{"id":"https://openalex.org/W2897028039","doi":"https://doi.org/10.3390/sym10100525","title":"Feedforward Neural Networks with a Hidden Layer Regularization Method","display_name":"Feedforward Neural Networks with a Hidden Layer Regularization Method","publication_year":2018,"publication_date":"2018-10-19","ids":{"openalex":"https://openalex.org/W2897028039","doi":"https://doi.org/10.3390/sym10100525","mag":"2897028039"},"language":"en","primary_location":{"id":"doi:10.3390/sym10100525","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10100525","pdf_url":"https://www.mdpi.com/2073-8994/10/10/525/pdf?version=1539935987","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/10/10/525/pdf?version=1539935987","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022324179","display_name":"Habtamu Zegeye Alemu","orcid":"https://orcid.org/0000-0002-2729-6134"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Habtamu Zegeye Alemu","raw_affiliation_strings":["School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China"],"raw_orcid":"https://orcid.org/0000-0002-2729-6134","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101502207","display_name":"Wei Wu","orcid":"https://orcid.org/0000-0002-2018-7058"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wei Wu","raw_affiliation_strings":["School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048022062","display_name":"Junhong Zhao","orcid":"https://orcid.org/0000-0001-7031-3828"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Junhong Zhao","raw_affiliation_strings":["School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China","institution_ids":["https://openalex.org/I27357992"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101502207"],"corresponding_institution_ids":["https://openalex.org/I27357992"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":3.218,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.93645852,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"10","issue":"10","first_page":"525","last_page":"525"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12676","display_name":"Machine Learning and ELM","score":0.9983999729156494,"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/T12676","display_name":"Machine Learning and ELM","score":0.9983999729156494,"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/T10320","display_name":"Neural Networks and Applications","score":0.9980000257492065,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9972000122070312,"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/regularization","display_name":"Regularization (linguistics)","score":0.7992103099822998},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6316641569137573},{"id":"https://openalex.org/keywords/regularization-perspectives-on-support-vector-machines","display_name":"Regularization perspectives on support vector machines","score":0.6257861256599426},{"id":"https://openalex.org/keywords/feedforward-neural-network","display_name":"Feedforward neural network","score":0.5910712480545044},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5618976354598999},{"id":"https://openalex.org/keywords/feed-forward","display_name":"Feed forward","score":0.5091049075126648},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45501816272735596},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4412633776664734},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.42553552985191345},{"id":"https://openalex.org/keywords/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.41185638308525085},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.38539746403694153},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3031154274940491},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.16098865866661072}],"concepts":[{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.7992103099822998},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6316641569137573},{"id":"https://openalex.org/C141718189","wikidata":"https://www.wikidata.org/wiki/Q7309628","display_name":"Regularization perspectives on support vector machines","level":4,"score":0.6257861256599426},{"id":"https://openalex.org/C47702885","wikidata":"https://www.wikidata.org/wiki/Q5441227","display_name":"Feedforward neural network","level":3,"score":0.5910712480545044},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5618976354598999},{"id":"https://openalex.org/C38858127","wikidata":"https://www.wikidata.org/wiki/Q5441228","display_name":"Feed