{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T08:33:08Z","timestamp":1777537988802,"version":"3.51.4"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2017,6,13]],"date-time":"2017-06-13T00:00:00Z","timestamp":1497312000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100012166","name":"973 Program","doi-asserted-by":"crossref","award":["2015CB351703"],"award-info":[{"award-number":["2015CB351703"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61372152"],"award-info":[{"award-number":["61372152"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Doctoral Scientific Research Foundation of Xi\u2019an University of Technology","award":["103-256081611"],"award-info":[{"award-number":["103-256081611"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Process Lett"],"published-print":{"date-parts":[[2018,2]]},"DOI":"10.1007\/s11063-017-9646-y","type":"journal-article","created":{"date-parts":[[2017,6,13]],"date-time":"2017-06-13T11:32:37Z","timestamp":1497353557000},"page":"233-252","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Chebyshev Functional Link Artificial Neural Network Based on Correntropy Induced Metric"],"prefix":"10.1007","volume":"47","author":[{"given":"Wentao","family":"Ma","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiandong","family":"Duan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haiquan","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Badong","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,6,13]]},"reference":[{"key":"9646_CR1","volume-title":"Fundamentals of artificial neural networks","author":"MH Hassoun","year":"1995","unstructured":"Hassoun MH (1995) Fundamentals of artificial neural networks. MIT press, Cambridge"},{"issue":"5","key":"9646_CR2","first-page":"1316","volume":"7","author":"MH Hassoun","year":"1996","unstructured":"Hassoun MH (1996) Artificial neural networks for modelling and control of nonlinear systems [book reviews]. IEEE Trans Neural Netw 7(5):1316","journal-title":"IEEE Trans Neural Netw"},{"key":"9646_CR3","volume-title":"Adaptive pattern recognition and neural networks","author":"Y-H Pao","year":"1989","unstructured":"Pao Y-H (1989) Adaptive pattern recognition and neural networks. Addison-Wesley, Reading"},{"key":"9646_CR4","doi-asserted-by":"crossref","unstructured":"Hassoun MH, Clark DW (1988) An adaptive attentive learning algorithm for single-layer neural networks. In: IEEE international conference on neural networks, pp 431\u2013440","DOI":"10.1109\/ICNN.1988.23876"},{"issue":"4","key":"9646_CR5","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1109\/TSMCB.2002.1018769","volume":"32","author":"JC Patra","year":"2002","unstructured":"Patra JC, Kot AC (2002) Nonlinear dynamic system identification using Chebyshev functional link artificial neural networks. IEEE Trans Syst Man Cybern Part B Cybern 32(4):505\u2013511","journal-title":"IEEE Trans Syst Man Cybern Part B Cybern"},{"issue":"13","key":"9646_CR6","doi-asserted-by":"crossref","first-page":"2642","DOI":"10.1016\/j.ins.2007.01.006","volume":"177","author":"WD Weng","year":"2007","unstructured":"Weng WD, Yang CS, Lin RC (2007) A channel equalizer using reduced decision feedback Chebyshev functional link artificial neural networks. Inf Sci 177(13):2642\u20132654","journal-title":"Inf Sci"},{"key":"9646_CR7","doi-asserted-by":"crossref","unstructured":"Mili F, Hamdi M (2012) A hybrid evolutionary functional link artificial neural network for data mining and classification. In: 2012 IEEE 6th international conference on sciences of electronics, technologies of information and telecommunications (SETIT), pp 917\u2013924","DOI":"10.1109\/SETIT.2012.6482037"},{"issue":"6","key":"9646_CR8","doi-asserted-by":"crossref","first-page":"1333","DOI":"10.1016\/j.jss.2012.01.025","volume":"85","author":"S