T11233","display_name":"Advanced Adaptive Filtering Techniques","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10326","display_name":"Indoor and Outdoor Localization Technologies","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/quaternion","display_name":"Quaternion","score":0.9374377727508545},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.8040426969528198},{"id":"https://openalex.org/keywords/reproducing-kernel-hilbert-space","display_name":"Reproducing kernel Hilbert space","score":0.7162162661552429},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.605139970779419},{"id":"https://openalex.org/keywords/polynomial-kernel","display_name":"Polynomial kernel","score":0.5331014394760132},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.525088906288147},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4443613290786743},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.43762776255607605},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4050747752189636},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3850020170211792},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.377765953540802},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36027538776397705},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.3560175895690918},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2672021985054016},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.1814335286617279},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1543126404285431},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06108945608139038}],"concepts":[{"id":"https://openalex.org/C200127275","wikidata":"https://www.wikidata.org/wiki/Q173853","display_name":"Quaternion","level":2,"score":0.9374377727508545},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.8040426969528198},{"id":"https://openalex.org/C80884492","wikidata":"https://www.wikidata.org/wiki/Q3345678","display_name":"Reproducing kernel Hilbert space","level":3,"score":0.7162162661552429},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.605139970779419},{"id":"https://openalex.org/C160446489","wikidata":"https://www.wikidata.org/wiki/Q7226642","display_name":"Polynomial kernel","level":4,"score":0.5331014394760132},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.525088906288147},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4443613290786743},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.43762776255607605},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4050747752189636},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3850020170211792},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.377765953540802},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36027538776397705},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.3560175895690918},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2672021985054016},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.1814335286617279},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1543126404285431},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06108945608139038}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/lsp.2015.2457294","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lsp.2015.2457294","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Signal Processing Letters","raw_type":"journal-article"},{"id":"pmh:oai:www.repository.cam.ac.uk:1810/248995","is_oa":true,"landing_page_url":"https://www.repository.cam.ac.uk/handle/1810/248995","pdf_url":"https://www.repository.cam.ac.uk/handle/1810/248995","source":{"id":"https://openalex.org/S4306401776","display_name":"Apollo (University of Cambridge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I241749","host_organization_name":"University of Cambridge","host_organization_lineage":["https://openalex.org/I241749"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:www.repository.cam.ac.uk:1810/248995","is_oa":true,"landing_page_url":"https://www.repository.cam.ac.uk/handle/1810/248995","pdf_url":"https://www.repository.cam.ac.uk/handle/1810/248995","source":{"id":"https://openalex.org/S4306401776","display_name":"Apollo (University of Cambridge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I241749","host_organization_name":"University of Cambridge","host_organization_lineage":["https://openalex.org/I241749"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},"sustainable_development_goals":[{"score":0.5,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G1856340036","display_name":null,"funder_award_id":"EP/L000776/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5070881316","display_name":"Unifying audio signal processing and machine learning: a fundamental framework for machine hearing","funder_award_id":"EP/L000776/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G756866442","display_name":null,"funder_award_id":"EP/H026266/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1551479102.pdf","grobid_xml":"https://content.openalex.org/works/W1551479102.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1563088657","https://openalex.org/W1975681165","https://openalex.org/W1982175152","https://openalex.org/W2003891054","https://openalex.org/W2014158063","https://openalex.org/W2027467343","https://openalex.org/W2091669036","https://openalex.org/W2109743529","https://openalex.org/W2111052925","https://openalex.org/W2137226992","https://openalex.org/W2139320579","https://openalex.org/W2153290280","https://openalex.org/W2167932108","https://openalex.org/W2588559030","https://openalex.org/W2725819117","https://openalex.org/W2798121865","https://openalex.org/W4247710323","https://openalex.org/W6680532697"],"related_works":["https://openalex.org/W2232554483","https://openalex.org/W2535206775","https://openalex.org/W4247446331","https://openalex.org/W4243330733","https://openalex.org/W2172290429","https://openalex.org/W1975708617","https://openalex.org/W3118393464","https://openalex.org/W25117969","https://openalex.org/W3168604437","https://openalex.org/W177392165"],"abstract_inverted_index":{"Quaternion":[0],"reproducing":[1],"kernel":[2,95],"Hilbert":[3],"spaces":[4],"(QRKHS)":[5],"have":[6],"been":[7],"proposed":[8],"recently":[9],"and":[10,75,80],"provide":[11],"a":[12,57,92],"high-dimensional":[13],"feature":[14],"space":[15],"(alternative":[16],"to":[17,42,60],"the":[18,33,44,48,103],"real-valued":[19],"multikernel":[20],"approach)":[21],"for":[22],"general":[23,36,86],"kernel-learning":[24],"applications.":[25,108],"The":[26],"current":[27],"challenge":[28],"within":[29],"quaternion-kernel":[30],"learning":[31],"is":[32,65,90,100],"lack":[34],"of":[35,47,96,105],"quaternion-valued":[37,62],"kernels,":[38,63],"which":[39,99],"are":[40],"necessary":[41],"exploit":[43],"full":[45],"advantages":[46],"QRKHS":[49],"theory":[50],"in":[51,102],"real-world":[52],"problems.":[53],"This":[54],"letter":[55],"proposes":[56],"novel":[58],"way":[59],"design":[61],"this":[64,85],"achieved":[66],"by":[67],"transforming":[68],"three":[69],"complex":[70],"kernels":[71],"into":[72],"quaternion":[73,94],"ones":[74],"then":[76],"combining":[77],"their":[78],"real":[79],"imaginary":[81],"parts.":[82],"Building":[83],"on":[84,91],"construction,":[87],"our":[88],"emphasis":[89],"new":[93],"polynomial":[97],"features,":[98],"assessed":[101],"prediction":[104],"bodysensor":[106],"networks":[107]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}