Advertisement

Correlation Dimension and the Quality of Forecasts Given by a Neural Network

  • Krzysztof Michalak
  • Halina Kwasnicka
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3526)

Abstract

The problem addressed in this paper is searching for a dependence between the correlation dimension of a time series and the mean square error (MSE) obtained when predicting the future time series values using a multilayer perceptron. The relation between the correlantion dimension and the ability of a neural network to adapt to sample data represented by in-sample mean square error is also studied. The dependence between correlation dimension and in-sample and out-of-sample MSE is found in many real-life as well as artificial time series. The results presented in the paper were obtained using various neural network sizes and various activation functions of the output layer neurons.

Keywords

Time Series Mean Square Error Correlation Dimension Multilayer Perceptron Sigmoid Activation Function 
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.
    Grassberger, P., Procaccia, I.: Characterization of strange attractors. Physical Review Letters 50(5), 346–349 (1983)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Camastra, F., Vinciarelli, A.: Intrinsic Dimension Estimation of Data: An Approach Based on Grassberger-Procaccia’s Algorithm. Neural Processing Letters 14(1), 27–34 (2001)MATHCrossRefGoogle Scholar
  3. 3.
    Sheng, Z., et al.: Determining the input dimension of a neural network for nonlinear time series prediction. Chinese Physics 12(6), 594–598 (2003)CrossRefGoogle Scholar
  4. 4.
    Takens, F.: Detecting Strange Attractors in Turbulence. In: Proceedings of the Symposion on Dynamical Systems and Turbulence (1983)Google Scholar
  5. 5.
    Willmott: Matsuura and Collaborators’ Global Climate Resource Pages, http://climate.geog.udel.edu/~climate/

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Krzysztof Michalak
    • 1
  • Halina Kwasnicka
    • 1
  1. 1.Faculty Division of Computer ScienceWroclaw University of TechnologyWroclawPoland

Personalised recommendations