Dehuri","year":"2012","unstructured":"Dehuri S, Roy R, Cho SB et al (2012) An improved swarm optimized functional link artificial neural network (ISO-FLANN) for classification. J Syst Softw 85(6):1333\u20131345","journal-title":"J Syst Softw"},{"issue":"2","key":"9646_CR9","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/0165-1684(94)00152-P","volume":"43","author":"JC Patra","year":"1995","unstructured":"Patra JC, Pal RNA (1995) Functional link artificial neural network for adaptive channel equalization. Signal Process 43(2):181\u2013195","journal-title":"Signal Process"},{"issue":"6","key":"9646_CR10","doi-asserted-by":"crossref","first-page":"1979","DOI":"10.1109\/TMTT.2012.2189239","volume":"60","author":"M Li","year":"2012","unstructured":"Li M, Liu J, Jiang Y et al (2012) Complex-Chebyshev functional link neural network behavioral model for broadband wireless power amplifiers. IEEE Trans Microw Theory Tech 60(6):1979\u20131989","journal-title":"IEEE Trans Microw Theory Tech"},{"key":"9646_CR11","doi-asserted-by":"crossref","unstructured":"Mall S, Chakraverty S (2017) Single layer Chebyshev neural network model for solving elliptic partial differential equations. Neural Process Lett 45(3):825\u2013840","DOI":"10.1007\/s11063-016-9551-9"},{"key":"9646_CR12","doi-asserted-by":"crossref","unstructured":"Patra JC, Chin WC, Meher PK et al (2008) Legendre-FLANN-based nonlinear channel equalization in wireless communication system. In: IEEE international conference on systems, man and cybernetics, pp 1826\u20131831","DOI":"10.1109\/ICSMC.2008.4811554"},{"key":"9646_CR13","unstructured":"Peterson LE, Larine KV (2008) Hermite\/Laguerre neural networks for classification of artificial fingerprints from optical coherence tomography. In: IEEE seventh international conference on machine learning and applications, pp 637\u2013643"},{"issue":"2","key":"9646_CR14","doi-asserted-by":"crossref","first-page":"931","DOI":"10.1016\/j.asoc.2011.09.013","volume":"12","author":"S Chakravarty","year":"2012","unstructured":"Chakravarty S, Dash PKA (2012) PSO based integrated functional link net and interval type-2 fuzzy logic system for predicting stock market indices. Appl Soft Comput 12(2):931\u2013941","journal-title":"Appl Soft Comput"},{"issue":"3","key":"9646_CR15","doi-asserted-by":"crossref","first-page":"834","DOI":"10.1016\/j.sigpro.2009.09.001","volume":"90","author":"H Zhao","year":"2010","unstructured":"Zhao H, Zeng X, Zhang J (2010) Adaptive reduced feedback FLNN filter for active control of nonlinear noise processes. Signal Process 90(3):834\u2013847","journal-title":"Signal Process"},{"issue":"2","key":"9646_CR16","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1007\/s11063-012-9247-8","volume":"38","author":"B Xu","year":"2013","unstructured":"Xu B, Wang Y, Yang X (2013) Navigation satellite clock error prediction based on functional network. Neural Process Lett 38(2):305\u2013320","journal-title":"Neural Process Lett"},{"issue":"6","key":"9646_CR17","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1109\/3477.735405","volume":"28","author":"TT Lee","year":"1998","unstructured":"Lee TT, Jeng JT (1998) The Chebyshev-polynomials-based unified model neural networks for function approximation. IEEE Trans Syst Man Cybern Part B Cybern 28(6):925\u2013935","journal-title":"IEEE Trans Syst Man Cybern Part B Cybern"},{"issue":"2","key":"9646_CR18","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/s00521-009-0288-5","volume":"19","author":"S Dehuri","year":"2010","unstructured":"Dehuri S, Cho SB (2010) A comprehensive survey on functional link neural networks and an adaptive PSO-BP learning for CFLNN. Neural Comput Appl 