{"id":"https://openalex.org/W3033656597","doi":"https://doi.org/10.3934/mfc.2020010","title":"Modeling interactive components by coordinate kernel polynomial models","display_name":"Modeling interactive components by coordinate kernel polynomial models","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3033656597","doi":"https://doi.org/10.3934/mfc.2020010","mag":"3033656597"},"language":"en","primary_location":{"id":"doi:10.3934/mfc.2020010","is_oa":true,"landing_page_url":"https://doi.org/10.3934/mfc.2020010","pdf_url":null,"source":{"id":"https://openalex.org/S4210238810","display_name":"Mathematical Foundations of Computing","issn_l":"2577-8838","issn":["2577-8838"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Foundations of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/mfc.2020010","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016055499","display_name":"Xin Guo","orcid":"https://orcid.org/0000-0002-7465-9356"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]},{"id":"https://openalex.org/I169615421","display_name":"Middle Tennessee State University","ror":"https://ror.org/02n1hzn07","country_code":"US","type":"education","lineage":["https://openalex.org/I169615421"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["HK","US"],"is_corresponding":false,"raw_author_name":"Xin Guo","raw_affiliation_strings":["Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN 37132, USA","Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China","Division of Biostatistics, University of California, Berkeley, Berkeley, CA 94720, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN 37132, USA","institution_ids":["https://openalex.org/I169615421"]},{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China","institution_ids":["https://openalex.org/I14243506"]},{"raw_affiliation_string":"Division of Biostatistics, University of California, Berkeley, Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017399049","display_name":"Lexin Li","orcid":"https://orcid.org/0000-0003-2962-1989"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]},{"id":"https://openalex.org/I169615421","display_name":"Middle Tennessee State University","ror":"https://ror.org/02n1hzn07","country_code":"US","type":"education","lineage":["https://openalex.org/I169615421"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["HK","US"],"is_corresponding":false,"raw_author_name":"Lexin Li","raw_affiliation_strings":["Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China","Division of Biostatistics, University of California, Berkeley, Berkeley, CA 94720, USA","Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN 37132, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China","institution_ids":["https://openalex.org/I14243506"]},{"raw_affiliation_string":"Division of Biostatistics, University of California, Berkeley, Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN 37132, USA","institution_ids":["https://openalex.org/I169615421"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089720861","display_name":"Qiang Wu","orcid":"https://orcid.org/0000-0002-4698-6966"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]},{"id":"https://openalex.org/I169615421","display_name":"Middle Tennessee State University","ror":"https://ror.org/02n1hzn07","country_code":"US","type":"education","lineage":["https://openalex.org/I169615421"]},{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["HK","US"],"is_corresponding":false,"raw_author_name":"Qiang Wu","raw_affiliation_strings":["Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China","Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN 37132, USA","Division of Biostatistics, University of California, Berkeley, Berkeley, CA 94720, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China","institution_ids":["https://openalex.org/I14243506"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN 37132, USA","institution_ids":["https://openalex.org/I169615421"]},{"raw_affiliation_string":"Division of Biostatistics, University of California, Berkeley, Berkeley, CA 94720, USA","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.5207,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.94000159,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"3","issue":"4","first_page":"263","last_page":"277"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9916999936103821,"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":0.9916999936103821,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9311000108718872,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9200000166893005,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/kernel","display_name":"Kernel (algebra)","score":0.6906825304031372},{"id":"https://openalex.org/keywords/polynomial-kernel","display_name":"Polynomial kernel","score":0.6332999467849731},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5978981852531433},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5920805335044861},{"id":"https://openalex.org/keywords/kernel-principal-component-analysis","display_name":"Kernel principal component analysis","score":0.5800228714942932},{"id":"https://openalex.org/keywords/polynomial-regression","display_name":"Polynomial regression","score":0.5482781529426575},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5036532282829285},{"id":"https://openalex.org/keywords/perspective","display_name":"Perspective (graphical)","score":0.4623137414455414},{"id":"https://openalex.org/keywords/kernel-method","display_name":"Kernel method","score":0.4587768018245697},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.4465804994106293},{"id":"https://openalex.org/keywords/kernel-regression","display_name":"Kernel regression","score":0.44632527232170105},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.43556058406829834},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.37992286682128906},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37272346019744873},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3693774938583374},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.35961735248565674},{"id":"https://openalex.org/keywords/regression-analysis","display_name":"Regression