{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T06:03:31Z","timestamp":1773813811172,"version":"3.50.1"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"3-4","license":[{"start":{"date-parts":[[2012,2,15]],"date-time":"2012-02-15T00:00:00Z","timestamp":1329264000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Comput & Applic"],"published-print":{"date-parts":[[2013,3]]},"DOI":"10.1007\/s00521-012-0860-2","type":"journal-article","created":{"date-parts":[[2012,2,14]],"date-time":"2012-02-14T05:50:32Z","timestamp":1329198632000},"page":"541-550","source":"Crossref","is-referenced-by-count":34,"title":["A modified extreme learning machine with sigmoidal activation functions"],"prefix":"10.1007","volume":"22","author":[{"given":"Zhixiang X.","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Houying Y.","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuguang G.","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2012,2,15]]},"reference":[{"key":"860_CR1","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1007\/BF02551274","volume":"2","author":"G Cybenko","year":"1989","unstructured":"Cybenko G (1989) Approximation by superposition of sigmoidal function. Math Control Signals Syst 2:303\u2013314","journal-title":"Math Control Signals Syst"},{"key":"860_CR2","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/0893-6080(89)90003-8","volume":"2","author":"KI Funahashi","year":"1989","unstructured":"Funahashi KI (1989) On the approximate realization of continuous mappings by neural networks. Neural Netw 2:183\u2013192","journal-title":"Neural Netw"},{"key":"860_CR3","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/0893-6080(91)90009-T","volume":"4","author":"K Hornik","year":"1991","unstructured":"Hornik K (1991) Approximation capabilities of multilayer feedforward networks. Neural Netw 4:251\u2013257","journal-title":"Neural Netw"},{"key":"860_CR4","doi-asserted-by":"crossref","first-page":"626","DOI":"10.1016\/j.neucom.2007.07.024","volume":"71","author":"FL Cao","year":"2008","unstructured":"Cao FL, Xie TF, Xu ZB (2008) The estimate for approximation error of neural networks: a constructive approach. Neurocomputing 71:626\u2013630","journal-title":"Neurocomputing"},{"key":"860_CR5","doi-asserted-by":"crossref","first-page":"1441","DOI":"10.1016\/j.apm.2008.02.009","volume":"33","author":"FL Cao","year":"2009","unstructured":"Cao FL, Zhang YQ, He ZR (2009) Interpolation and rate of convergence by a class of neural networks. Appl Math Model 33:1441\u20131456","journal-title":"Appl Math Model"},{"key":"860_CR6","doi-asserted-by":"crossref","first-page":"1563","DOI":"10.1016\/j.mcm.2008.07.031","volume":"49","author":"FL Cao","year":"2009","unstructured":"Cao FL, Zhang R (2009) The errors of approximation for feedforward neural networks in the Lp metric. Math Comput Model 49:1563\u20131572","journal-title":"Math Comput Model"},{"key":"860_CR7","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1016\/j.neucom.2010.08.018","volume":"74","author":"FL Cao","year":"2010","unstructured":"Cao FL, Lin SB, Xu ZB (2010) Approximation capabilities of interpolation neural networks. Neurocomputing 74:457\u2013460","journal-title":"Neurocomputing"},{"key":"860_CR8","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1360\/02yf0221","volume":"47","author":"ZB Xu","year":"2004","unstructured":"Xu ZB, Cao FL (2004) The essential order of approximation for neural networks. Sci China Ser F Inf Sci 47:97\u2013112","journal-title":"Sci China Ser F Inf Sci"},{"key":"860_CR9","doi-asserted-by":"crossref","first-page":"914","DOI":"10.1016\/j.neunet.2005.03.013","volume":"18","author":"ZB Xu","year":"2005","unstructured":"Xu ZB, Cao FL (2005) Simultaneous L p approximation order for neural networks. Neural Netw 18:914\u2013923","journal-title":"Neural Netw"},{"key":"860_CR10","doi-asserted-by":"crossref","first-page":"904","DOI":"10.1109\/72.392252","volume":"6","author":"TP Chen","year":"1995","unstructured":"Chen TP, Chen H (1995) Approximation capability to functions of several variables, nonlinear functionals, and operators by radial basis function neural networks. IEEE Trans Neural Netw 6:904\u2013910","journal-title":"IEEE Trans Neural Netw"},{"key":"860_CR11","doi-asserted-by":"crossref","first-page":"911","DOI":"10.1109\/72.392253","volume":"6","author":"TP Chen","year":"1995","unstructured":"Chen TP, Chen H (1995) Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems. IEEE Trans Neural Netw 6:911\u2013917","journal-title":"IEEE Trans Neural Netw"},{"key":"860_CR12","doi-asserted-by":"crossref","first-page":"1897","DOI":"10.1016\/j.camwa.2003.06.008","volume":"47","author":"N Hahm","year":"2004","unstructured":"Hahm N, Hong BI (2004) An approximation by neural networks with a fixed weight. Comput Math Appl 47:1897\u20131903","journal-title":"Comput Math Appl"},{"key":"860_CR13","unstructured":"Lan Y, Soh YC, Huang GB (2010, April) Random search enhancement of error minimized extreme learning machine. In: ESANN 2010 proceedings, European symposium on artificial neural networks\u2014computational intelligence and machine learning, pp 327\u2013332"},{"key":"860_CR14","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1109\/72.655045","volume":"9","author":"GB Huang","year":"1998","unstructured":"Huang GB, Babri HA (1998) Upper bounds on the number of hidden neurons in feedforward networks with arbitrary bounded nonlinear activation functions. IEEE Trans Neural Netw 9:224\u2013229","journal-title":"IEEE Trans