19(2):187\u2013205","journal-title":"Neural Comput Appl"},{"issue":"8","key":"9646_CR19","doi-asserted-by":"crossref","first-page":"1946","DOI":"10.1016\/j.sigpro.2008.01.029","volume":"88","author":"H Zhao","year":"2008","unstructured":"Zhao H, Zhang J (2008) Functional link neural network cascaded with Chebyshev orthogonal polynomial for nonlinear channel equalization. Signal Process 88(8):1946\u20131957","journal-title":"Signal Process"},{"issue":"1","key":"9646_CR20","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1016\/j.asoc.2005.08.001","volume":"7","author":"S Purwar","year":"2007","unstructured":"Purwar S, Kar IN, Jha AN (2007) On-line system identification of complex systems using Chebyshev neural networks. Appl Soft Comput 7(1):364\u2013372","journal-title":"Appl Soft Comput"},{"issue":"9","key":"9646_CR21","doi-asserted-by":"crossref","first-page":"1457","DOI":"10.1109\/TNN.2010.2050333","volume":"21","author":"AM Zou","year":"2010","unstructured":"Zou AM, Kumar KD, Hou ZG (2010) Quaternion-based adaptive output feedback attitude control of spacecraft using Chebyshev neural networks. IEEE Trans Neural Netw 21(9):1457\u20131471","journal-title":"IEEE Trans Neural Netw"},{"key":"9646_CR22","volume-title":"Matrix computation","author":"GH Golub","year":"1983","unstructured":"Golub GH, Van Loan CF (1983) Matrix computation. Johns Hopkins University Press, Baltimore"},{"issue":"11","key":"9646_CR23","doi-asserted-by":"crossref","first-page":"5286","DOI":"10.1109\/TSP.2007.896065","volume":"55","author":"W Liu","year":"2007","unstructured":"Liu W, Pokharel PP, Pr\u00edncipe JC (2007) Correntropy: properties and applications in non-Gaussian signal processing. IEEE Trans Signal Process 55(11):5286\u20135298","journal-title":"IEEE Trans Signal Process"},{"key":"9646_CR24","doi-asserted-by":"crossref","unstructured":"Singh A, Principe JC (2009) Using correntropy as cost function in adaptive filters. In: Proceedings of international joint conference on neural networks, pp 2950\u20132955","DOI":"10.1109\/IJCNN.2009.5178823"},{"issue":"7","key":"9646_CR25","doi-asserted-by":"crossref","first-page":"880","DOI":"10.1109\/LSP.2014.2319308","volume":"21","author":"B Chen","year":"2014","unstructured":"Chen B, Xing L, Liang J et al (2014) Steady-state mean-square error analysis for adaptive filtering under the maximum correntropy criterion. IEEE Signal Process Lett 21(7):880\u2013884","journal-title":"IEEE Signal Process Lett"},{"key":"9646_CR26","doi-asserted-by":"crossref","unstructured":"Zhao S, Chen B, Principe JC (2011) Kernel adaptive filtering with maximum correntropy criterion. In: Proceedings of international joint conference on neural networks, pp 2012\u20132017","DOI":"10.1109\/IJCNN.2011.6033473"},{"issue":"7","key":"9646_CR27","doi-asserted-by":"crossref","first-page":"2708","DOI":"10.1016\/j.jfranklin.2015.03.039","volume":"352","author":"W Ma","year":"2015","unstructured":"Ma W, Qu H, Gui G, Xu L, Zhao J, Chen B (2015) Maximum correntropy criterion based sparse adaptive filtering algorithms for robust channel estimation under non-Gaussian environments. J Frankl Inst 352(7):2708\u20132727","journal-title":"J Frankl Inst"},{"issue":"13","key":"9646_CR28","doi-asserted-by":"crossref","first-page":"3376","DOI":"10.1109\/TSP.2016.2539127","volume":"64","author":"B Chen","year":"2016","unstructured":"Chen B, Xing L, Zhao H, Zheng N, Principe JC (2016) Generalized correntropy for robust adaptive filtering. IEEE Trans Signal Process 64(13):3376\u20133387","journal-title":"IEEE Trans Signal Process"},{"key":"9646_CR29","doi-asserted-by":"crossref","unstructured":"Yuan X, Hu BG (2009) Robust feature extraction via information theoretic learning. In: Proceedings of the 26th annual international