Skip to main content
Erschienen in: Neural Processing Letters 2/2016

01.10.2016

Architecture Selection of ELM Networks Based on Sensitivity of Hidden Nodes

verfasst von: Junhai Zhai, Qingyan Shao, Xizhao Wang

Erschienen in: Neural Processing Letters | Ausgabe 2/2016

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Extreme learning machine (ELM) was proposed as a new algorithm for training single-hidden layer feed-forward neural networks (SLFNs). One of the issues in EML is how to determine the architecture of SLFNs. Based on sensitivity of hidden nodes, an approach of architecture selection of ELM networks by applying a pruned method was proposed in this paper. The proposed pruning method utilizes sensitivity to measure the significance of hidden nodes. Beginning from an initial large number of hidden nodes, the insignificant nodes with lower sensitivity are then pruned. Experimental results on ten UCI data sets show that the proposed approach can obtain compact network architecture that generate comparable prediction accuracy on unseen samples.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Huang GB, Zhu QY, Siew CK (2006) Extreme learning machine: theory and applications. Neurocomputing 70:489–501CrossRef Huang GB, Zhu QY, Siew CK (2006) Extreme learning machine: theory and applications. Neurocomputing 70:489–501CrossRef
2.
Zurück zum Zitat Huang GB, Wang DH, Lan Y (2011) Extreme learning machines: a survey. Int J Mach Learn Cybern 2:107–122CrossRef Huang GB, Wang DH, Lan Y (2011) Extreme learning machines: a survey. Int J Mach Learn Cybern 2:107–122CrossRef
3.
Zurück zum Zitat Huang GB, Chen L, Siew CK (2006) Universal approximation using incremental constructive feedforward networks with random hidden nodes. IEEE Trans Neural Netw 17:879–892CrossRef Huang GB, Chen L, Siew CK (2006) Universal approximation using incremental constructive feedforward networks with random hidden nodes. IEEE Trans Neural Netw 17:879–892CrossRef
4.
Zurück zum Zitat Cortes C, Vapnik V (1995) Support vector networks. Mach Learn 20:273–297MATH Cortes C, Vapnik V (1995) Support vector networks. Mach Learn 20:273–297MATH
5.
Zurück zum Zitat Haykin S (1999) Neural networks: a comprehensive foundation. Prentice Hall, New Jersey, pp 178–228MATH Haykin S (1999) Neural networks: a comprehensive foundation. Prentice Hall, New Jersey, pp 178–228MATH
6.
Zurück zum Zitat Battiti R (1992) First and second order methods for learning: between the steepest descent and Newton’s method. Neural Comput 2:141–166CrossRef Battiti R (1992) First and second order methods for learning: between the steepest descent and Newton’s method. Neural Comput 2:141–166CrossRef
7.
Zurück zum Zitat LeCun Y, Denker JS, Solla SA (1990) Optimal brain damage. In: Touretzky DS (ed) Advances in neural information processing systems, vol 2. Morgan Kaufmann Publishers Inc., San Francisco, pp 598–605 LeCun Y, Denker JS, Solla SA (1990) Optimal brain damage. In: Touretzky DS (ed) Advances in neural information processing systems, vol 2. Morgan Kaufmann Publishers Inc., San Francisco, pp 598–605
8.
Zurück zum Zitat Hassibi B, Stork DG, Wolff GJ (1993) Optimal brain surgeon and general network pruning. In: IEEE international conference on neural networks, 28 March–1 April 1993, San Francisco, CA, vol 1, pp 293–299 Hassibi B, Stork DG, Wolff GJ (1993) Optimal brain surgeon and general network pruning. In: IEEE international conference on neural networks, 28 March–1 April 1993, San Francisco, CA, vol 1, pp 293–299