analysis","score":0.3112908899784088},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.2841583490371704},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.1912519931793213},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13077181577682495},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.10327675938606262}],"concepts":[{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6906825304031372},{"id":"https://openalex.org/C160446489","wikidata":"https://www.wikidata.org/wiki/Q7226642","display_name":"Polynomial kernel","level":4,"score":0.6332999467849731},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5978981852531433},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5920805335044861},{"id":"https://openalex.org/C182335926","wikidata":"https://www.wikidata.org/wiki/Q17093020","display_name":"Kernel principal component analysis","level":4,"score":0.5800228714942932},{"id":"https://openalex.org/C120068334","wikidata":"https://www.wikidata.org/wiki/Q45343","display_name":"Polynomial regression","level":3,"score":0.5482781529426575},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5036532282829285},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.4623137414455414},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.4587768018245697},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.4465804994106293},{"id":"https://openalex.org/C200695384","wikidata":"https://www.wikidata.org/wiki/Q1739319","display_name":"Kernel regression","level":3,"score":0.44632527232170105},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.43556058406829834},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.37992286682128906},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37272346019744873},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3693774938583374},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.35961735248565674},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.3112908899784088},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.2841583490371704},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.1912519931793213},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13077181577682495},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.10327675938606262},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3934/mfc.2020010","is_oa":true,"landing_page_url":"https://doi.org/10.3934/mfc.2020010","pdf_url":null,"source":{"id":"https://openalex.org/S4210238810","display_name":"Mathematical Foundations of Computing","issn_l":"2577-8838","issn":["2577-8838"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Foundations of Computing","raw_type":"journal-article"},{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/88208","is_oa":false,"landing_page_url":"http://hdl.handle.net/10397/88208","pdf_url":null,"source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"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":"Journal/Magazine Article"}],"best_oa_location":{"id":"doi:10.3934/mfc.2020010","is_oa":true,"landing_page_url":"https://doi.org/10.3934/mfc.2020010","pdf_url":null,"source":{"id":"https://openalex.org/S4210238810","display_name":"Mathematical Foundations of Computing","issn_l":"2577-8838","issn":["2577-8838"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Foundations of Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W62188234","https://openalex.org/W1597405158","https://openalex.org/W1973167793","https://openalex.org/W2012449009","https://openalex.org/W2033222113","https://openalex.org/W2053609837","https://openalex.org/W2080726496","https://openalex.org/W2083575259","https://openalex.org/W2102201073","https://openalex.org/W2103972570","https://openalex.org/W2108198948","https://openalex.org/W2115390216","https://openalex.org/W2121033924","https://openalex.org/W2122825543","https://openalex.org/W2122925131","https://openalex.org/W2128833476","https://openalex.org/W2135046866","https://openalex.org/W2145295623","https://openalex.org/W2146766088","https://openalex.org/W2148603752","https://openalex.org/W2164535072","https://openalex.org/W2182468807","https://openalex.org/W2310653300","https://openalex.org/W2579923771","https://openalex.org/W2911111822","https://openalex.org/W2956975562","https://openalex.org/W2962918401","https://openalex.org/W2989661724","https://openalex.org/W3004943848","https://openalex.org/W3016405139","https://openalex.org/W4313169793"],"related_works":["https://openalex.org/W2393746448","https://openalex.org/W1984421104","https://openalex.org/W2512565647","https://openalex.org/W2384322977","https://openalex.org/W2001772920","https://openalex.org/W2164869055","https://openalex.org/W2182834820","https://openalex.org/W2071590642","https://openalex.org/W2149803014","https://openalex.org/W2890196891"],"abstract_inverted_index":{"We":[0],"proposed":[1],"the":[2,35,59,62],"use":[3],"of":[4,61],"coordinate":[5,15],"kernel":[6,9,16],"polynomials":[7],"in":[8],"regression.":[10],"This":[11],"new":[12],"approach,":[13],"called":[14],"polynomial":[17],"regression,":[18],"can":[19],"simultaneously":[20],"identify":[21,48],"active":[22],"variables":[23],"and":[24,38,69],"effective":[25,49],"interactive":[26,50],"components.":[27,51],"Reparametrization":[28],"refinement":[29],"is":[30],"found":[31],"critical":[32],"to":[33,47,57,74],"improve":[34],"modeling":[36],"accuracy":[37],"prediction":[39],"power.":[40],"The":[41],"post-training":[42],"component":[43],"selection":[44],"allows":[45],"one":[46],"Generalization":[52],"error":[53],"bounds":[54],"are":[55,72],"used":[56,73],"explain":[58],"effectiveness":[60],"algorithm":[63],"from":[64],"a":[65],"learning":[66],"theory":[67],"perspective":[68],"simulation":[70],"studies":[71],"show":[75],"its":[76],"empirical":[77],"effectiveness.":[78]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":22}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}