Extreme learning machines: a survey

Original Article

Abstract

Computational intelligence techniques have been used in wide applications. Out of numerous computational intelligence techniques, neural networks and support vector machines (SVMs) have been playing the dominant roles. However, it is known that both neural networks and SVMs face some challenging issues such as: (1) slow learning speed, (2) trivial human intervene, and/or (3) poor computational scalability. Extreme learning machine (ELM) as emergent technology which overcomes some challenges faced by other techniques has recently attracted the attention from more and more researchers. ELM works for generalized single-hidden layer feedforward networks (SLFNs). The essence of ELM is that the hidden layer of SLFNs need not be tuned. Compared with those traditional computational intelligence techniques, ELM provides better generalization performance at a much faster learning speed and with least human intervene. This paper gives a survey on ELM and its variants, especially on (1) batch learning mode of ELM, (2) fully complex ELM, (3) online sequential ELM, (4) incremental ELM, and (5) ensemble of ELM.

Keywords

Extreme learning machine Support vector machine ELM kernel ELM feature space Ensemble Incremental learning Online sequential learning 

References

  1. 1.
    Rumelhart DE, Hinton GE, Williams RJ (1986) Learning representations by back-propagation errors. Nature 323:533–536CrossRefGoogle Scholar
  2. 2.
    Cortes C, Vapnik V (1995) Support vector networks. Mach Learn 20(3):273–297MATHGoogle Scholar
  3. 3.
    Rosenblatt F (1962) Principles of neurodynamics: perceptrons and the theory of brain mechanisms. Spartan Books, New YorkMATHGoogle Scholar
  4. 4.
    Lowe D (1989) Adaptive radial basis function nonlinearities and the problem of generalisation. In: Proceedings of first IEE international conference on artificial neural networks, pp 171–175Google Scholar
  5. 5.
    Huang G-B, Zhu Q-Y, Siew C-K (2004) 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, 25–29 July 2004, pp 985–990Google Scholar
  6. 6.
    Huang G-B, Zhu Q-Y, Siew C-K (2006) Extreme learning machine: theory and applications. Neurocomputing 70:489–501CrossRefGoogle Scholar
  7. 7.
    Huang G-B, Chen L, Siew C-K (2006) Universal approximation using incremental constructive feedforward networks with random hidden nodes. IEEE Trans Neural Netw 17(4):879–892CrossRefGoogle Scholar
  8. 8.
    Huang G-B, Chen L (2007) Convex incremental extreme learning machine. Neurocomputing 70:3056–3062CrossRefGoogle Scholar
  9. 9.
    Huang G-B, Chen L (2008) Enhanced random search based incremental extreme learning machine. Neurocomputing 71:3460–3468CrossRefGoogle Scholar
  10. 10.
    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(2):525–536MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Huang S-C, Huang Y-F (1991) Bounds on the number of hidden neurons in multilayer perceptrons. IEEE Trans Neural Netw 2(1):47–55CrossRefGoogle Scholar
  12. 12.
    Sartori MA, Antsaklis PJ (1991) A simple method to derive bounds on the size and to train multilayer neural networks. IEEE Trans Neural Netw 2(4):467–471CrossRefGoogle Scholar
  13. 13.
    Huang G-B, 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(1):224–229CrossRefGoogle Scholar
  14. 14.
    Gallant A, White H (1992) There exists a neural network that does not make avoidable mistakes. In: White H (ed) Artificial neural networks: approximation and learning theory. Blackwell, Oxford, pp 5–11Google Scholar
  15. 15.
    Hornik K (1991) Approximation capabilities of multilayer feedforward networks. Neural Netw 4:251–257CrossRefGoogle Scholar
  16. 16.
    Leshno M, Lin VY, Pinkus A, Schocken S (1993) Multilayer feedforward networks with a nonpolynomial activation function can approximate any function. Neural Netw 6:861–867CrossRefGoogle Scholar
  17. 17.
    Park J, Sandberg IW (1991) Universal approximation using radial-basis-function networks. Neural Comput 3:246–257CrossRefGoogle Scholar
  18. 18.
    Hornik K, Stinchcombe M, White H (1989) Multilayer feedforward networks are universal approximators. Neural Netw 2:359–366CrossRefGoogle Scholar
  19. 19.