Neural Netw"},{"key":"860_CR15","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1016\/j.neucom.2005.12.126","volume":"70","author":"GB Huang","year":"2006","unstructured":"Huang GB, Zhu QY, Siew CK (2006) Extreme learning machine: theory and applications. Neurocomputing 70:489\u2013501","journal-title":"Neurocomputing"},{"key":"860_CR16","unstructured":"Huang GB, Zhu QY, Siew CK (2004) Extreme learning machine: a new learning scheme of feedforward neural networks. In: 2004 IEEE international joint conference on neural networks, vol 2, pp 985\u2013990"},{"key":"860_CR17","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1109\/18.661502","volume":"44","author":"PL Bartlett","year":"1998","unstructured":"Bartlett PL (1998) The sample complexity of pattern classification with neural networks: the size of the weights is more important than the size of the network. IEEE Trans Inf Theory 44:525\u2013536","journal-title":"IEEE Trans Inf Theory"},{"key":"860_CR18","doi-asserted-by":"crossref","first-page":"1352","DOI":"10.1109\/TNN.2009.2024147","volume":"20","author":"G Feng","year":"2009","unstructured":"Feng G, Huang GB, Lin Q, Gay R (2009) Error minimized extreme learning machine with growth of hidden nodes and incremental learning. IEEE Trans Neural Netw 20:1352\u20131357","journal-title":"IEEE Trans Neural Netw"},{"key":"860_CR19","doi-asserted-by":"crossref","first-page":"3056","DOI":"10.1016\/j.neucom.2007.02.009","volume":"70","author":"GB Huang","year":"2007","unstructured":"Huang GB, Chen L (2007) Convex incremental extreme learning machine. Neurocomputing 70:3056\u20133062","journal-title":"Neurocomputing"},{"key":"860_CR20","doi-asserted-by":"crossref","first-page":"3460","DOI":"10.1016\/j.neucom.2007.10.008","volume":"71","author":"GB Huang","year":"2008","unstructured":"Huang GB, Chen L (2008) Enhanced random search based incremental extreme learning machine. Neurocomputing 71:3460\u20133468","journal-title":"Neurocomputing"},{"key":"860_CR21","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1109\/TNN.2006.875977","volume":"17","author":"GB Huang","year":"2006","unstructured":"Huang GB, Chen L, Siew CK (2006) Universal approximation using incremental constructive feedforward networks with random hidden nodes. IEEE Trans Neural Netw 17:879\u2013892","journal-title":"IEEE Trans Neural Netw"},{"issue":"16","key":"860_CR22","doi-asserted-by":"crossref","first-page":"2483","DOI":"10.1016\/j.neucom.2010.11.030","volume":"74","author":"YG Wang","year":"2011","unstructured":"Wang YG, Cao FL, Yuan YB (2011) A study on effectiveness of extreme learning machine. Neurocomputing 74(16):2483\u20132490","journal-title":"Neurocomputing"},{"key":"860_CR23","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1109\/TNN.2003.809401","volume":"14","author":"GB Huang","year":"2003","unstructured":"Huang GB (2003) Learning capability and storage capacity of two-hidden-layer feedforward networks. IEEE Trans Neural Netw 14:274\u2013281","journal-title":"IEEE Trans Neural Netw"},{"key":"860_CR24","volume-title":"Generalized inverse of matrices and its applications","author":"CR Rao","year":"1971","unstructured":"Rao CR, Mitra SK (1971) Generalized inverse of matrices and its applications. Wiley, New York"},{"key":"860_CR25","unstructured":"R\u00e4tsch G, Onoda T, M\u00fcller KR (1998) An improvement of AdaBoost to avoid overfitting. In: Proceedings of the 5th international conference on neural information processing (ICONIP 1998)"},{"key":"860_CR26","doi-asserted-by":"crossref","unstructured":"Romero E, Alqu\u00e9zar R (2002) A new incremental method for function approximation using feed-forward neural networks. In: Proceedings of the 2002 international joint conference on neural networks (IJCNN\u20192002), pp 1968\u20131973","DOI":"10.1109\/IJCNN.2002.1007821"},{"key":"860_CR27","volume-title":"Matrices: theory and applications","author":"D Serre","year":"2000","unstructured":"Serre D (2000) Matrices: theory and applications. Springer, New York"},{"key":"860_CR28","unstructured":"Frank A, Asuncion A (2010) UCI machine learning repository. University of California, School of Information and Computer Science, Irvine. http:\/\/archive.ics.uci.edu\/ml"},{"key":"860_CR29","unstructured":"Freund Y, Schapire RE (1996) Experiments with a new boosting algorithm. In: Machine learning: proceedings of the 13th international conference, pp 148\u2013156"},{"key":"860_CR30","doi-asserted-by":"crossref","unstructured":"Wilson DR, Martinez TR (1996, June) Heterogeneous radial basis function networks. In: IEEE international conference on neural networks (ICNN\u201996), pp 1263\u20131267","DOI":"10.1109\/ICNN.1996.549079"}],"container-title":["Neural Computing and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-012-0860-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00521-012-0860-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00521-012-0860-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,20]],"date-time":"2025-03-20T18:33:32Z","timestamp":1742495612000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00521-012-0860-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,2,15]]},"references-count":30,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2013,3]]}},"alternative-id":["860"],"URL":"https:\/\/doi.org\/10.1007\/s00521-012-0860-2","relation":{},"ISSN":["0941-0643","1433-3058"],"issn-type":[{"value":"0941-0643","type":"print"},{"value":"1433-3058","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,2,15]]}}}