{"id":"https://openalex.org/W2146287682","doi":"https://doi.org/10.1109/tnn.2010.2082561","title":"Periodic Activation Function and a Modified Learning Algorithm for the Multivalued Neuron","display_name":"Periodic Activation Function and a Modified Learning Algorithm for the Multivalued Neuron","publication_year":2010,"publication_date":"2010-11-10","ids":{"openalex":"https://openalex.org/W2146287682","doi":"https://doi.org/10.1109/tnn.2010.2082561","mag":"2146287682","pmid":"https://pubmed.ncbi.nlm.nih.gov/21047711"},"language":"en","primary_location":{"id":"doi:10.1109/tnn.2010.2082561","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnn.2010.2082561","pdf_url":null,"source":{"id":"https://openalex.org/S42080949","display_name":"IEEE Transactions on Neural Networks","issn_l":"1045-9227","issn":["1045-9227","1941-0093"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5052101553","display_name":"Igor Aizenberg","orcid":"https://orcid.org/0000-0002-5994-6568"},"institutions":[{"id":"https://openalex.org/I51380931","display_name":"Texas A&M University \u2013 Texarkana","ror":"https://ror.org/01x3z9745","country_code":"US","type":"education","lineage":["https://openalex.org/I51380931"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Igor Aizenberg","raw_affiliation_strings":["Texas A&M University-Texarkana, 75505, USA. igor.aizenberg@tamut.edu","Texas A&M University-Texarkana, Texarkana, TX"],"affiliations":[{"raw_affiliation_string":"Texas A&M University-Texarkana, 75505, USA. igor.aizenberg@tamut.edu","institution_ids":["https://openalex.org/I51380931"]},{"raw_affiliation_string":"Texas A&M University-Texarkana, Texarkana, TX","institution_ids":["https://openalex.org/I51380931"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5052101553"],"corresponding_institution_ids":["https://openalex.org/I51380931"],"apc_list":null,"apc_paid":null,"fwci":7.2167,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.97042517,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"21","issue":"12","first_page":"1939","last_page":"1949"},"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/T11236","display_name":"Control Systems and Identification","score":0.9887999892234802,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T10820","display_name":"Fuzzy Logic and Control Systems","score":0.9800999760627747,"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/activation-function","display_name":"Activation function","score":0.6386085748672485},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5647350549697876},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5536987781524658},{"id":"https://openalex.org/keywords/neuron","display_name":"Neuron","score":0.5275784730911255},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4810055196285248},{"id":"https://openalex.org/keywords/biological-neuron-model","display_name":"Biological neuron model","score":0.4551924467086792},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.4519840478897095},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.4190451502799988},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.38469791412353516},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.30774492025375366},{"id":"https://openalex.org/keywords/neuroscience","display_name":"Neuroscience","score":0.18320640921592712},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.06454214453697205},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06272119283676147}],"concepts":[{"id":"https://openalex.org/C38365724","wikidata":"https://www.wikidata.org/wiki/Q4677469","display_name":"Activation function","level":3,"score":0.6386085748672485},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5647350549697876},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5536987781524658},{"id":"https://openalex.org/C2778794669","wikidata":"https://www.wikidata.org/wiki/Q43054","display_name":"Neuron","level":2,"score":0.5275784730911255},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4810055196285248},{"id":"https://openalex.org/C186565885","wikidata":"https://www.wikidata.org/wiki/Q1651163","display_name":"Biological neuron