    Cybenko G (1989) Approximation by superpositions of a sigmoidal function. Math Control Signals Syst 2(4):303–314MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Funahashi K (1989) On the approximate realization of continuous mappings by neural networks. Neural Netw 2:183–192CrossRefGoogle Scholar
  21. 21.
    Stinchcombe M, White H (1992) Universal approximation using feedforward networks with non-sigmoid hidden layer activation functions. In: White H (ed) Artificial neural networks: approximation and learning theory. Blackwell, Oxford, pp 29–40Google Scholar
  22. 22.
    Barron AR (1993) Universal approximation bounds for superpositions of a sigmoidal function. IEEE Trans Inf Theory 39(3):930–945MathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    Kwok T-Y, Yeung D-Y (1997) Objective functions for training new hidden units in constructive neural networks. IEEE Trans Neural Netw 8(5):1131–1148CrossRefGoogle Scholar
  24. 24.
    Meir R, Maiorov VE (2000) On the optimality of neural-network approximation using incremental algorithms. IEEE Trans Neural Netw 11(2):323–337CrossRefGoogle Scholar
  25. 25.
    Romero E (2001) Function approximation with SAOCIF: a general sequential method and a particular algorithm with feed-forward neural networks. Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya. http://www.lsi.upc.es/dept/techreps/html/R01-41.html
  26. 26.
    Huang G-B (2003) Learning capability and storage capacity of two-hidden-layer feedforward networks. IEEE Trans Neural Netw 14(2):274–281CrossRefGoogle Scholar
  27. 27.
    Corwin EM, Logar AM, Oldham WJB (1994) An iterative method for training multilayer networks with threshold function. IEEE Trans Neural Netw 5(3):507–508CrossRefGoogle Scholar
  28. 28.
    Toms DJ (1990) Training binary node feedforward neural networks by backpropagation of error. Electron Lett 26(21):1745–1746CrossRefGoogle Scholar
  29. 29.
    Goodman RM, Zeng Z (1994) A learning algorithm for multi-layer perceptrons with hard-limiting threshold units. In: Proceedings of the 1994 IEEE workshop of neural networks for signal processing, pp 219–228Google Scholar
  30. 30.
    Plagianakos VP, Magoulas GD, Nousis NK, Vrahatis MN (2001) Training multilayer networks with discrete activation functions. In: Proceedings of the IEEE international joint conference on neural networks (IJCNN’2001), Washington, DC, USAGoogle Scholar
  31. 31.
    Voxman WL, Roy J, Goetschel H (1981) Advanced calculus: an introduction to modern analysis. Marcel Dekker, New YorkGoogle Scholar
  32. 32.
    Broomhead DS, Lowe D (1988) Multivariable functional interpolation and adaptive networks. Complex Syst 2:321–355MathSciNetMATHGoogle Scholar
  33. 33.
    Igelnik B, Pao YH (1995) Stochastic choice of basis functions in adaptive function approximation and the functional-link net. IEEE Trans Neural Netw 6(6):1320–1329CrossRefGoogle Scholar
  34. 34.
    Huang G-B, Li M-B, Chen L, Siew C-K (2008) Incremental extreme learning machine with fully complex hidden nodes. Neurocomputing 71:576–583CrossRefGoogle Scholar
  35. 35.
    Huang G-B, Siew C-K (2004) Extreme learning machine: RBF network case. In: Proceedings of the eighth international conference on control, automation, robotics and vision (ICARCV 2004), vol 2, Kunming, China, 6–9 Dec 2004, pp 1029–1036Google Scholar
  36. 36.
    Huang G-B, Zhu Q-Y, Mao K-Z, Siew C-K, Saratchandran P, Sundararajan N (2006) Can threshold networks be trained directly?. IEEE Trans Circuits Syst II 53(3):187–191CrossRefGoogle Scholar
  37. 37.
    Serre D (2002) Matrices: theory and applications. Springer, New YorkMATHGoogle Scholar
  38. 38.
    Rao CR, Mitra SK (1971) Generalized inverse of matrices and its applications. Wiley, New YorkMATHGoogle Scholar
  39. 39.
    Huang G-B, Zhou H, Ding X, Zhang R (2010) Extreme learning machine for regression and multi-class classification. IEEE Trans Pattern Anal Mach Intell (submitted)Google Scholar
  40. 40.
