{"id":"https://openalex.org/W1754345609","doi":"https://doi.org/10.48550/arxiv.cs/0207018","title":"Definitions of distance function in radial basis function approach","display_name":"Definitions of distance function in radial basis function approach","publication_year":2002,"publication_date":"2002-07-04","ids":{"openalex":"https://openalex.org/W1754345609","doi":"https://doi.org/10.48550/arxiv.cs/0207018","mag":"1754345609"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:cs/0207018","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/cs/0207018","pdf_url":"https://arxiv.org/pdf/cs/0207018","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/cs/0207018","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100344143","display_name":"Wen Chen","orcid":"https://orcid.org/0000-0001-5678-4949","observed_orcids":["https://orcid.org/0000-0001-5678-4949","https://orcid.org/0000-0003-2013-9176"]},"institutions":[{"id":"https://openalex.org/I137975476","display_name":"Shinshu University","ror":"https://ror.org/0244rem06","country_code":"JP","type":"education","lineage":["https://openalex.org/I137975476"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Chen, W.","raw_affiliation_strings":["Shinshu University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shinshu University","institution_ids":["https://openalex.org/I137975476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100344143"],"corresponding_institution_ids":["https://openalex.org/I137975476"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9502000212669373,"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"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9502000212669373,"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"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.031300000846385956,"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":0.002400000113993883,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/radial-basis-functions","display_name":"radial basis functions","score":0.9860000014305115},{"id":"https://openalex.org/keywords/distance-metrics","display_name":"distance measures","score":0.8730000257492065},{"id":"https://openalex.org/keywords/geodesic-distance","display_name":"geodesic distance","score":0.8420000076293945},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.824999988079071}],"concepts":[{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.8746883273124695},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.6523164510726929},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5930788516998291},{"id":"https://openalex.org/C80269521","wikidata":"https://www.wikidata.org/wiki/Q7280269","display_name":"Radial function","level":2,"score":0.5417066812515259},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.5322475433349609},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5304068326950073},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.46323534846305847},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4534771740436554},{"id":"https://openalex.org/C71169176","wikidata":"https://www.wikidata.org/wiki/Q7512907","display_name":"Signed distance function","level":2,"score":0.4399033784866333},{"id":"https://openalex.org/C132917294","wikidata":"https://www.wikidata.org/wiki/Q2679684","display_name":"Radial basis function network","level":4,"score":0.4152049422264099},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40277931094169617},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3781103193759918},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28218984603881836},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17975234985351562},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0675014853477478},{"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:cs/0207018","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/cs/0207018","pdf_url":"https://arxiv.org/pdf/cs/0207018","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"doi:10.48550/arxiv.cs/0207018","doi":"https://doi.org/10.48550/arxiv.cs/0207018","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.cs/0207018","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:cs/0207018","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/cs/0207018","pdf_url":"https://arxiv.org/pdf/cs/0207018","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1540737741","https://openalex.org/W2034120412","https://openalex.org/W2504622078","https://openalex.org/W2963126596"],"related_works":["https://openalex.org/W4230534566","https://openalex.org/W2105180757","https://openalex.org/W1992876914","https://openalex.org/W3040050968","https://openalex.org/W157952102","https://openalex.org/W2127045326","https://openalex.org/W1480102187","https://openalex.org/W2009646067","https://openalex.org/W2765868124","https://openalex.org/W1989173802"],"abstract_inverted_index":{"Very":[0],"few":[1],"studies":[2],"involve":[3],"how":[4],"to":[5,25,59],"construct":[6],"the":[7,16,32,35,49],"efficient":[8],"RBFs":[9,28],"by":[10],"means":[11],"of":[12,55],"problem":[13,66],"features.":[14],"Recently":[15],"present":[17],"author":[18],"presented":[19],"general":[20],"solution":[21],"RBF":[22],"(GS-RBF)":[23],"methodology":[24],"create":[26],"operator-dependent":[27],"successfully":[29],"[1].":[30],"On":[31],"other":[33],"hand,":[34],"normal":[36],"radial":[37],"basis":[38],"function":[39,47,62],"(RBF)":[40],"is":[41,58],"defined":[42],"via":[43],"Euclidean":[44],"space":[45],"distance":[46,51,61,73],"or":[48],"geodesic":[50],"[2].":[52],"This":[53],"purpose":[54],"this":[56],"note":[57],"redefine":[60],"in":[63],"conjunction":[64],"with":[65],"features,":[67],"which":[68],"include":[69],"problem-dependent":[70],"and":[71],"time-space":[72],"function.":[74]},"counts_by_year":[],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2025-10-10T00:00:00"}