forward","level":2,"score":0.5091049075126648},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45501816272735596},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4412633776664734},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.42553552985191345},{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.41185638308525085},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.38539746403694153},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3031154274940491},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.16098865866661072},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym10100525","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10100525","pdf_url":"https://www.mdpi.com/2073-8994/10/10/525/pdf?version=1539935987","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:933f83944b2e404da28190e1fb6bf69b","is_oa":true,"landing_page_url":"https://doaj.org/article/933f83944b2e404da28190e1fb6bf69b","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 10, Iss 10, p 525 (2018)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/10/10/525/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym10100525","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym10100525","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym10100525","pdf_url":"https://www.mdpi.com/2073-8994/10/10/525/pdf?version=1539935987","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2897028039.pdf","grobid_xml":"https://content.openalex.org/works/W2897028039.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W1498436455","https://openalex.org/W1902150074","https://openalex.org/W2002016471","https://openalex.org/W2025594527","https://openalex.org/W2031001353","https://openalex.org/W2041891835","https://openalex.org/W2059174629","https://openalex.org/W2088350412","https://openalex.org/W2100964683","https://openalex.org/W2101927907","https://openalex.org/W2104948848","https://openalex.org/W2106398669","https://openalex.org/W2111719156","https://openalex.org/W2135046866","https://openalex.org/W2138019504","https://openalex.org/W2145085734","https://openalex.org/W2151669914","https://openalex.org/W2154987621","https://openalex.org/W2156150815","https://openalex.org/W2158143121","https://openalex.org/W2159196737","https://openalex.org/W2294378923","https://openalex.org/W2394043783","https://openalex.org/W2730619644","https://openalex.org/W3022436500","https://openalex.org/W6665370899","https://openalex.org/W6677103964","https://openalex.org/W6682104965","https://openalex.org/W6730382033","https://openalex.org/W7052510944"],"related_works":["https://openalex.org/W2366023887","https://openalex.org/W2062975788","https://openalex.org/W2388364587","https://openalex.org/W2935233291","https://openalex.org/W2385735574","https://openalex.org/W2030398504","https://openalex.org/W4298516010","https://openalex.org/W2050033254","https://openalex.org/W2075210326","https://openalex.org/W2062342781"],"abstract_inverted_index":{"In":[0,166],"this":[1],"paper,":[2],"we":[3],"propose":[4],"a":[5,11,21,32,38,57,59,81],"group":[6,22,82],"Lasso":[7,23,61,170],"regularization":[8,14,24,35,62,77,149,171],"term":[9,25,36],"as":[10,31],"hidden":[12,33,47,75,147,154,187],"layer":[13,34,48,76,148,155,188],"method":[15,63,78,125,150,172],"for":[16,158],"feedforward":[17,52],"neural":[18,53,108],"networks.":[19],"Adding":[20],"into":[26,66],"the":[27,43,51,71,90,99,107,114,136,168,175,179],"standard":[28,67],"error":[29,68],"function":[30,69],"is":[37,64],"fruitful":[39],"approach":[40],"to":[41,86,130,134],"eliminate":[42],"redundant":[44,153,176,186],"or":[45],"unnecessary":[46],"neurons":[49,156],"from":[50],"network":[54,109],"structure.":[55],"As":[56],"comparison,":[58],"popular":[60],"introduced":[65],"of":[70,83,164,178],"network.":[72],"Our":[73],"novel":[74],"can":[79,94,105],"force":[80],"outgoing":[84],"weights":[85,177],"become":[87],"smaller":[88],"during":[89],"training":[91,100],"process":[92],"and":[93,111,133],"eventually":[95],"be":[96],"removed":[97],"after":[98],"process.":[101],"This":[102],"means":[103],"it":[104,112,182],"simplify":[106],"structure":[110],"minimizes":[113],"computational":[115],"cost.":[116],"Numerical":[117],"simulations":[118],"are":[119],"provided":[120],"by":[121],"using":[122],"K-fold":[123],"cross-validation":[124],"with":[126],"K":[127],"=":[128],"5":[129],"avoid":[131],"overtraining":[132],"select":[135],"best":[137],"learning":[138],"parameters.":[139],"The":[140],"numerical":[141],"results":[142],"show":[143],"that":[144],"our":[145],"proposed":[146],"prunes":[151,173],"more":[152],"consistently":[157],"each":[159],"benchmark":[160],"dataset":[161],"without":[162],"loss":[163],"accuracy.":[165],"contrast,":[167],"existing":[169],"only":[174],"network,":[180],"but":[181],"cannot":[183],"prune":[184],"any":[185],"neurons.":[189]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}