model","level":3,"score":0.4551924467086792},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.4519840478897095},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.4190451502799988},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.38469791412353516},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30774492025375366},{"id":"https://openalex.org/C169760540","wikidata":"https://www.wikidata.org/wiki/Q207011","display_name":"Neuroscience","level":1,"score":0.18320640921592712},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.06454214453697205},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06272119283676147},{"id":"https://openalex.org/C13280743","wikidata":"https://www.wikidata.org/wiki/Q131089","display_name":"Geodesy","level":1,"score":0.0},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.0}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016208","descriptor_name":"Databases, Factual","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016208","descriptor_name":"Databases, Factual","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016208","descriptor_name":"Databases, Factual","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":2,"locations":[{"id":"doi:10.1109/tnn.2010.2082561","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnn.2010.2082561","pdf_url":null,"source":{"id":"https://openalex.org/S42080949","display_name":"IEEE Transactions on Neural Networks","issn_l":"1045-9227","issn":["1045-9227","1941-0093"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks","raw_type":"journal-article"},{"id":"pmid:21047711","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/21047711","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W65876386","https://openalex.org/W127031351","https://openalex.org/W142384176","https://openalex.org/W639538290","https://openalex.org/W1517161096","https://openalex.org/W1594058661","https://openalex.org/W1764686324","https://openalex.org/W1823937713","https://openalex.org/W1894035673","https://openalex.org/W1964900693","https://openalex.org/W1975642869","https://openalex.org/W1978524241","https://openalex.org/W2016812413","https://openalex.org/W2047515252","https://openalex.org/W2059983106","https://openalex.org/W2087834767","https://openalex.org/W2100322562","https://openalex.org/W2102029306","https://openalex.org/W2105050785","https://openalex.org/W2108159555","https://openalex.org/W2124776405","https://openalex.org/W2126944419","https://openalex.org/W2131816943","https://openalex.org/W2132048588","https://openalex.org/W2136892987","https://openalex.org/W2143369703","https://openalex.org/W2150953991","https://openalex.org/W2156909104","https://openalex.org/W2161694749","https://openalex.org/W2161780063","https://openalex.org/W2169691379","https://openalex.org/W2476841360","https://openalex.org/W2487295360","https://openalex.org/W2549243812","https://openalex.org/W3120740533","https://openalex.org/W4246639841","https://openalex.org/W4248510537","https://openalex.org/W4292692317","https://openalex.org/W4299792679","https://openalex.org/W6630894543"],"related_works":["https://openalex.org/W3178259930","https://openalex.org/W1769982787","https://openalex.org/W3184949856","https://openalex.org/W3035839890","https://openalex.org/W2076468557","https://openalex.org/W4387066885","https://openalex.org/W2031806409","https://openalex.org/W4281997648","https://openalex.org/W3099906890","https://openalex.org/W2371090464"],"abstract_inverted_index":{"In":[0],"this":[1,68,89],"paper,":[2,69],"we":[3],"consider":[4],"a":[5,18,52,83,91,95,140,157,165,177],"new":[6],"periodic":[7,61,96],"activation":[8,62,97],"function":[9,98],"for":[10,130],"the":[11,29,33,48,109,127,131,184],"multivalued":[12,85,92],"neuron":[13,19,90,93],"(MVN).":[14],"The":[15,100,112],"MVN":[16,34,49,179],"is":[17,65,103,114,133,137,161],"with":[20,94],"complex-valued":[21],"weights":[22],"and":[23,39,78,146,176],"inputs/output,":[24],"which":[25,64,169],"are":[26,180],"located":[27],"on":[28,126],"unit":[30],"circle.":[31],"Although":[32],"outperforms":[35],"many":[36],"other":[37],"neurons":[38],"MVN-based":[40],"neural":[41],"networks":[42],"have":[43],"shown":[44,138,163],"their":[45],"high":[46],"potential,":[47],"still":[50],"has":[51],"limited":[53],"capability":[54],"of":[55,108,183],"learning":[56,123],"highly":[57],"nonlinear":[58],"functions.":[59],"A":[60,122],"function,":[63],"introduced":[66],"in":[67,117],"makes":[70],"it":[71],"possible":[72],"to":[73],"learn":[74,145,171],"nonlinearly":[75,172],"separable":[76,173],"problems":[77,151],"non-threshold":[79],"multiple-valued":[80],"functions":[81],"using":[82,156],"single":[84,141,158],"neuron.":[86,159],"We":[87],"call":[88],"(MVN-P).":[99],"MVN-Ps":[101],"functionality":[102],"much":[104],"higher":[105],"than":[106],"that":[107,139,152,164],"regular":[110,178],"MVN.":[111],"MVN-P":[113,132,142],"more":[115],"efficient":[116],"solving":[118],"various":[119],"classification":[120,150],"problems.":[121],"algorithm":[124],"based":[125],"error-correction":[128],"rule":[129],"also":[134,162],"presented.":[135],"It":[136,160],"can":[143,170],"easily":[144],"solve":[147],"those":[148],"benchmark":[149],"were":[153],"considered":[154],"unsolvable":[155],"universal":[166],"binary":[167],"neuron,":[168],"Boolean":[174],"functions,":[175],"particular":[181],"cases":[182],"MVN-P.":[185]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":7}],"updated_date":"2026-01-13T01:12:25.745995","created_date":"2025-10-10T00:00:00"}
