{"id":"https://openalex.org/W2099345067","doi":"https://doi.org/10.1109/ijcnn.2003.1224030","title":"Design of kernels for support multivector machines involving the clifford geometric product and the conformal geometric neuron","display_name":"Design of kernels for support multivector machines involving the clifford geometric product and the conformal geometric neuron","publication_year":2004,"publication_date":"2004-06-22","ids":{"openalex":"https://openalex.org/W2099345067","doi":"https://doi.org/10.1109/ijcnn.2003.1224030","mag":"2099345067"},"language":"en","primary_location":{"id":"doi:10.1109/ijcnn.2003.1224030","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2003.1224030","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the International Joint Conference on Neural Networks, 2003.","raw_type":"proceedings-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/A5017356611","display_name":"Eduardo Bayro\u2013Corrochano","orcid":"https://orcid.org/0000-0002-4738-3593"},"institutions":[{"id":"https://openalex.org/I68368234","display_name":"Center for Research and Advanced Studies of the National Polytechnic Institute","ror":"https://ror.org/009eqmr18","country_code":"MX","type":"facility","lineage":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"E. Bayro-Corrochano","raw_affiliation_strings":["Computer Science Department, CINVESTAV, Centro de Investigaci\u00f3n y de Estudios Avanzados, Guadalajara, Jalisco, Mexico"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, CINVESTAV, Centro de Investigaci\u00f3n y de Estudios Avanzados, Guadalajara, Jalisco, Mexico","institution_ids":["https://openalex.org/I68368234"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111881152","display_name":"N. Arana","orcid":null},"institutions":[{"id":"https://openalex.org/I68368234","display_name":"Center for Research and Advanced Studies of the National Polytechnic Institute","ror":"https://ror.org/009eqmr18","country_code":"MX","type":"facility","lineage":["https://openalex.org/I59361560","https://openalex.org/I68368234"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"N. Arana","raw_affiliation_strings":["Computer Science Department, CINVESTAV, Centro de Investigaci\u00f3n y de Estudios Avanazados del Instituto Polit\u00e9cnico Nacional, Guadalajara, Jalisco, Mexico"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, CINVESTAV, Centro de Investigaci\u00f3n y de Estudios Avanazados del Instituto Polit\u00e9cnico Nacional, Guadalajara, Jalisco, Mexico","institution_ids":["https://openalex.org/I68368234"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046960382","display_name":"R. Vallejo","orcid":null},"institutions":[{"id":"https://openalex.org/I129858807","display_name":"Universidad de Guanajuato","ror":"https://ror.org/058cjye32","country_code":"MX","type":"education","lineage":["https://openalex.org/I129858807"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"R. Vallejo","raw_affiliation_strings":["Escuela de Economia, Universidad de Guanajuato, Guanajuato, Mexico"],"affiliations":[{"raw_affiliation_string":"Escuela de Economia, Universidad de Guanajuato, Guanajuato, Mexico","institution_ids":["https://openalex.org/I129858807"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5017356611"],"corresponding_institution_ids":["https://openalex.org/I68368234"],"apc_list":null,"apc_paid":null,"fwci":2.3071,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.87247597,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"4","issue":null,"first_page":"2893","last_page":"2898"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9907000064849854,"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":0.9907000064849854,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9782999753952026,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.95660001039505,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/geometric-algebra","display_name":"Geometric algebra","score":0.9624886512756348},{"id":"https://openalex.org/keywords/multivector","display_name":"Multivector","score":0.9615768194198608},{"id":"https://openalex.org/keywords/conformal-geometric-algebra","display_name":"Conformal geometric algebra","score":0.883632481098175},{"id":"https://openalex.org/keywords/universal-geometric-algebra","display_name":"Universal geometric algebra","score":0.8204590082168579},{"id":"https://openalex.org/keywords/clifford-algebra","display_name":"Clifford algebra","score":0.7596609592437744},{"id":"https://openalex.org/keywords/geometric-transformation","display_name":"Geometric transformation","score":0.5867860317230225},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5539238452911377},{"id":"https://openalex.org/keywords/geometric-modeling","display_name":"Geometric modeling","score":0.5485901236534119},{"id":"https://openalex.org/keywords/geometric-design","display_name":"Geometric design","score":0.5382421016693115},{"id":"https://openalex.org/keywords/conformal-map","display_name":"Conformal