{"id":"https://openalex.org/W2082500594","doi":"https://doi.org/10.1007/s10444-004-3140-6","title":"Positive definite dot product kernels in learning theory","display_name":"Positive definite dot product kernels in learning theory","publication_year":2005,"publication_date":"2005-01-19","ids":{"openalex":"https://openalex.org/W2082500594","doi":"https://doi.org/10.1007/s10444-004-3140-6","mag":"2082500594"},"language":"en","primary_location":{"id":"doi:10.1007/s10444-004-3140-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10444-004-3140-6","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","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/A5111473339","display_name":"Fangyan Lu","orcid":null},"institutions":[{"id":"https://openalex.org/I3923682","display_name":"Soochow University","ror":"https://ror.org/05t8y2r12","country_code":"CN","type":"education","lineage":["https://openalex.org/I3923682"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Fangyan Lu","raw_affiliation_strings":["Department of Mathematics, Suzhou University, Suzhou, 215006, Peoples\u2019s Republic of China","Department of Mathematics, Suzhou University, Suzhou, Peoples\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Suzhou University, Suzhou, 215006, Peoples\u2019s Republic of China","institution_ids":["https://openalex.org/I3923682"]},{"raw_affiliation_string":"Department of Mathematics, Suzhou University, Suzhou, Peoples\u2019s Republic of China","institution_ids":["https://openalex.org/I3923682"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029471997","display_name":"Hongwei Sun","orcid":null},"institutions":[{"id":"https://openalex.org/I159948400","display_name":"Jinan University","ror":"https://ror.org/02xe5ns62","country_code":"CN","type":"education","lineage":["https://openalex.org/I159948400"]},{"id":"https://openalex.org/I34949971","display_name":"University of Jinan","ror":"https://ror.org/02mjz6f26","country_code":"CN","type":"education","lineage":["https://openalex.org/I34949971"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongwei Sun","raw_affiliation_strings":["School of Science, Jinan University (West), Jinan, 230000, Peoples\u2019s Republic of China","School of Science, Jinan University (West), Jinan, Peoples\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Science, Jinan University (West), Jinan, 230000, Peoples\u2019s Republic of China","institution_ids":["https://openalex.org/I34949971","https://openalex.org/I159948400"]},{"raw_affiliation_string":"School of Science, Jinan University (West), Jinan, Peoples\u2019s Republic of China","institution_ids":["https://openalex.org/I159948400"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111473339"],"corresponding_institution_ids":["https://openalex.org/I3923682"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":2.8209,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.89713306,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"22","issue":"2","first_page":"181","last_page":"198"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.992900013923645,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.992900013923645,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9886999726295471,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9771000146865845,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/positive-definiteness","display_name":"Positive definiteness","score":0.8527791500091553},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.8458556532859802},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7739109396934509},{"id":"https://openalex.org/keywords/dot-product","display_name":"Dot product","score":0.7259691953659058},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6485469937324524},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5911655426025391},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5447003841400146},{"id":"https://openalex.org/keywords/polynomial-kernel","display_name":"Polynomial kernel","score":0.5421037077903748},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5303474068641663},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5059975981712341},{"id":"https://openalex.org/keywords/computational-science-and-engineering","display_name":"Computational Science and Engineering","score":0.48981067538261414},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.44064462184906006},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43234843015670776},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36435580253601074},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.3313669264316559},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19225603342056274},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.16153892874717712},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.1542835235595703},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09785008430480957},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09180322289466858},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07866683602333069}],"concepts":[{"id":"https://openalex.org/C2778265155","wikidata":"https://www.wikidata.org/wiki/Q7233276","display_name":"Positive definiteness","level":4,"score":0.8527791500091553},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.8458556532859802},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7739109396934509},{"id":"https://openalex.org/C32900221","wikidata":"https://www.wikidata.org/wiki/Q181365","display_name":"Dot product","level":2,"score":0.7259691953659058},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6485469937324524},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5911655426025391},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5447003841400146},{"id":"https://openalex.org/C160446489","wikidata":"https://www.wikidata.org/wiki/Q7226642","display_name":"Polynomial kernel","level":4,"score":0.5421037077903748},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5303474068641663},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5059975981712341},{"id":"https://openalex.org/C68597687","wikidata":"https://www.wikidata.org/wiki/Q362601","display_name":"Computational Science and Engineering","level":2,"score":0.48981067538261414},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.44064462184906006},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43234843015670776},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36435580253601074},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.3313669264316559},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19225603342056274},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.16153892874717712},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.1542835235595703},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09785008430480957},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09180322289466858},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07866683602333069},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10444-004-3140-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10444-004-3140-6","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320309893","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23"},{"id":"https://openalex.org/F4320322170","display_name":"University of Hong Kong","ror":"https://ror.org/02zhqgq86"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W90602582","https://openalex.org/W146536823","https://openalex.org/W593575362","https://openalex.org/W797193083","https://openalex.org/W1515416301","https://openalex.org/W1968436459","https://openalex.org/W2009047292","https://openalex.org/W2039402388","https://openalex.org/W2047278710","https://openalex.org/W2061872779","https://openalex.org/W2079278943","https://openalex.org/W2110652811","https://openalex.org/W2141224867","https://openalex.org/W2146766088","https://openalex.org/W2148603752","https://openalex.org/W2149614431","https://openalex.org/W2158781299","https://openalex.org/W2746534045","https://openalex.org/W4244829582","https://openalex.org/W4285719527","https://openalex.org/W4298876635"],"related_works":["https://openalex.org/W2369793817","https://openalex.org/W2364489971","https://openalex.org/W2361979571","https://openalex.org/W3208377712","https://openalex.org/W2043819621","https://openalex.org/W2063005030","https://openalex.org/W2147922812","https://openalex.org/W4205226845","https://openalex.org/W2373372131","https://openalex.org/W2082500594"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