9.
Zurück zum Zitat Monari G, Dreyfus G (2002) Local overfitting control via leverages. Neural Comput 6:1481–1506CrossRefMATH Monari G, Dreyfus G (2002) Local overfitting control via leverages. Neural Comput 6:1481–1506CrossRefMATH
10.
Zurück zum Zitat 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 Networks 20:1352–1357CrossRef 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 Networks 20:1352–1357CrossRef
11.
Zurück zum Zitat Lan Y, Soh YC, Huang GB (2010) Constructive hidden nodes selection of extreme learning machine for regression. Neurocomputing 73:3191–3199CrossRef Lan Y, Soh YC, Huang GB (2010) Constructive hidden nodes selection of extreme learning machine for regression. Neurocomputing 73:3191–3199CrossRef
12.
Zurück zum Zitat Huang GB, Li MB, Chen L, Siew CK (2008) Incremental extreme learning machine with fully complex hidden nodes. Neurocomputing 71:576–583CrossRef Huang GB, Li MB, Chen L, Siew CK (2008) Incremental extreme learning machine with fully complex hidden nodes. Neurocomputing 71:576–583CrossRef
13.
Zurück zum Zitat Huang GB, Chen L (2008) Enhanced random search based incremental extreme learning machine. Neurocomputing 71:3060–3068 Huang GB, Chen L (2008) Enhanced random search based incremental extreme learning machine. Neurocomputing 71:3060–3068
14.
Zurück zum Zitat Huang GB, Chen L (2007) Convex incremental extreme learning machine. Neurocomputing 70:3056–3062CrossRef Huang GB, Chen L (2007) Convex incremental extreme learning machine. Neurocomputing 70:3056–3062CrossRef
15.
Zurück zum Zitat Rong HJ, Ong YS, Tan AH, Zhu Z (2008) A fast pruned-extreme learning machine for classification problem. Neurocomputing 72:359–366CrossRef Rong HJ, Ong YS, Tan AH, Zhu Z (2008) A fast pruned-extreme learning machine for classification problem. Neurocomputing 72:359–366CrossRef
16.
Zurück zum Zitat Miche Y, Sorjamaa A, Bas P, Simula O (2010) OP-ELM: optimally pruned extreme learning machine. IEEE Trans Neural Networks 21:158–162CrossRef Miche Y, Sorjamaa A, Bas P, Simula O (2010) OP-ELM: optimally pruned extreme learning machine. IEEE Trans Neural Networks 21:158–162CrossRef
17.
Zurück zum Zitat Akaike H (1973) Information theory and an extension of the maximum likelihood principle. In: Petrov BN, Csaki F (eds) Second international symposium on information theory. Academiai Kiado, Budapest, pp 267–281 Akaike H (1973) Information theory and an extension of the maximum likelihood principle. In: Petrov BN, Csaki F (eds) Second international symposium on information theory. Academiai Kiado, Budapest, pp 267–281
18.
Zurück zum Zitat Similä T, Tikka J (2005) Multiresponse sparse regression with application to multidimensional scaling. Proc Int Conf Artif Neural Netw 3697/2005:97–102 Similä T, Tikka J (2005) Multiresponse sparse regression with application to multidimensional scaling. Proc Int Conf Artif Neural Netw 3697/2005:97–102
20.
Zurück zum Zitat Myers RH (1990) Classical and modern regression with applications, 2nd edn. Duxbury, Pacific Grove Myers RH (1990) Classical and modern regression with applications, 2nd edn. Duxbury, Pacific Grove
21.
Zurück zum Zitat Andrs BC, Pedro JGL, Jos-Luis SG (2013) Neural architecture design based on extreme learning machine. Neural Netw 48:19–24CrossRef Andrs BC, Pedro JGL, Jos-Luis SG (2013) Neural architecture design based on extreme learning machine. Neural Netw 48:19–24CrossRef
22.