map","score":0.535990834236145},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.522577166557312},{"id":"https://openalex.org/keywords/geometric-primitive","display_name":"Geometric primitive","score":0.47535985708236694},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4502257704734802},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4111612141132355},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32115742564201355},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2401658594608307},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.22298023104667664},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.21595245599746704},{"id":"https://openalex.org/keywords/algebra-representation","display_name":"Algebra representation","score":0.11393928527832031},{"id":"https://openalex.org/keywords/division-algebra","display_name":"Division algebra","score":0.07311800122261047}],"concepts":[{"id":"https://openalex.org/C180671464","wikidata":"https://www.wikidata.org/wiki/Q1186649","display_name":"Geometric algebra","level":4,"score":0.9624886512756348},{"id":"https://openalex.org/C26238338","wikidata":"https://www.wikidata.org/wiki/Q2377336","display_name":"Multivector","level":5,"score":0.9615768194198608},{"id":"https://openalex.org/C147898140","wikidata":"https://www.wikidata.org/wiki/Q5160252","display_name":"Conformal geometric algebra","level":5,"score":0.883632481098175},{"id":"https://openalex.org/C64228544","wikidata":"https://www.wikidata.org/wiki/Q17152794","display_name":"Universal geometric algebra","level":5,"score":0.8204590082168579},{"id":"https://openalex.org/C100856211","wikidata":"https://www.wikidata.org/wiki/Q674689","display_name":"Clifford algebra","level":3,"score":0.7596609592437744},{"id":"https://openalex.org/C56435381","wikidata":"https://www.wikidata.org/wiki/Q1196371","display_name":"Geometric transformation","level":3,"score":0.5867860317230225},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5539238452911377},{"id":"https://openalex.org/C104065381","wikidata":"https://www.wikidata.org/wiki/Q1002535","display_name":"Geometric modeling","level":2,"score":0.5485901236534119},{"id":"https://openalex.org/C40319758","wikidata":"https://www.wikidata.org/wiki/Q5535477","display_name":"Geometric design","level":2,"score":0.5382421016693115},{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.535990834236145},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.522577166557312},{"id":"https://openalex.org/C181095308","wikidata":"https://www.wikidata.org/wiki/Q1541599","display_name":"Geometric primitive","level":2,"score":0.47535985708236694},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4502257704734802},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4111612141132355},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32115742564201355},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2401658594608307},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.22298023104667664},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.21595245599746704},{"id":"https://openalex.org/C14394260","wikidata":"https://www.wikidata.org/wiki/Q4723980","display_name":"Algebra representation","level":3,"score":0.11393928527832031},{"id":"https://openalex.org/C138354692","wikidata":"https://www.wikidata.org/wiki/Q1231309","display_name":"Division algebra","level":4,"score":0.07311800122261047}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ijcnn.2003.1224030","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2003.1224030","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the International Joint Conference on Neural Networks, 2003.","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W122875470","https://openalex.org/W1582195077","https://openalex.org/W2022718409","https://openalex.org/W2103496339","https://openalex.org/W2148603752","https://openalex.org/W2486389867"],"related_works":["https://openalex.org/W1006411175","https://openalex.org/W2579897398","https://openalex.org/W2099688444","https://openalex.org/W2972738333","https://openalex.org/W3022175278","https://openalex.org/W2099345067","https://openalex.org/W2358887633","https://openalex.org/W2423076461","https://openalex.org/W2129397513","https://openalex.org/W2332420753"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"the":[3,13,23,28,49,61,64],"design":[4,24],"of":[5,25,35,63],"kernels":[6,26],"for":[7,53],"nonlinear":[8,36],"support":[9],"vector":[10],"machines":[11],"using":[12],"Clifford":[14,29],"geometric":[15,31,44,51,54],"algebra":[16],"framework.":[17],"In":[18],"this":[19],"study":[20],"we":[21],"present":[22],"involving":[27],"or":[30],"product":[32],"making":[33],"use":[34],"mappings":[37],"which":[38],"map":[39],"multi-vectors":[40],"into":[41],"higher":[42],"dimensional":[43],"algebra.":[45],"We":[46],"introduce":[47],"also":[48],"conformal":[50],"neuron":[52],"classification.":[55],"Experiments":[56],"are":[57],"given":[58],"to":[59],"demonstrate":[60],"usefulness":[62],"approach.":[65]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}