{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T00:02:47Z","timestamp":1780444967820,"version":"3.54.1"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,8,6]],"date-time":"2021-08-06T00:00:00Z","timestamp":1628208000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2021,8,6]],"date-time":"2021-08-06T00:00:00Z","timestamp":1628208000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Soft Comput"],"published-print":{"date-parts":[[2023,2]]},"DOI":"10.1007\/s00500-021-06093-6","type":"journal-article","created":{"date-parts":[[2021,8,6]],"date-time":"2021-08-06T10:08:26Z","timestamp":1628244506000},"page":"1797-1808","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A new hybrid neural network classifier based on adaptive neuron and multiplicative neuron"],"prefix":"10.1007","volume":"27","author":[{"given":"Erdin\u00e7","family":"Kolay","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5548-8475","authenticated-orcid":false,"given":"Taner","family":"Tun\u00e7","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,8,6]]},"reference":[{"key":"6093_CR1","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1016\/j.tjem.2018.08.001","volume":"18","author":"H Akoglu","year":"2018","unstructured":"Akoglu H (2018) User\u2019s guide to correlation coefficients. Turk J Emerg Med 18:91\u201393. https:\/\/doi.org\/10.1016\/j.tjem.2018.08.001","journal-title":"Turk J Emerg Med"},{"key":"6093_CR2","volume-title":"Pattern recognition and machine learning","author":"CM Bishop","year":"2006","unstructured":"Bishop CM (2006) Pattern recognition and machine learning. Academic Press, New York"},{"key":"6093_CR3","unstructured":"Blake CL, Merz CJ (1998) UCI Repository of machine learning databases. University of California. http:\/\/archive.ics.uci.edu\/ml\/"},{"key":"6093_CR4","doi-asserted-by":"publisher","first-page":"185","DOI":"10.1111\/j.1468-0394.2010.00565.x","volume":"28","author":"C Chuang","year":"2011","unstructured":"Chuang C (2011) Huang S A hybrid neural network approach for credit scoring. Exp Syst 28:185\u2013196. https:\/\/doi.org\/10.1111\/j.1468-0394.2010.00565.x","journal-title":"Exp Syst"},{"key":"6093_CR5","doi-asserted-by":"publisher","unstructured":"Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the MHS\u201995 sixth \u0131nternational symposium micro machine human science, pp 39\u201343. doi:https:\/\/doi.org\/10.1109\/MHS.1995.494215.","DOI":"10.1109\/MHS.1995.494215"},{"key":"6093_CR6","unstructured":"Engelbrecht AP (2001) Cooperative learning in neural networks using particle swarm optimizers. Annu Res Conf South Afr Inst Comput Sci Inf Technol, pp 84\u201390"},{"key":"6093_CR7","doi-asserted-by":"publisher","DOI":"10.1007\/s10489-016-0767-1","author":"H Faris","year":"2016","unstructured":"Faris H, Aljarah I, Mirjalili S (2016) Training feedforward neural networks using multi-verse optimizer for binary classification problems. Appl Intell. https:\/\/doi.org\/10.1007\/s10489-016-0767-1","journal-title":"Appl Intell"},{"key":"6093_CR8","doi-asserted-by":"crossref","unstructured":"Ghazali R (2009) Application of pi-sigma neural networks and ridge polynomial neural networks to financial time series prediction, 271\u2013273.","DOI":"10.4018\/978-1-59904-897-0.ch012"},{"key":"6093_CR9","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1142\/S0129065792000255","volume":"03","author":"J Ghosh","year":"1995","unstructured":"Ghosh J, Shin Y (1995) Ecient higher-order neural networks for classification and function approximation. Int J Neural Syst 03:323\u2013350","journal-title":"Int J Neural Syst"},{"key":"6093_CR10","doi-asserted-by":"publisher","first-page":"989","DOI":"10.1109\/72.329697","volume":"5","author":"MT Hagan","year":"1994","unstructured":"Hagan MT, Menhaj MB (1994) Training feedforward networks with the marquardt algorithm. IEEE Trans Neural Netw 5:989\u2013993. https:\/\/doi.org\/10.1109\/72.329697","journal-title":"IEEE Trans Neural Netw"},{"key":"6093_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-012-1315-5","author":"C Hakan","year":"2013","unstructured":"Hakan C, Erol A (2013) Robust multilayer neural network based on median neuron model. Neural Comput Appl. https:\/\/doi.org\/10.1007\/s00521-012-1315-5","journal-title":"Neural Comput