    Hoerl AE, Kennard RW (1970) Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12(1):55–67MathSciNetMATHCrossRefGoogle Scholar
  41. 41.
    Toh K-A (2008) Deterministic neural classification. Neural Comput 20(6):1565–1595MathSciNetMATHCrossRefGoogle Scholar
  42. 42.
    Deng W, Zheng Q, Chen L (2009) Regularized extreme learning machine. In: IEEE symposium on computational intelligence and data mining (CIDM2009), 30 March 2009–2 April 2009, pp 389–395Google Scholar
  43. 43.
    Man Z, Lee K, Wang D, Cao Z, Miao C (2011) A new robust training algorithm for a class of single-hidden layer feedforward neural networks. Neurocomputing (in press)Google Scholar
  44. 44.
    Miche Y, van Heeswijk M, Bas P, Simula O, Lendasse A (2011) TROP-ELM: a double-regularized elm using lars and tikhonov regularization. Neurocomputing (in press)Google Scholar
  45. 45.
    Drucker H, Burges CJ, Kaufman L, Smola A, Vapnik V (1997) Support vector regression machines. In: Mozer M, Jordan J, Petscbe T (eds) Neural information processing systems, vol 9. MIT Press, Cambridge, pp 155–161Google Scholar
  46. 46.
    Hsu C-W, Lin C-J (2002) A comparison of methods for multiclass support vector machines. IEEE Trans Neural Netw 13(2):415–425CrossRefGoogle Scholar
  47. 47.
    Lin K-M, Lin C-J (2003) A study on reduced support vector machines. IEEE Trans Neural Netw 14(6):1449–1459CrossRefGoogle Scholar
  48. 48.
    Lee Y-J, Mangasarian OL (2001) RSVM: reduced support vector machines. In: Proceedings of the SIAM international conference on data mining, Chicago, USA, 5–7 Apr 2001Google Scholar
  49. 49.
    Suykens JAK, Vandewalle J (1997) Least squares support vector machine classifiers. Neural Process Lett 9(3):293–300CrossRefGoogle Scholar
  50. 50.
    Frénay B, Verleysen M (2010) Using SVMs with randomised feature spaces: an extreme learning approach. In: Proceedings of the 18th European symposium on artificial neural networks (ESANN), Bruges, Belgium, 28–30 Apr 2010, pp 315–320Google Scholar
  51. 51.
    Frénay B, Verleysen M (2011) Parameter-insensitive kernel in extreme learning for non-linear support vector regression. Neurocomputing (in press)Google Scholar
  52. 52.
    Li M-B, Huang G-B, Saratchandran P, Sundararajan N (2005) Fully complex extreme learning machine. Neurocomputing 68:306–314CrossRefGoogle Scholar
  53. 53.
    Cha I, Kassam SA (1995) Channel equalization using adaptive complex radial basis function networks. IEEE J Sel Areas Commun 13:122–131CrossRefGoogle Scholar
  54. 54.
    Jianping D, Sundararajan N, Saratchandran P (2002) Communication channel equalization using complex-valued minimal radial basis function neural networks. IEEE Trans Neural Netw 13:687–696CrossRefGoogle Scholar
  55. 55.
    Kim T, Adali T (2003) Approximation by fully complex multilayer perseptrons. Neural Comput 15:1641–1666MATHCrossRefGoogle Scholar
  56. 56.
    LeCun Y, Bottou L, Orr GB, Müller K-R (1998) Efficient BackProp. Lect Notes Comput Sci 1524:9–50Google Scholar
  57. 57.
    Platt J (1991) A resource-allocating network for function interpolation. Neural Comput 3:213–225MathSciNetCrossRefGoogle Scholar
  58. 58.
    Kadirkamanathan V, Niranjan M (1993) A function estimation approach to sequential learning with neural networks. Neural Comput 5:954–975CrossRefGoogle Scholar
  59. 59.
    Yingwei L, Sundararajan N, Saratchandran P (1997) A sequential learning scheme for function approximation using minimal radial basis function (RBF) neural networks. Neural Comput 9:461–478MATHCrossRefGoogle Scholar
  60. 60.
    Yingwei L, Sundararajan N, Saratchandran P (1998) Performance evaluation of a sequential minimal radial basis function (RBF) neural network learning algorithm. IEEE Trans Neural Netw 9(2):308–318CrossRefGoogle Scholar
  61. 61.