conference on machine learning (ACM), pp 1193\u20131200","DOI":"10.1145\/1553374.1553526"},{"issue":"8","key":"9646_CR30","doi-asserted-by":"crossref","first-page":"2074","DOI":"10.1162\/NECO_a_00155","volume":"23","author":"R He","year":"2011","unstructured":"He R, Zheng WS, Hu BG et al (2011) A regularized correntropy framework for robust pattern recognition. Neural Comput 23(8):2074\u20132100","journal-title":"Neural Comput"},{"issue":"7\u20138","key":"9646_CR31","doi-asserted-by":"crossref","first-page":"1977","DOI":"10.1007\/s00521-012-1184-y","volume":"23","author":"HJ Xing","year":"2013","unstructured":"Xing HJ, Wang XM (2013) Training extreme learning machine via regularized correntropy criterion. Neural Comput Appl 23(7\u20138):1977\u20131986","journal-title":"Neural Comput Appl"},{"issue":"4","key":"9646_CR32","doi-asserted-by":"crossref","first-page":"1657","DOI":"10.1109\/TPWRS.2009.2030291","volume":"24","author":"RJ Bessa","year":"2009","unstructured":"Bessa RJ, Miranda V, Gama J (2009) Entropy and correntropy against minimum square error in offline and online three-day ahead wind power forecasting. IEEE Trans Power Syst 24(4):1657\u20131666","journal-title":"IEEE Trans Power Syst"},{"issue":"1","key":"9646_CR33","first-page":"135","volume":"10","author":"H Qu","year":"2013","unstructured":"Qu H, Ma W, Zhao J, Wang T (2013) Prediction method for network traffic based on maximum correntropy criterion. China Commun 10(1):135\u2013142","journal-title":"China Commun"},{"key":"9646_CR34","doi-asserted-by":"crossref","unstructured":"Chalasani R, Principe JC (2010) Self organizing maps with the correntropy induced metric. In: The 2010 international joint conference on neural networks (IJCNN), pp 1\u20136","DOI":"10.1109\/IJCNN.2010.5596565"},{"key":"9646_CR35","doi-asserted-by":"crossref","unstructured":"Seth S, Pr\u00edncipe JC (2008) Compressed signal reconstruction using the correntropy induced metric. In: IEEE international conference on acoustics, speech and signal processing, pp. 3845\u20133848","DOI":"10.1109\/ICASSP.2008.4518492"},{"issue":"8","key":"9646_CR36","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1109\/LSP.2012.2204435","volume":"19","author":"B Chen","year":"2012","unstructured":"Chen B, Principe JC (2012) Maximum correntropy estimation is a smoothed MAP estimation. IEEE Signal Process Lett 19(8):491\u2013494","journal-title":"IEEE Signal Process Lett"},{"issue":"10","key":"9646_CR37","doi-asserted-by":"crossref","first-page":"1723","DOI":"10.1109\/LSP.2015.2428713","volume":"22","author":"B Chen","year":"2015","unstructured":"Chen B, Wang J, Zhao H, Zheng N, Principe JC (2015) Convergence of a fixed-point algorithm under maximum correntropy criterion. IEEE Signal Process Lett 22(10):1723\u20131727","journal-title":"IEEE Signal Process Lett"},{"issue":"10","key":"9646_CR38","doi-asserted-by":"crossref","first-page":"7149","DOI":"10.3390\/e17107149","volume":"17","author":"Z Wu","year":"2015","unstructured":"Wu Z, Peng S, Chen B, Zhao H (2015) Robust hammerstein adaptive filtering under maximum correntropy criterion. Entropy 17(10):7149\u20137166","journal-title":"Entropy"},{"issue":"1","key":"9646_CR39","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/s11063-007-9043-z","volume":"26","author":"R Ebrahimpour","year":"2007","unstructured":"Ebrahimpour R, Kabir E, Yousefi MR (2007) Face detection using mixture of MLP experts. Neural Process Lett 26(1):69\u201382","journal-title":"Neural Process Lett"},{"issue":"2","key":"9646_CR40","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1023\/A:1026289910256","volume":"18","author":"N Benoudjit","year":"2003","unstructured":"Benoudjit N, Verleysen M (2003) On the kernel widths in radial-basis function