What are Extreme Learning Machines? Filling the Gap Between Frank Rosenblatt’s Dream and John von Neumann’s Puzzle

Schmidt WF, Kraaijveld MA, Duin RPW. Feed forward neural networks with random weights. In: Proceedings of 11th IAPR international conference on pattern recognition methodology and systems, Hague, Netherlands, p. 1–4, 1992.

Pao Y-H, Park G-H, Sobajic DJ. Learning and generalization characteristics of the random vector functional-link net. Neurocomputing. 1994;6:163–80.

Huang G-B. Reply to comments on ‘the extreme learning machine’. IEEE Trans Neural Netw. 2008;19(8):1495–6.

Huang G-B, Li M-B, Chen L, Siew C-K. Incremental extreme learning machine with fully complex hidden nodes. Neurocomputing. 2008;71:576–83.

Huang G-B, Chen L. Enhanced random search based incremental extreme learning machine. Neurocomputing. 2008;71:3460–8.

Huang G-B. An insight into extreme learning machines: random neurons, random features and kernels. Cogn Comput. 2014;6(3):376–90.

Huang G, Song S, Gupta JND, Wu C. Semi-supervised and unsupervised extreme learning machines. IEEE Trans Cybern. 2014;44(12):2405–17.

Huang G-B, Bai Z, Kasun LLC, Vong CM. Local receptive fields based extreme learning machine. IEEE Comput Intell Mag. 2015;10(2):18–29.

Rosenblatt F. The perceptron: a probabilistic model for information storage and organization in the brain. Psychol Rev. 1958;65(6):386–408.

Rahimi A, Recht B. Random features for large-scale kernel machines. In: Proceedings of the 2007 neural information processing systems (NIPS2007), p. 1177–1184, 3–6 Dec 2007.

Le Q, Sarlós T, Smola A. Fastfood approximating kernel expansions in loglinear time. In: Proceedings of the 30th international conference on machine learning, Atlanta, USA, p. 16–21, June 2013.

Huang P-S, Deng L, Hasegawa-Johnson M, He X. Random features for kernel deep convex network. In: Proceedings of the 38th international conference on acoustics, speech, and signal processing (ICASSP 2013), Vancouver, Canada, p. 26–31, May 2013.

Widrow B, Greenblatt A, Kim Y, Park D. The no-prop algorithm: a new learning algorithm for multilayer neural networks. Neural Netw. 2013;37:182–8.

Bartlett PL. 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 Inform Theory. 1998;44(2):525–36.

Cortes C, Vapnik V. Support vector networks. Mach Learn. 1995;20(3):273–97.

Suykens JAK, Vandewalle J. Least squares support vector machine classifiers. Neural Process Lett. 1999;9(3):293–300.

Minsky M, Papert S. Perceptrons: an introduction to computational geometry. Cambridge: MIT Press; 1969.

Huang G-B. Learning capability of neural networks. Ph.D. thesis, Nanyang Technological University, Singapore, 1998.

von Neumann J. Probabilistic logics and the synthesis of reliable organisms from unreliable components. In: Shannon CE, McCarthy J, editors. Automata studies. Princeton: Princeton University Press; 1956. p. 43–98.

von Neumann J. The general and logical theory of automata. In: Jeffress LA, editor. Cerebral mechanisms in behavior. New York: Wiley; 1951. p. 1–41.

Park J, Sandberg IW. Universal approximation using radial-basis-function networks. Neural Comput. 1991;3:246–57.

Leshno M, Lin VY, Pinkus A, Schocken S. Multilayer feedforward networks with a nonpolynomial activation function can approximate any function. Neural Netw. 1993;6:861–7.

Huang G-B, Zhou H, Ding X, Zhang R. Extreme learning machine for regression and multiclass classification. IEEE Trans Syst Man Cybern B. 2012;42(2):513–29.

Huang G-B, Zhu Q-Y, Siew C-K. Extreme learning machine: a new learning scheme of feedforward neural networks. In: Proceedings of international joint conference on neural networks (IJCNN2004), vol. 2, Budapest, Hungary, p. 985–990, 25–29 July 2004.

Huang G-B, Chen L, Siew C-K. Universal approximation using incremental constructive feedforward networks with random hidden nodes. IEEE Trans Neural Netw. 2006;17(4):879–92.

Huang G-B, Chen L. Convex incremental extreme learning machine. Neurocomputing. 2007;70:3056–62.

Sosulski DL, Bloom ML, Cutforth T, Axel R, Datta SR. Distinct representations of olfactory information in different cortical centres. Nature. 2011;472:213–6.

Eliasmith C, Stewart TC, Choo X, Bekolay T, DeWolf T, Tang Y, Rasmussen D. A large-scale model of the functioning brain. Science. 2012;338:1202–5.

Barak O, Rigotti M, Fusi S. The sparseness of mixed selectivity neurons controls the generalization–discrimination trade-off. J Neurosci. 2013;33(9):3844–56.

Rigotti M, Barak O, Warden MR, Wang X-J, Daw ND, Miller EK, Fusi S. The importance of mixed selectivity in complex cognitive tasks. Nature. 2013;497:585–90.

Baum E. On the capabilities of multilayer perceptrons. J Complex. 1988;4:193–215.

Igelnik B, Pao Y-H. Stochastic choice of basis functions in adaptive function approximation and the functional-link net. IEEE Trans Neural Netw. 1995;6(6):1320–9.

Tamura S, Tateishi M. Capabilities of a four-layered feedforward neural network: four layers versus three. IEEE Trans Neural Netw. 1997;8(2):251–5.