Zurück zum Zitat Wang X, Shao Q, Qi M, Zhai J (2013) Architecture selection for networks trained with extreme learning machine using localized generalization error model. Neurocomputing 102:1–9CrossRef Wang X, Shao Q, Qi M, Zhai J (2013) Architecture selection for networks trained with extreme learning machine using localized generalization error model. Neurocomputing 102:1–9CrossRef
23.
Zurück zum Zitat Deng W, Zheng Q, Chen L (2009) Regularized extrem learning machine. In: IEEE symposiumon computational intelligence and data mining, 30 March–2 April 2009, Nashville, TN, pp 389–395 Deng W, Zheng Q, Chen L (2009) Regularized extrem learning machine. In: IEEE symposiumon computational intelligence and data mining, 30 March–2 April 2009, Nashville, TN, pp 389–395
24.
Zurück zum Zitat Shao H, Japkowicz N (2012) Applying least angle regression to ELM. In: Kosseim L, Inkpen D (eds) Canadian AI, LNAI 7310. pp 170–180 Shao H, Japkowicz N (2012) Applying least angle regression to ELM. In: Kosseim L, Inkpen D (eds) Canadian AI, LNAI 7310. pp 170–180
25.
Zurück zum Zitat Miche Y, Heeswijk M, Bas P, Simula O, Lendasse A (2011) TROP-ELM: a double-regularized ELM using LARS and Tikhonov regularization. Neurocomputing 74:2413–2421CrossRef Miche Y, Heeswijk M, Bas P, Simula O, Lendasse A (2011) TROP-ELM: a double-regularized ELM using LARS and Tikhonov regularization. Neurocomputing 74:2413–2421CrossRef
26.
Zurück zum Zitat Hoerl AE, Kennard R (1970) Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12:55–67CrossRefMATH Hoerl AE, Kennard R (1970) Ridge regression: biased estimation for nonorthogonal problems. Technometrics 12:55–67CrossRefMATH
27.
Zurück zum Zitat Tibshirani R (1996) Regression shrinkage and selection via the lasso. J R Stat Soc Ser B 58:267–288MathSciNetMATH Tibshirani R (1996) Regression shrinkage and selection via the lasso. J R Stat Soc Ser B 58:267–288MathSciNetMATH
28.
29.
Zurück zum Zitat Neumann K, Steil JJ (2013) Optimizing extreme learning machines via ridge regression and batch intrinsic plasticity. Neurocomputing 102:23–30CrossRef Neumann K, Steil JJ (2013) Optimizing extreme learning machines via ridge regression and batch intrinsic plasticity. Neurocomputing 102:23–30CrossRef
30.
Zurück zum Zitat Liao SZ, Feng C (2014) Meta-ELM: ELM with ELM hidden nodes. Neurocomputing 128:81–87CrossRef Liao SZ, Feng C (2014) Meta-ELM: ELM with ELM hidden nodes. Neurocomputing 128:81–87CrossRef
31.
Zurück zum Zitat Ahila R, Sadasivam V, Manimala K (2015) An integrated PSO for parameter determination and feature selection of ELM and its application in classification of power system disturbances. Appl Soft Comput 32:23–37CrossRef Ahila R, Sadasivam V, Manimala K (2015) An integrated PSO for parameter determination and feature selection of ELM and its application in classification of power system disturbances. Appl Soft Comput 32:23–37CrossRef
32.
Zurück zum Zitat Tavares LD, Saldanha RR, Vieira DAG (2015) Extreme learning machine with parallel layer perceptrons. Neurocomputing 166:164–171CrossRef Tavares LD, Saldanha RR, Vieira DAG (2015) Extreme learning machine with parallel layer perceptrons. Neurocomputing 166:164–171CrossRef
33.
Zurück zum Zitat Yang JB, Shen KQ, Ong CJ (2009) Feature selection for MLP neural network: the use of random permutation of probabilistic outputs. IEEE Trans Neural Netw 20:1911–1922CrossRef Yang JB, Shen KQ, Ong CJ (2009) Feature selection for MLP neural network: the use of random permutation of probabilistic outputs. IEEE Trans Neural Netw 20:1911–1922CrossRef
