{"id":"https://openalex.org/W4393054777","doi":"https://doi.org/10.54097/xwvpkd67","title":"A Sigma-Pi-Sigma Neural Network Model with Graph Regularity Term","display_name":"A Sigma-Pi-Sigma Neural Network Model with Graph Regularity Term","publication_year":2024,"publication_date":"2024-03-11","ids":{"openalex":"https://openalex.org/W4393054777","doi":"https://doi.org/10.54097/xwvpkd67"},"language":"en","primary_location":{"id":"doi:10.54097/xwvpkd67","doi":"https://doi.org/10.54097/xwvpkd67","is_oa":true,"landing_page_url":"https://doi.org/10.54097/xwvpkd67","pdf_url":"https://drpress.org/ojs/index.php/fcis/article/download/17883/17395","source":{"id":"https://openalex.org/S4387283309","display_name":"Frontiers in Computing and Intelligent Systems","issn_l":"2832-6024","issn":["2832-6024"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Computing and Intelligent Systems","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://drpress.org/ojs/index.php/fcis/article/download/17883/17395","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5104064329","display_name":"Qianru Huang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I27599042","display_name":"Xi'an Polytechnic University","ror":"https://ror.org/03442p831","country_code":"CN","type":"education","lineage":["https://openalex.org/I27599042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qianru Huang","raw_affiliation_strings":["Xi'an Polytechnic University, Xi'an, Shaanxi, 710600, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Xi'an Polytechnic University, Xi'an, Shaanxi, 710600, China","institution_ids":["https://openalex.org/I27599042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109694133","display_name":"Qingmei Dong","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I27599042","display_name":"Xi'an Polytechnic University","ror":"https://ror.org/03442p831","country_code":"CN","type":"education","lineage":["https://openalex.org/I27599042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qingmei Dong","raw_affiliation_strings":["Xi'an Polytechnic University, Xi'an, Shaanxi, 710600, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Xi'an Polytechnic University, Xi'an, Shaanxi, 710600, China","institution_ids":["https://openalex.org/I27599042"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Yunlong Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I27599042","display_name":"Xi'an Polytechnic University","ror":"https://ror.org/03442p831","country_code":"CN","type":"education","lineage":["https://openalex.org/I27599042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yunlong Liu","raw_affiliation_strings":["Xi'an Polytechnic University, Xi'an, Shaanxi, 710600, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Xi'an Polytechnic University, Xi'an, Shaanxi, 710600, China","institution_ids":["https://openalex.org/I27599042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101321440","display_name":"Deqing Ji","orcid":"https://orcid.org/0009-0001-9979-0465","observed_orcids":["https://orcid.org/0009-0001-9979-0465"]},"institutions":[{"id":"https://openalex.org/I27599042","display_name":"Xi'an Polytechnic University","ror":"https://ror.org/03442p831","country_code":"CN","type":"education","lineage":["https://openalex.org/I27599042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Deqing Ji","raw_affiliation_strings":["Xi'an Polytechnic University, Xi'an, Shaanxi, 710600, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Xi'an Polytechnic University, Xi'an, Shaanxi, 710600, China","institution_ids":["https://openalex.org/I27599042"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022385306","display_name":"Qinwei Fan","orcid":"https://orcid.org/0000-0002-1017-3496","observed_orcids":["https://orcid.org/0000-0002-1017-3496"]},"institutions":[{"id":"https://openalex.org/I27599042","display_name":"Xi'an Polytechnic University","ror":"https://ror.org/03442p831","country_code":"CN","type":"education","lineage":["https://openalex.org/I27599042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qinwei Fan","raw_affiliation_strings":["Xi'an Polytechnic University, Xi'an, Shaanxi, 710600, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Xi'an Polytechnic University, Xi'an, Shaanxi, 710600, China","institution_ids":["https://openalex.org/I27599042"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I27599042"],"apc_list":null,"apc_paid":null,"fwci":0.147,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.42785114,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"7","issue":"2","first_page":"34","last_page":"37"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9955999851226807,"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":0.9955999851226807,"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/T12676","display_name":"Machine Learning and ELM","score":0.0035000001080334187,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/higher-order-neural-networks","display_name":"higher order neural