{"id":"https://openalex.org/W2548552774","doi":"https://doi.org/10.1109/igarss.2016.7729721","title":"Proof of hidden node number and experiments on RBF network for well log data inversion","display_name":"Proof of hidden node number and experiments on RBF network for well log data inversion","publication_year":2016,"publication_date":"2016-07-01","ids":{"openalex":"https://openalex.org/W2548552774","doi":"https://doi.org/10.1109/igarss.2016.7729721","mag":"2548552774"},"language":"en","primary_location":{"id":"doi:10.1109/igarss.2016.7729721","is_oa":false,"landing_page_url":"https://doi.org/10.1109/igarss.2016.7729721","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE International Geoscience and Remote Sensing Symposium (IGARSS)","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/A5101537676","display_name":"Kou\u2010Yuan Huang","orcid":"https://orcid.org/0000-0001-9900-8480"},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Kou-Yuan Huang","raw_affiliation_strings":["Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan","institution_ids":["https://openalex.org/I148366613"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108648018","display_name":"Liang\u2010Chi Shen","orcid":null},"institutions":[{"id":"https://openalex.org/I44461941","display_name":"University of Houston","ror":"https://ror.org/048sx0r50","country_code":"US","type":"education","lineage":["https://openalex.org/I44461941"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Liang-Chi Shen","raw_affiliation_strings":["Department of Electrical & Computer Engineering, University of Houston, Texas, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical & Computer Engineering, University of Houston, Texas, USA","institution_ids":["https://openalex.org/I44461941"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016036041","display_name":"Jiun-Der You","orcid":null},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Jiun-Der You","raw_affiliation_strings":["Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan","institution_ids":["https://openalex.org/I148366613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039698003","display_name":"Li\u2010Sheng Weng","orcid":null},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Li-Sheng Weng","raw_affiliation_strings":["Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan","institution_ids":["https://openalex.org/I148366613"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07625965,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"i","issue":null,"first_page":"2791","last_page":"2794"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9997000098228455,"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":0.9997000098228455,"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/T10057","display_name":"Face and Expression Recognition","score":0.9793000221252441,"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"}},{"id":"https://openalex.org/T12676","display_name":"Machine Learning and ELM","score":0.9677000045776367,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/perceptron","display_name":"Perceptron","score":0.6217252612113953},{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.5226804614067078},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5151240229606628},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.5037540793418884},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4664881229400635},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4644598662853241},{"id":"https://openalex.org/keywords/radial-basis-function","display_name":"Radial basis function","score":0.4614070951938629},{"id":"https://openalex.org/keywords/node","display_name":"Node (physics)","score":0.4546438455581665},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4450339078903198},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4229142367839813},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33205336332321167},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2358189821243286},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11930125951766968}],"concepts":[{"id":"https://openalex.org/C60908668","wikidata":"https://www.wikidata.org/wiki/Q690207","display_name":"Perceptron","level":3,"score":0.6217252612113953},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.5226804614067078},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5151240229606628},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.5037540793418884},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4664881229400635},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4644598662853241},{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.4614070951938629},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.4546438455581665},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4450339078903198},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4229142367839813},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33205336332321167},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2358189821243286},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11930125951766968},{"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/C109007969","wikidata":"https://www.wikidata.org/wiki/Q749565","display_name":"Structural basin","level":2,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/igarss.2016.7729721","is_oa":false,"landing_page_url":"https://doi.org/10.1109/igarss.2016.7729721","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE International Geoscience and Remote Sensing Symposium (IGARSS)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1498436455","https://openalex.org/W1524100745","https://openalex.org/W1973245942","https://openalex.org/W2011909934","https://openalex.org/W2021505500","https://openalex.org/W2117435895","https://openalex.org/W2283511499","https://openalex.org/W2766736793","https://openalex.org/W3140509714","https://openalex.org/W4245400733","https://openalex.org/W6677620293","https://openalex.org/W6682610290"],"related_works":["https://openalex.org/W2009525028","https://openalex.org/W4321064619","https://openalex.org/W2076561698","https://openalex.org/W2053599029","https://openalex.org/W3011179836","https://openalex.org/W2962925412","https://openalex.org/W2023672523","https://openalex.org/W2096715552","https://openalex.org/W1598419248","https://openalex.org/W2502272432"],"abstract_inverted_index":{"In":[0,81],"the":[1,10,18,25,36,39,58,65,72,82,109,116],"multilayer":[2],"perceptron":[3],"(MLP),":[4],"there":[5],"was":[6],"a":[7,31],"theorem":[8,37],"about":[9],"maximum":[11],"number":[12,19,66,110],"of":[13,20,41,45,67,111],"separable":[14],"regions":[15],"(M)":[16],"given":[17],"hidden":[21,68,112],"nodes":[22,69,113],"(H)":[23],"in":[24],"input":[26],"d-dimensional":[27],"space.":[28],"We":[29,49],"propose":[30],"recurrence":[32,42],"relation":[33,43],"to":[34,63],"prove":[35],"using":[38],"expansion":[40],"instead":[44],"proof":[46],"by":[47,71,115],"induction.":[48],"use":[50],"three-layer":[51,75],"radial":[52],"basis":[53],"function":[54],"net":[55],"(RBF)":[56],"on":[57],"well":[59,88,92],"log":[60,89,93],"data":[61,94],"inversion":[62],"test":[64],"determined":[70,114],"theorem.":[73,117],"The":[74,104],"RBF":[76],"has":[77],"more":[78],"nonlinear":[79],"mapping.":[80],"experiments,":[83],"we":[84],"have":[85],"31":[86],"simulated":[87],"data.":[90],"25":[91],"are":[95,101],"used":[96],"for":[97,102],"training,":[98],"and":[99],"6":[100],"testing.":[103],"experimental":[105],"results":[106],"can":[107],"support":[108]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}