34.
Zurück zum Zitat Huang GB (2003) Learning capability and storage capacity of two-hidden-layer feedforward networks. IEEE Trans Neural Netw 14:274–281CrossRef Huang GB (2003) Learning capability and storage capacity of two-hidden-layer feedforward networks. IEEE Trans Neural Netw 14:274–281CrossRef
35.
Zurück zum Zitat Serre D (2002) Matrices: theory and applications. Springer, New YorkMATH Serre D (2002) Matrices: theory and applications. Springer, New YorkMATH
36.
Zurück zum Zitat Bishop CM (1996) Neural networks for pattern recognition. Clarendon Press, Oxford, pp 129–168MATH Bishop CM (1996) Neural networks for pattern recognition. Clarendon Press, Oxford, pp 129–168MATH
37.
Zurück zum Zitat Mallows CL (2000) Some comments on \(C_p\). Technometrics 42:87–94 Mallows CL (2000) Some comments on \(C_p\). Technometrics 42:87–94
38.
Zurück zum Zitat Yan X, Su XG (2009) Linear regression analysis: theory and computing. World Scientific Publishing Co. Pte. Ltd., SingaporeCrossRefMATH Yan X, Su XG (2009) Linear regression analysis: theory and computing. World Scientific Publishing Co. Pte. Ltd., SingaporeCrossRefMATH
39.
Zurück zum Zitat Liu X, Gao C, Li P (2012) A comparative analysis of support vector machines and extreme learning machines. Neural Netw 33:58–66CrossRefMATH Liu X, Gao C, Li P (2012) A comparative analysis of support vector machines and extreme learning machines. Neural Netw 33:58–66CrossRefMATH
40.
Zurück zum Zitat Golub G, Charles F, Loan V (1983) Matrix computations. Johns Hopkins University Press, BaltimoreMATH Golub G, Charles F, Loan V (1983) Matrix computations. Johns Hopkins University Press, BaltimoreMATH
41.
Zurück zum Zitat Khan JA, Aelst SV, Zamara RH (2007) Robust linear model selection based on least angle regression. J Am Stat Assoc 102:1289–1299MathSciNetCrossRefMATH Khan JA, Aelst SV, Zamara RH (2007) Robust linear model selection based on least angle regression. J Am Stat Assoc 102:1289–1299MathSciNetCrossRefMATH
42.
Zurück zum Zitat Dougherty J, Kohavi R, Sahami M (1995) Supervised and unsupervised discretization of continuous features. In: Proceedings of the twelfth international conference. Morgan Kaufmann Publishers, San Francisco, pp 194–202 Dougherty J, Kohavi R, Sahami M (1995) Supervised and unsupervised discretization of continuous features. In: Proceedings of the twelfth international conference. Morgan Kaufmann Publishers, San Francisco, pp 194–202
44.
Zurück zum Zitat Hastie T, Tibshirani R, Friedman J (2009) The elements of statistical learning: data mining, inference, and prediction, 2nd edn. Springer, New YorkCrossRefMATH Hastie T, Tibshirani R, Friedman J (2009) The elements of statistical learning: data mining, inference, and prediction, 2nd edn. Springer, New YorkCrossRefMATH
45.
Zurück zum Zitat Janez D (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1–30MathSciNetMATH Janez D (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1–30MathSciNetMATH
Metadaten
Titel
Architecture Selection of ELM Networks Based on Sensitivity of Hidden Nodes
verfasst von
Junhai Zhai
Qingyan Shao
Xizhao Wang
Publikationsdatum
01.10.2016
Verlag
Springer US
Erschienen in
Neural Processing Letters / Ausgabe 2/2016
Print ISSN: 1370-4621
Elektronische ISSN: 1573-773X
DOI
https://doi.org/10.1007/s11063-015-9470-1

Weitere Artikel der Ausgabe 2/2016

Neural Processing Letters 2/2016 Zur Ausgabe

Neuer Inhalt