Appl"},{"key":"6093_CR12","doi-asserted-by":"publisher","DOI":"10.1007\/s10489-017-0951-y","author":"A Hatamlou","year":"2017","unstructured":"Hatamlou A (2017) A hybrid bio-inspired algorithm and its application. Appl Intel. https:\/\/doi.org\/10.1007\/s10489-017-0951-y","journal-title":"Appl Intel"},{"key":"6093_CR13","doi-asserted-by":"publisher","first-page":"440","DOI":"10.1142\/S2010194512005521","volume":"09","author":"NA Husa\u0131n\u0131","year":"2012","unstructured":"Husa\u0131n\u0131 NA, Ghazal\u0131 R, Naw\u0131 NM, Isma\u0131l LH (2012) The effect of network parameters on pi-sigma neural network for temperature forecasting. Int J Mod Phys Conf Ser 09:440\u2013447. https:\/\/doi.org\/10.1142\/S2010194512005521","journal-title":"Int J Mod Phys Conf Ser"},{"key":"6093_CR14","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1016\/S0925-2312(02)00629-X","volume":"55","author":"AJ Hussain","year":"2003","unstructured":"Hussain AJ, Liatsis P (2003) Recurrent pi-sigma networks for DPCM image coding. Neurocomputing 55:363\u2013382. https:\/\/doi.org\/10.1016\/S0925-2312(02)00629-X","journal-title":"Neurocomputing"},{"key":"6093_CR15","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1023\/A:1022995128597","volume":"17","author":"J Ilonen","year":"2003","unstructured":"Ilonen J, Kamarainen J-K, Lampinen J (2003) Differential evolution training algorithm for feed-forward neural networks. Neural Process Lett 17:93\u2013105. https:\/\/doi.org\/10.1023\/A:1022995128597","journal-title":"Neural Process Lett"},{"key":"6093_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/s10489-014-0618-x","author":"W Jia","year":"2015","unstructured":"Jia W, Zhao D, Shen T, Ding S, Zhao Y, Hu C (2015) An optimized classification algorithm by BP neural network based on PLS and HCA. Appl Intel. https:\/\/doi.org\/10.1007\/s10489-014-0618-x","journal-title":"Appl Intel"},{"key":"6093_CR17","doi-asserted-by":"publisher","first-page":"997","DOI":"10.1109\/TSMCB.2003.818557","volume":"34","author":"C-F Juang","year":"2004","unstructured":"Juang C-F (2004) A hybrid of genetic algorithm and particle swarm optimization for recurrent network design. IEEE Trans Syst Man Cybern B Cybern 34:997\u20131006. https:\/\/doi.org\/10.1109\/TSMCB.2003.818557","journal-title":"IEEE Trans Syst Man Cybern B Cybern"},{"key":"6093_CR18","first-page":"318","volume":"4617","author":"D Karaboga","year":"2007","unstructured":"Karaboga D, Akay B, Ozturk C (2007) Artificial bee colony (ABC) optimization algorithm for training feed-forward neural. Int Conf Model Decis Artif Intel 4617:318\u2013329","journal-title":"Int Conf Model Decis Artif Intel"},{"issue":"2012","key":"6093_CR19","doi-asserted-by":"publisher","first-page":"23","DOI":"10.5815\/ijisa.2012.07.03","volume":"4","author":"K Khan","year":"2012","unstructured":"Khan K, Sahai A (2012) A comparison of BA, GA, PSO, BP and LM for training feed forward neural networks in e-learning context. Int J Intell Syst Appl 4(2012):23\u201329. https:\/\/doi.org\/10.5815\/ijisa.2012.07.03","journal-title":"Int J Intell Syst Appl"},{"key":"6093_CR20","doi-asserted-by":"publisher","first-page":"59","DOI":"10.5923\/j.ajis.20160603.01","volume":"6","author":"E Kolay","year":"2016","unstructured":"Kolay E, Tun\u00e7 T, E\u011frio\u011flu E (2016) Classification with some artificial neural network classifiers trained a modified particle swarm optimization. Am J Intel 6:59\u201365. https:\/\/doi.org\/10.5923\/j.ajis.20160603.01","journal-title":"Am J Intel"},{"key":"6093_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1023\/A:1022967523886","volume":"17","author":"CK Li","year":"2003","unstructured":"Li CK (2003) A sigma-pi-sigma neural network (SPSNN). Neural Process Lett 17:1\u201319. https:\/\/doi.org\/10.1023\/A:1022967523886","journal-title":"Neural Process Lett"},{"key":"6093_CR22","doi-asserted-by":"publisher","unstructured":"Li H (2009) Particle swarm optimization algorithm with exponent decreasing inertia weight and stochastic mutation, pp 66\u201369. doi:https:\/\/doi.org\/10.1109\/ICIC.2009.24.","DOI":"10.1109\/ICIC.2009.24"},{"key":"6093_CR23","doi-asserted-by":"publisher","first-page":"648","DOI":"10.1109\/TPAMI.2005.64","volume":"27","author":"C Lim","year":"2005","unstructured":"Lim C, Leong J, Kuan M (2005) A hybrid neural network system for pattern classification tasks with missing features. IEEE Trans Pattern Anal Mach Intel 27:648\u2013653","journal-title":"IEEE Trans Pattern Anal Mach Intel"},{"key":"6093_CR24","doi-asserted-by":"publisher","first-page":"10604","DOI":"10.1016\/j.eswa.2009.02.055","volume":"36","author":"Y Marinakis","year":"2009","unstructured":"Marinakis Y, Marinaki M, Doumpos M, Zopounidis C (2009) Ant colony and particle swarm optimization for financial classification problems. Exp Syst Appl 36:10604\u201310611. https:\/\/doi.org\/10.1016\/j.eswa.2009.02.055","journal-title":"Exp Syst Appl"},{"key":"6093_CR25","doi-asserted-by":"publisher","unstructured":"Mendes R, Cortez P, Rocha M, Neves J (2002) Particle swarms for feedforward neural network training. In: Proceedings of the 2002 International Joint Conference Neural Networks IJCNN02 Cat No02CH37290 6: 1895\u20131899. doi:https:\/\/doi.org\/10.1109\/IJCNN.2002.1007808.","DOI":"10.1109\/IJCNN.2002.1007808"},{"key":"6093_CR26","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1007\/s10489-014-0645-7","volume":"43","author":"S Mirjalili","year":"2015","unstructured":"Mirjalili S (2015) How effective is the Grey Wolf optimizer in training multi-layer perceptrons. Appl Intell 43:150\u2013161. https:\/\/doi.org\/10.1007\/s10489-014-0645-7","journal-title":"Appl Intell"},{"key":"6093_CR27","unstructured":"Montana DJ, Davis L (1989) Training feedforward neural networks using genetic algorithms. 762\u2013767."},{"key":"6093_CR28","doi-asserted-by":"publisher","unstructured":"Nayak J, Naik B, Behera HS (2014) A hybrid PSO-GA based Pi sigma neural network (PSNN) with standard back propagation gradient descent learning for classification. In: Proceedings of the 2014 International Conference on Controlled Instrumentation, Communication Computer Technology ICCICCT 2014. pp 878\u2013885. doi:https:\/\/doi.org\/10.1109\/ICCICCT.2014.6993082.","DOI":"10.1109\/ICCICCT.2014.6993082"},{"key":"6093_CR29","doi-asserted-by":"publisher","unstructured":"Nie Y (2008) A hybrid genetic learning algorithm for Pi-sigma neural network and the analysis of its convergence. pp 19\u201323. doi:https:\/\/doi.org\/10.1109\/ICNC.2008.896.","DOI":"10.1109\/ICNC.2008.896"},{"key":"6093_CR30","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1016\/0893-6080(92)90008-7","volume":"5","author":"B Nienhuis","year":"1992","unstructured":"Nienhuis B (1992) Improving the convergence of the back-propagation algorithm. Neural Netw 5:465\u2013471","journal-title":"Neural Netw"},{"key":"6093_CR31","first-page":"133","volume":"3","author":"S Panigrahi","year":"2013","unstructured":"Panigrahi S, Bhoi AK, Karali Y (2013) A modified differential evolution algorithm trained pi-sigma neural network for pattern classification. Int J Soft Comput Eng 3:133\u2013136","journal-title":"Int J Soft Comput Eng"},{"key":"6093_CR32","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1109\/TEVC.2004.826071","volume":"8","author":"A Ratnaweera","year":"2004","unstructured":"Ratnaweera A, Halgamuge SK, Watson HC (2004) Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients. IEEE Trans Evol Comput 8:240\u2013255. https:\/\/doi.org\/10.1109\/TEVC.2004.826071","journal-title":"IEEE Trans Evol Comput"},{"key":"6093_CR33","unstructured":"Riedmiller M (1993) A direct adaptive method for faster backpropagation learning: the RPROP algorithm. IEEE Int Conf Neural Netw"},{"key":"6093_CR34","doi-asserted-by":"publisher","DOI":"10.1016\/B978-1-4832-1446-7.50035-2","author":"DE Rumelhart","year":"1988","unstructured":"Rumelhart DE, Hinton GE, Williams RJ (1988) Learning \u0131nternal representations by error propagation. Read Cogn Sci. https:\/\/doi.org\/10.1016\/B978-1-4832-1446-7.50035-2","journal-title":"Read Cogn Sci"},{"key":"6093_CR35","unstructured":"Shekara S, Reddy S, Wang L, Devabhaktuni V, Nelapati P (2011) A hybrid neural network model and encoding technique for enhanced classification of energy consumption data. pp 1\u20138."