Principle J, Chen B. Universal approximation with convex optimization: gimmick or reality? IEEE Comput Intell Mag. 2015;10(2):68–77.

Lowe D. Adaptive radial basis function nonlinearities and the problem of generalisation. In: Proceedings of first IEE international conference on artificial neural networks, p. 171–175, 1989.

Huang G-B, Zhu Q-Y, Mao KZ, Siew C-K, Saratchandran P, Sundararajan N. Can threshold networks be trained directly? IEEE Trans Circuits Syst II. 2006;53(3):187–91.

Li M-B, Huang G-B, Saratchandran P, Sundararajan N. Fully complex extreme learning machine. Neurocomputing. 2005;68:306–14.

Tang J, Deng C, Huang G-B. Extreme learning machine for multilayer perceptron. IEEE Trans Neural Netw Learn Syst. 2015;. doi: 10.1109/TNNLS.2015.2424995 .

Kasun LLC, Zhou H, Huang G-B, Vong CM. Representational learning with extreme learning machine for big data. IEEE Intell Syst. 2013;28(6):31–4.

Jarrett K, Kavukcuoglu K, Ranzato M, LeCun Y. What is the best multi-stage architecture for object recognition. In: Proceedings of the 2009 IEEE 12th international conference on computer vision, Kyoto, Japan, 29 Sept–2 Oct 2009.

Saxe AM, Koh PW, Chen Z, Bhand M, Suresh B, Ng AY. On random weights and unsupervised feature learning. In: Proceedings of the 28th international conference on machine learning, Bellevue, USA, 28 June–2 July 2011.

Cox D, Pinto N. Beyond simple features: a large-scale feature search approach to unconstrained face recognition. In: IEEE international conference on automatic face and gesture recognition and workshops. IEEE, p. 8–15, 2011.

McDonnell MD, Vladusich T. Enhanced image classification with a fast-learning shallow convolutional neural network. In: Proceedings of international joint conference on neural networks (IJCNN’2015), Killarney, Ireland, 12–17 July 2015.

Zeng Y, Xu X, Fang Y, Zhao K. Traffic sign recognition using extreme learning classifier with deep convolutional features. In: The 2015 international conference on intelligence science and big data engineering (IScIDE 2015), Suzhou, China, June 14–16, 2015.

Suykens JAK, Gestel TV, Brabanter JD, Moor BD, Vandewalle J. Least squares support vector machines. Singapore: World Scientific; 2002.

Rahimi A, Recht B. Uniform approximation of functions with random bases. In: Proceedings of the 2008 46th annual allerton conference on communication, control, and computing, p. 555–561, 23–26 Sept 2008

Daubechies I. Orthonormal bases of compactly supported wavelets. Commun Pure Appl Math. 1988;41:909–96.

Daubechies I. The wavelet transform, time-frequency localization and signal analysis. IEEE Trans Inform Theory. 1990;36(5):961–1005.

Miche Y, Sorjamaa A, Bas P, Simula O, Jutten C, Lendasse A. OP-ELM: optimally pruned extreme learning machine. IEEE Trans Neural Netw. 2010;21(1):158–62.

Kim T, Adali T. Approximation by fully complex multilayer perceptrons. Neural Comput. 2003;15:1641–66.

Chen CLP. A rapid supervised learning neural network for function interpolation and approximation. IEEE Trans Neural Netw. 1996;7(5):1220–30.

Chen CLP, Wan JZ. A rapid learning and dynamic stepwise updating algorithm for flat neural networks and the applications to time-series prediction. IEEE Trans Syst Man Cybern B Cybern. 1999;29(1):62–72.

Huang G-B, Zhu Q-Y, Siew C-K. Extreme learning machine: theory and applications. Neurocomputing. 2006;70:489–501.

White H. An additional hidden unit test for neglected nonlinearity in multilayer feedforward networks. In: Proceedings of the international conference on neural networks, p. 451–455, 1989.

Poggio T, Mukherjee S, Rifkin R, Rakhlin A, Verri A. “ $$b$$ b ”, A.I. Memo No. 2001–011, CBCL Memo 198, Artificial Intelligence Laboratory, Massachusetts Institute of Technology, 2001.

Steinwart I, Hush D, Scovel C. Training SVMs without offset. J Mach Learn Res. 2011;12(1):141–202.

Luo J, Vong C-M, Wong P-K. Sparse bayesian extreme learning machine for multi-classification. IEEE Trans Neural Netw Learn Syst. 2014;25(4):836–43.

Decherchi S, Gastaldo P, Leoncini A, Zunino R. Efficient digital implementation of extreme learning machines for classification. IEEE Trans Circuits Syst II. 2012;59(8):496–500.

Bai Z, Huang G-B, Wang D, Wang H, Westover MB. Sparse extreme learning machine for classification. IEEE Trans Cybern. 2014;44(10):1858–70.

Frénay B, van Heeswijk M, Miche Y, Verleysen M, Lendasse A. Feature selection for nonlinear models with extreme learning machines. Neurocomputing. 2013;102:111–24.

Broomhead DS, Lowe D. Multivariable functional interpolation and adaptive networks. Complex Syst. 1988;2:321–55.

Ferrari S, Stengel RF. Smooth function approximation using neural networks. IEEE Trans Neural Netw. 2005;16(1):24–38.

Wang LP, Wan CR. Comments on ‘the extreme learning machine’. IEEE Trans Neural Netw. 2008;19(8):1494–5.

Chen S, Cowan CFN, Grant PM. Orthogonal least squares learning algorithm for radial basis function networks. IEEE Trans Neural Netw. 1991;2(2):302–9.