    Salmerón M, Ortega J, Puntonet CG, Prieto A (2001) Improved RAN sequential prediction using orthogonal techniques. Neurocomputing 41:153–172Google Scholar
  62. 62.
    Rojas I, Pomares H, Bernier JL, Ortega J, Pino B, Pelayo FJ, Prieto A (2002) Time series analysis using normalized PG-RBF network with regression weights. Neurocomputing 42:267–285MATHCrossRefGoogle Scholar
  63. 63.
    Huang G-B, Saratchandran P, Sundararajan N (2004) An efficient sequential learning algorithm for growing and pruning RBF (GAP-RBF) networks. IEEE Trans Syst Man Cybern Part B 34(6):2284–2292CrossRefGoogle Scholar
  64. 64.
    Huang G-B, Saratchandran P, Sundararajan N (2005) A generalized growing and pruning RBF (GGAP-RBF) neural network for function approximation. IEEE Trans Neural Netw 16(1):57–67CrossRefGoogle Scholar
  65. 65.
    Liang N-Y, Huang G-B, Saratchandran P, Sundararajan N (2006) A fast and accurate on-line sequential learning algorithm for feedforward networks. IEEE Trans Neural Netw 17(6):1411–1423CrossRefGoogle Scholar
  66. 66.
    Chong EKP,  Zak SH (2001) An introduction to optimization. Wiley, New YorkMATHGoogle Scholar
  67. 67.
    Golub GH, Loan CFV (1996) Matrix computations, 3rd edn. The Johns Hopkins University Press, BaltimoreGoogle Scholar
  68. 68.
    Mackey MC, Glass L (1997) Oscillation and chaos in physiological control systems. Science 197:287–289CrossRefGoogle Scholar
  69. 69.
    Vapnik VN (1998) Statistical learning theory. Wiley, New YorkMATHGoogle Scholar
  70. 70.
    Smola A, Schölkopf B (1998) A tutorial on support vector regression. NeuroCOLT2 technical report NC2-TR-1998-030Google Scholar
  71. 71.
    Hansen LK, Salamon P (1990) Neural network ensemble. IEEE Trans Pattern Anal Mach Intell 12(10):993–1001CrossRefGoogle Scholar
  72. 72.
    Breiman L (1996) Bagging predictor. Mach Learn 24(2):123–140MathSciNetMATHGoogle Scholar
  73. 73.
    Schapire RE (1990) The strength of weak learnability. Mach Learn 5(2):197–227Google Scholar
  74. 74.
    Freund Y (1995) Boosting a weak algorithm by majority. Inf Comput 121(2):256–285MathSciNetMATHCrossRefGoogle Scholar
  75. 75.
    Freund Y, Schapire RE (1997) A decision-theoretic generalization of online learning and an application to boosting. J Comput Syst Sci 55:119–139MathSciNetMATHCrossRefGoogle Scholar
  76. 76.
    Sun Z-L, Choi T-M, Au K-F, Yu Y (2008) Sales forecasting using extreme learning machine with applications in fashion retailing. Decis Support Syst 46(1):411–419CrossRefGoogle Scholar
  77. 77.
    van Heeswijk M, Miche Y, Lindh-Knuutila T, Hilbers PA, Honkela T, Oja E, Lendasse A (2009) Adaptive ensemble models of extreme learning machines for time series prediction. Lect Notes Comput Sci 5769:305–314CrossRefGoogle Scholar
  78. 78.
    van Heeswijk M, Miche Y, Oja E, Lendasse A (2011) Gpu-accelerated and parallelized ELM ensembles for large-scale regression. Neurocomputing (in press)Google Scholar
  79. 79.
    Minku FL, Inoue H, Yao X (2011) Negative correlation in incremental learning. Nat Comp (in press)Google Scholar
  80. 80.
    Sun Y, Yuan Y, Wang G (2011) An OS-ELM based distributed ensemble classification framework in p2p networks. Neurocomputing (in press)Google Scholar
  81. 81.
    Lan Y, Soh YC, Huang G-B (2009) Ensemble of online sequential extreme learning machine. Neurocomputing 72:3391–3395CrossRefGoogle Scholar
  82. 82.
    Rong H-J, Ong Y-S, Tan A-H, Zhu Z (2008) A fast pruned-extreme learning machine for classification problem. Neurocomputing 72:359–366CrossRefGoogle Scholar
  83. 83.