},{"key":"6093_CR36","doi-asserted-by":"publisher","unstructured":"Shin Y, Ghosh J (1991) The pi-sigma network: an efficient higher-order neural network for\\npattern classification and function approximation. IJCNN-91-Seattle Int Jt Conf Neural Netw. doi:https:\/\/doi.org\/10.1109\/IJCNN.1991.155142.","DOI":"10.1109\/IJCNN.1991.155142"},{"key":"6093_CR37","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/241690","author":"T Tunc","year":"2012","unstructured":"Tunc T (2012) A new hybrid method logistic regression and feedforward neural network for lung cancer data. Math Problem Eng. https:\/\/doi.org\/10.1155\/2012\/241690","journal-title":"Math Problem Eng"},{"key":"6093_CR38","doi-asserted-by":"publisher","first-page":"1341","DOI":"10.1162\/neco.1996.8.7.1341","volume":"8","author":"DH Wolpert","year":"1996","unstructured":"Wolpert DH (1996) The lack of a priori distinctions between learning algorithms. Neural Comput 8:1341\u20131390. https:\/\/doi.org\/10.1162\/neco.1996.8.7.1341","journal-title":"Neural Comput"},{"key":"6093_CR39","doi-asserted-by":"publisher","unstructured":"Yadav RN (2003) Classification using single neuron. doi:https:\/\/doi.org\/10.1109\/INDIN.2003.1300258","DOI":"10.1109\/INDIN.2003.1300258"},{"key":"6093_CR40","doi-asserted-by":"publisher","first-page":"1157","DOI":"10.1016\/j.asoc.2006.01.003","volume":"7","author":"RN Yadav","year":"2007","unstructured":"Yadav RN, Kalra PK, John J (2007) Time series prediction with single multiplicative neuron model. Appl Soft Comput 7:1157\u20131163. https:\/\/doi.org\/10.1016\/j.asoc.2006.01.003","journal-title":"Appl Soft Comput"},{"key":"6093_CR41","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2012.01.023","author":"M Yaghini","year":"2012","unstructured":"Yaghini M, Khoshraftar MM, Fallahi M (2012) Engineering applications of artificial \u0131ntelligence a hybrid algorithm for artificial neural network training. Eng Appl Artif Intell. https:\/\/doi.org\/10.1016\/j.engappai.2012.01.023","journal-title":"Eng Appl Artif Intell"},{"key":"6093_CR42","doi-asserted-by":"publisher","first-page":"1340","DOI":"10.1016\/j.dss.2012.12.006","volume":"54","author":"U Yolcu","year":"2013","unstructured":"Yolcu U, Egrioglu E, Aladag CH (2013) A new linear and nonlinear artificial neural network model for time series forecasting. Decis Support Syst 54:1340\u20131347. https:\/\/doi.org\/10.1016\/j.dss.2012.12.006","journal-title":"Decis Support Syst"},{"key":"6093_CR43","doi-asserted-by":"publisher","first-page":"1026","DOI":"10.1016\/j.amc.2006.07.025","volume":"185","author":"J Zhang","year":"2007","unstructured":"Zhang J, Zhang J, Lok T, Lyu MR (2007) A hybrid particle swarm optimization: back-propagation algorithm for feedforward neural network training. Appl Math Comput 185:1026\u20131037. https:\/\/doi.org\/10.1016\/j.amc.2006.07.025","journal-title":"Appl Math Comput"},{"key":"6093_CR44","doi-asserted-by":"publisher","first-page":"2805","DOI":"10.1016\/j.eswa.2008.01.061","volume":"36","author":"L Zhao","year":"2009","unstructured":"Zhao L, Yang Y (2009) PSO-based single multiplicative neuron model for time series prediction. Exp Syst Appl 36:2805\u20132812. https:\/\/doi.org\/10.1016\/j.eswa.2008.01.061","journal-title":"Exp Syst Appl"}],"container-title":["Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-021-06093-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00500-021-06093-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00500-021-06093-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,27]],"date-time":"2023-01-27T07:07:04Z","timestamp":1674803224000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00500-021-06093-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,6]]},"references-count":44,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2023,2]]}},"alternative-id":["6093"],"URL":"https:\/\/doi.org\/10.1007\/s00500-021-06093-6","relation":{},"ISSN":["1432-7643","1433-7479"],"issn-type":[{"value":"1432-7643","type":"print"},{"value":"1433-7479","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,6]]},"assertion":[{"value":"28 July 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 August 2021","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"This article does not contain any studies with human participants or animals performed by any of the authors.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"Informed consent was obtained from all individual participants included in the study.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Informed consent"}}]}}