Advertisement

A Linear Learning Method for Multilayer Perceptrons Using Least-Squares

  • Bertha Guijarro-Berdiñas
  • Oscar Fontenla-Romero
  • Beatriz Pérez-Sánchez
  • Paula Fraguela
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4881)

Abstract

Training multilayer neural networks is typically carried out using gradient descent techniques. Ever since the brilliant backpropagation (BP), the first gradient-based algorithm proposed by Rumelhart et al., novel training algorithms have appeared to become better several facets of the learning process for feed-forward neural networks. Learning speed is one of these. In this paper, a learning algorithm that applies linear-least-squares is presented. We offer the theoretical basis for the method and its performance is illustrated by its application to several examples in which it is compared with other learning algorithms and well known data sets. Results show that the new algorithm upgrades the learning speed of several backpropagation algorithms, while preserving good optimization accuracy. Due to its performance and low computational cost it is an interesting alternative, even for second order methods, particularly when dealing large networks and training sets.

Keywords

Neural Network Gradient Descent Scaled Conjugate Gradient Gradient Descent Technique Wine Dataset 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Rumelhart, D.E., Hinton, G.E., William, R.J.: Learning representations of back-propagation errors. Nature 323, 533–536 (1986)CrossRefGoogle Scholar
  2. 2.
    Vogl, T.P., Mangis, J.K., Rigler, A.K., Zink, W.T., Alkon, D.L.: Accelerating the convergence of back-propagation method. Biological Cybernetics 59, 257–263 (1988)CrossRefGoogle Scholar
  3. 3.
    Jacobs, R.A.: Increased rates of convergence through learning rate adaptation. Neural Networks 1(4), 295–308 (1988)CrossRefGoogle Scholar
  4. 4.
    LeCun, Y., Bottou, L., Orr, G.B., Müller, K.-R.: Efficient BackProp. In: Orr, G.B., Müller, K.-R. (eds.) Neural Networks: Tricks of the Trade. LNCS, vol. 1524, Springer, Heidelberg (1998)CrossRefGoogle Scholar
  5. 5.
    Hagan, M.T., Menhaj, M.: Training feedforward networks with the Marquardt algorithm. IEEE Transactions on Neural Networks 5(6), 989–993 (1994)CrossRefGoogle Scholar
  6. 6.
    Beale, E.M.L.: A derivation of conjugate gradients. In: Lootsma, F.A. (ed.) Numerical methods for nonlinear optimization, pp. 39–43. Academic Press, London (1972)Google Scholar
  7. 7.
    Biegler-König, F., Bärmann, F.: A Learning Algorithm for Multilayered Neural Networks Based on Linear Least-Squares Problems. Neural Networks 6, 127–131 (1993)CrossRefGoogle Scholar
  8. 8.
    Yam, J.Y.F., Chow, T.W.S, Leung, C.T.: A New method in determining the initial weights of feedforward neural networks. Neurocomputing 16(1), 23–32 (1997)CrossRefGoogle Scholar
  9. 9.
    Bishop, C.M.: Neural Networks for Pattern Recognition. Oxford University Press, New York (1995)Google Scholar
  10. 10.
    Castillo, E., Fontenla-Romero, O., Alonso Betanzos, A., Guijarro-Berdiñas, B.: A global optimum approach for one-layer neural networks. Neural Computation 14(6), 1429–1449 (2002)zbMATHCrossRefGoogle Scholar
  11. 11.
    Fontenla-Romero, O., Erdogmus, D., Principe, J.C., Alonso-Betanzos, A., Castillo, E.: Linear least-squares based methods for neural networks learning. In: Kaynak, O., Alpaydın, E., Oja, E., Xu, L. (eds.) ICANN 2003 and ICONIP 2003. LNCS, vol. 2714, pp. 84–91. Springer, Heidelberg (2003)Google Scholar
  12. 12.
    Erdogmus, D., Fontenla-Romero, O., Principe, J.C., Alonso-Betanzos, A., Castillo, E.: Linear-Least-Squares Initialization of Multilayer Perceptrons Through Backpropagation of the Desired Response. IEEE Transactions on Neural Networks 16(2), 325–337 (2005)CrossRefGoogle Scholar
  13. 13.
    Nguyen, D., Widrow, B.: Improving the learning speed of 2-layer neural networks by choosing initial values of the adaptive weights. In: Proceedings of the International Joint Conference on Neural Networks, vol. 3, pp. 21–26 (1990)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Bertha Guijarro-Berdiñas
    • 1
  • Oscar Fontenla-Romero
    • 1
  • Beatriz Pérez-Sánchez
    • 1
  • Paula Fraguela
    • 1
  1. 1.Department of Computer Science, Facultad de Informática, Universidad de A Coruña, Campus de Elviña s/n, 15071 A CoruñaSpain

Personalised recommendations