networks. Neural Process Lett 18(2):139\u2013154","journal-title":"Neural Process Lett"},{"issue":"16","key":"9646_CR41","doi-asserted-by":"crossref","first-page":"2526","DOI":"10.1016\/j.neucom.2010.11.037","volume":"74","author":"B Fr\u00e9nay","year":"2011","unstructured":"Fr\u00e9nay B, Verleysen M (2011) Parameter-insensitive kernel in extreme learning for non-linear support vector regression. Neurocomputing 74(16):2526\u20132531","journal-title":"Neurocomputing"},{"issue":"4","key":"9646_CR42","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1109\/TSMCB.2002.1018769","volume":"32","author":"JC Patra","year":"2002","unstructured":"Patra JC, Kot AC (2002) Nonlinear dynamic system identification using Chebyshev functional link artificial neural networks. IEEE Trans Syst Man Cybern Part B (Cybern) 32(4):505\u2013511","journal-title":"IEEE Trans Syst Man Cybern Part B (Cybern)"},{"key":"9646_CR43","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1016\/S0019-0578(99)00035-X","volume":"39","author":"JC Patra","year":"2000","unstructured":"Patra JC, Van den Bos A (2000) Modeling of an intelligent pressure sensor using functional link artificial neural networks. ISA Trans 39:15\u201327","journal-title":"ISA Trans"},{"issue":"11","key":"9646_CR44","doi-asserted-by":"crossref","first-page":"2251","DOI":"10.1016\/j.sigpro.2009.05.004","volume":"89","author":"JC Patra","year":"2009","unstructured":"Patra JC, Meher PK, Chakraborty G (2009) Nonlinear channel equalization for wireless communication systems using Legendre neural networks. Signal Process 89(11):2251\u20132262","journal-title":"Signal Process"},{"key":"9646_CR45","first-page":"484","volume":"8","author":"J Wang","year":"2011","unstructured":"Wang J, Wu W, Li Z et al (2011) Convergence of gradient method for double parallel feedforward neural network. Int J Numer Anal Model 8:484\u2013495","journal-title":"Int J Numer Anal Model"},{"issue":"2","key":"9646_CR46","doi-asserted-by":"crossref","first-page":"522","DOI":"10.1109\/TNN.2005.863460","volume":"17","author":"N Zhang","year":"2006","unstructured":"Zhang N, Wu W, Zheng G (2006) Convergence of gradient method with momentum for two-layer feedforward neural networks. IEEE Trans Neural Netw 17(2):522\u2013525","journal-title":"IEEE Trans Neural Netw"},{"key":"9646_CR47","volume-title":"Iterative solution of nonlinear equations in several variables","author":"JM Ortega","year":"1970","unstructured":"Ortega JM, Rheinboldt WC (1970) Iterative solution of nonlinear equations in several variables. Academic Press, New York"},{"issue":"7","key":"9646_CR48","doi-asserted-by":"crossref","first-page":"986","DOI":"10.1109\/5.231338","volume":"81","author":"M Shao","year":"1993","unstructured":"Shao M, Nikias CL (1993) Signal processing with fractional lower order moments: stable processes and their applications. Proc IEEE 81(7):986\u20131010","journal-title":"Proc IEEE"}],"container-title":["Neural Processing Letters"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11063-017-9646-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11063-017-9646-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11063-017-9646-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,18]],"date-time":"2020-05-18T00:12:10Z","timestamp":1589760730000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11063-017-9646-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,6,13]]},"references-count":48,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,2]]}},"alternative-id":["9646"],"URL":"https:\/\/doi.org\/10.1007\/s11063-017-9646-y","relation":{},"ISSN":["1370-4621","1573-773X"],"issn-type":[{"value":"1370-4621","type":"print"},{"value":"1573-773X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,6,13]]}}}