    Miche Y, Sorjamaa A, Lendasse A (2008) OP-ELM: theory, experiments and a toolbox. Lect Notes Comput Sci 5163:145–154CrossRefGoogle Scholar
  84. 84.
    Simila T, Tikka J (2005) Multiresponse sparse regression with application to multidimensional scaling. In: Proceedings in artificial neural networks: formal models and their applications, ICANN 2005, vol 3697, pp 97–102Google Scholar
  85. 85.
    Feng G, Huang G-B, Lin Q, Gay R (2009) Error minimized extreme learning machine with growth of hidden nodes and incremental learning. IEEE Trans Neural Netw 20(8):1352–1357CrossRefGoogle Scholar
  86. 86.
    Lan Y, Soh YC, Huang G-B (2010) Random search enhancement of error minimized extreme learning machine. In: European symposium on artificial neural networks (ESANN 2010), Bruges, Belgium, Apr 2010, pp 327–332Google Scholar
  87. 87.
    Li K, Huang G-B, Ge SS (2010) Fast construction of single hidden layer feedforward networks. In: Rozenberg G, Bäck T, Kok JN (eds) Handbook of natural computing. Springer, Berlin, Mar 2010Google Scholar
  88. 88.
    Mao K-Z, Bilings SA (1997) Algorithms for minimal model structure detection in nonlinear dynamic system identification. Int J Control 68(2):311–330MATHCrossRefGoogle Scholar
  89. 89.
    Lan Y, Soh YC, Huang G-B (2010) Constructive hidden nodes selection of extreme learning machine for regression. Neurocomputing 73:3191–3199CrossRefGoogle Scholar
  90. 90.
    Lan Y, Soh YC, Huang GB (2010) Two-stage extreme learning machine for regression. Neurocomputing 73:3028–3038CrossRefGoogle Scholar
  91. 91.
    Liu Q, He Q, Shi Z (2008) Extreme support vector machine classifier. Lect Notes Comput Sci 5012:222–233CrossRefGoogle Scholar
  92. 92.
    Huang G-B, Ding X, Zhou H (2010) Optimization method based extreme learning machine for classification. Neurocomputing 74:155–163CrossRefGoogle Scholar
  93. 93.
    Fletcher R (1981) Practical methods of optimization. In: Constrained optimization, vol 2. Wiley, New YorkGoogle Scholar
  94. 94.
    Handoko SD, Keong KC, Soon OY, Zhang GL, Brusic V (2006) Extreme learning machine for predicting hla-peptide binding. Lect Notes Comput Sci 3973:716–721CrossRefGoogle Scholar
  95. 95.
    Sun Z-L, Au K-F, Choi T-M (2008) A neuro-fuzzy inference system through integration of fuzzy logic and extreme learning machines. IEEE Trans Syst Man Cybern Part B Cybern 37(5):1321–1331CrossRefGoogle Scholar
  96. 96.
    Tang X, Han M (2009) Partial lanczos extreme learning machine for single-output regression problems. Neurocomputing 72(13-15):3066–3076CrossRefGoogle Scholar
  97. 97.
    Miche Y, Sorjamaa A, Bas P, Simula O, Jutten C, Lendasse A (2010) OP-ELM: optimally pruned extreme learning machine. IEEE Trans Neural Netw 21(1):158–162CrossRefGoogle Scholar
  98. 98.
    Yeu C-WT, Lim M-H, Huang G-B, Agarwal A, Ong Y-S (2006) A new machine learning paradigm for terrain reconstruction. IEEE Geosci Remote Sens Lett 3(3):382–386CrossRefGoogle Scholar
  99. 99.
    Soria-Olivas E, Gomez-Sanchis J, Martin JD, Vila-Frances J, Martinez M, Magdalena JR, Serrano AJ (2011) BELM: Bayesian extreme learning machine. IEEE Trans Neural Netw 22(3):505–509CrossRefGoogle Scholar
  100. 100.
    Xu Y, Dong ZY, Meng K, Zhang R, Wong KP (2011) Real-time transient stability assessment model using extreme learning machine. IET Gener Transm Distrib 5(3):314–322CrossRefGoogle Scholar
  101. 101.