networks","score":0.9350000023841858},{"id":"https://openalex.org/keywords/graph-neural-networks","display_name":"graph neural networks","score":0.5789999961853027},{"id":"https://openalex.org/keywords/overfitting","display_name":"overfitting","score":0.7129999995231628},{"id":"https://openalex.org/keywords/underfitting","display_name":"underfitting","score":0.9829999804496765},{"id":"https://openalex.org/keywords/model-generalization","display_name":"model generalization","score":0.7509999871253967},{"id":"https://openalex.org/keywords/hidden-neuron-selection","display_name":"hidden neuron selection","score":0.7020000219345093}],"concepts":[{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.8386637568473816},{"id":"https://openalex.org/C53009064","wikidata":"https://www.wikidata.org/wiki/Q167","display_name":"Pi","level":2,"score":0.7099121809005737},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.6406999230384827},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5456053614616394},{"id":"https://openalex.org/C23119410","wikidata":"https://www.wikidata.org/wiki/Q236908","display_name":"Six Sigma","level":3,"score":0.47694411873817444},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4262217879295349},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38586723804473877},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37714114785194397},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3278660178184509},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2943282723426819},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23555868864059448},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.11118480563163757},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07461526989936829},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05578821897506714},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.050849735736846924},{"id":"https://openalex.org/C137335462","wikidata":"https://www.wikidata.org/wiki/Q380772","display_name":"Lean manufacturing","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.54097/xwvpkd67","doi":"https://doi.org/10.54097/xwvpkd67","is_oa":true,"landing_page_url":"https://doi.org/10.54097/xwvpkd67","pdf_url":"https://drpress.org/ojs/index.php/fcis/article/download/17883/17395","source":{"id":"https://openalex.org/S4387283309","display_name":"Frontiers in Computing and Intelligent Systems","issn_l":"2832-6024","issn":["2832-6024"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Computing and Intelligent Systems","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.54097/xwvpkd67","doi":"https://doi.org/10.54097/xwvpkd67","is_oa":true,"landing_page_url":"https://doi.org/10.54097/xwvpkd67","pdf_url":"https://drpress.org/ojs/index.php/fcis/article/download/17883/17395","source":{"id":"https://openalex.org/S4387283309","display_name":"Frontiers in Computing and Intelligent Systems","issn_l":"2832-6024","issn":["2832-6024"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Computing and Intelligent Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4393054777.pdf","grobid_xml":"https://content.openalex.org/works/W4393054777.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W2095552930","https://openalex.org/W2141523690","https://openalex.org/W2905915262","https://openalex.org/W3022436500","https://openalex.org/W3093231382","https://openalex.org/W3217439888","https://openalex.org/W4214818503","https://openalex.org/W4220827019","https://openalex.org/W4281728148"],"related_works":["https://openalex.org/W2787222456","https://openalex.org/W7167224607","https://openalex.org/W4391453511","https://openalex.org/W4297878125","https://openalex.org/W4307727076","https://openalex.org/W4412156567","https://openalex.org/W4406015381","https://openalex.org/W4384071424","https://openalex.org/W2182205249","https://openalex.org/W4408914128"],"abstract_inverted_index":{"In":[0],"recent":[1],"years,":[2],"Sigma-Pi-Sigma":[3,58],"neural":[4,13,59],"network":[5,14,60],"(SPSNN)":[6],"as":[7],"a":[8,57,66],"special":[9],"kind":[10],"of":[11,32,51,84],"higher-order":[12],"has":[15],"attracted":[16],"wide":[17],"attention":[18],"for":[19],"its":[20],"fast":[21],"convergence":[22],"speed":[23],"and":[24,48,89],"good":[25],"approximation":[26],"ability.":[27],"However,":[28],"an":[29],"inappropriate":[30],"number":[31],"hidden":[33],"layer":[34],"neurons":[35],"may":[36],"also":[37],"lead":[38],"to":[39,70],"model":[40],"underfitting":[41],"or":[42],"overfitting,":[43],"which":[44],"affects":[45],"the":[46,52,71,77],"performance":[47],"generalization":[49],"ability":[50],"model.":[53],"Therefore,":[54],"we":[55],"propose":[56],"with":[61],"graph":[62,67],"regularity":[63,68],"by":[64],"adding":[65],"term":[69],"network.":[72],"The":[73],"results":[74],"show":[75],"that":[76],"proposed":[78],"algorithm":[79],"performs":[80],"well":[81],"in":[82],"terms":[83],"training":[85],"accuracy,":[86],"testing":[87],"accuracy":[88],"efficiency.":[90]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2024-03-22T00:00:00"}