    Barea R, Boquete L, Rodriguez-Ascariz JM, Ortega S, Lopez E (2011) Sensory system for implementing a human-computer interface based on electrooculography. Sensors 11(1):310–328CrossRefGoogle Scholar
  102. 102.
    Chang N-B, Han M, Yao W, Chen L-C, Xu S (2011) Change detection of land use and land cover in an urban region with SPOT-5 images and partial lanczos extreme learning machine. J Appl Remote Sens 4Google Scholar
  103. 103.
    Saraswathi S, Sundaram S, Sundararajan N, Zimmermann M, Nilsen-Hamilton M (2011) ICGA-PSO-ELM approach for accurate multiclass cancer classification resulting in reduced gene sets in which genes encoding secreted proteins are highly represented. IEEE ACM Trans Comput Biol Bioinforma 6(2):452–463CrossRefGoogle Scholar
  104. 104.
    Li F-C, Wang P-K, Wang G-E (2009) Comparison of the primitive classifiers with extreme learning machine in credit scoring. In: 2009 IEEE international conference on industrial engineering and engineering management, pp 685–688Google Scholar
  105. 105.
    Choi K, Toh K-A, Byun H (2011) Realtime training on mobile devices for face recognition applications. Pattern Recogn 44(2):386–400Google Scholar
  106. 106.
    Chen FL, Ou TY (2011) Sales forecasting system based on gray extreme learning machine with Taguchi method in retail industry. Expert Syst Appl 38(3):1336–1345CrossRefGoogle Scholar
  107. 107.
    Ye Y, Squartim S, Piazza F (2010) Incremental-based extreme learning machine algorithms for time-variant neural networks. Lect Notes Comput Sci 6215:9–16CrossRefGoogle Scholar
  108. 108.
    Suresh S, Saraswathi S, Sundararajan N (2010) Performance enhancement of extreme learning machine for multi-category sparse data classification problems. Eng Appl Artif Intell 23(7):1149–1157CrossRefGoogle Scholar
  109. 109.
    Li G, Liu M, Dong M (2010) A new online learning algorithm for structure-adjustable extreme learning machine. Comput Math Appl 60(3):377–389MathSciNetMATHCrossRefGoogle Scholar
  110. 110.
    Liu Y, Xu X, Wang C (2009) Simple ensemble of extreme learning machine. In: Proceedings of the 2009 2nd international congress on image and signal processing, pp 2177–2181Google Scholar
  111. 111.
    Deng W, Chen L (2010) Color image watermarking using regularized extreme learning machine. Neural Network World 20(3):317–330Google Scholar
  112. 112.
    Mohammed AA, Wu QMJ, Sid-Ahmed MA (2010) Application of wave atoms decomposition and extreme learning machine for fingerprint classification. Lect Notes Comput Sci 6112:246–256CrossRefGoogle Scholar
  113. 113.
    Minhas R, Baradarani A, Seifzadeh S, Wu QMJ (2010) Human action recognition using extreme learning machine based on visual vocabularies. Neurocomputing 73:1906–1917CrossRefGoogle Scholar
  114. 114.
    Malathi V, Marimuthu NS, Baskar S (2010) Intelligent approaches using support vector machine and extreme learning machine for transmission line protection. Neurocomputing 73:2160–2167CrossRefGoogle Scholar
  115. 115.
    Tang X-L, Han M (2010) Ternary reversible extreme learning machines: the incremental tri-training method for semi-supervised classification. Knowl Inf Syst 22(3):345–372CrossRefGoogle Scholar
  116. 116.
    Nizar AH, Dong ZY, Wang Y (2008) Power utility nontechnical loss analysis with extreme learning machine method. IEEE Trans Power Syst 23(3):946–955CrossRefGoogle Scholar
  117. 117.
    Cho JS, White H (2011) Testing correct model specification using extreme learning machines. Neurocomputing (in press)Google Scholar
  118. 118.
    Wang Y, Cao F, Yuan Y (2011) A study on effectiveness of extreme learning machine. Neurocomputing (in press)Google Scholar
  119. 119.
    Deng J, Li K, Irwin GW (2011) Fast automatic two-stage nonlinear model identification based on the extreme learning machine. Neurocomputing (in press)Google Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.School of Electrical and Electronic EngineeringNanyang Technological UniversitySingaporeSingapore
  2. 2.Department of Computer Science and Computer EngineeringLa Trobe UniversityMelbourneAustralia

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