Piecewise approximation and neural networks

Martina Révayová; Csaba Török

Kybernetika (2007)

  • Volume: 43, Issue: 4, page 547-559
  • ISSN: 0023-5954

Abstract

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The paper deals with the recently proposed autotracking piecewise cubic approximation (APCA) based on the discrete projective transformation, and neural networks (NN). The suggested new approach facilitates the analysis of data with complex dependence and relatively small errors. We introduce a new representation of polynomials that can provide different local approximation models. We demonstrate how APCA can be applied to especially noisy data thanks to NN and local estimations. On the other hand, the new approximation method also has its impact on neural networks. We show how APCA helps to decrease the computation time of feed forward NN.

How to cite

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Révayová, Martina, and Török, Csaba. "Piecewise approximation and neural networks." Kybernetika 43.4 (2007): 547-559. <http://eudml.org/doc/33879>.

@article{Révayová2007,
abstract = {The paper deals with the recently proposed autotracking piecewise cubic approximation (APCA) based on the discrete projective transformation, and neural networks (NN). The suggested new approach facilitates the analysis of data with complex dependence and relatively small errors. We introduce a new representation of polynomials that can provide different local approximation models. We demonstrate how APCA can be applied to especially noisy data thanks to NN and local estimations. On the other hand, the new approximation method also has its impact on neural networks. We show how APCA helps to decrease the computation time of feed forward NN.},
author = {Révayová, Martina, Török, Csaba},
journal = {Kybernetika},
keywords = {data smoothing; least squares and related methods; linear regression; approximation by polynomials; neural networks; Autotracking Piecewise Cubic Approximation; data smoothing},
language = {eng},
number = {4},
pages = {547-559},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Piecewise approximation and neural networks},
url = {http://eudml.org/doc/33879},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Révayová, Martina
AU - Török, Csaba
TI - Piecewise approximation and neural networks
JO - Kybernetika
PY - 2007
PB - Institute of Information Theory and Automation AS CR
VL - 43
IS - 4
SP - 547
EP - 559
AB - The paper deals with the recently proposed autotracking piecewise cubic approximation (APCA) based on the discrete projective transformation, and neural networks (NN). The suggested new approach facilitates the analysis of data with complex dependence and relatively small errors. We introduce a new representation of polynomials that can provide different local approximation models. We demonstrate how APCA can be applied to especially noisy data thanks to NN and local estimations. On the other hand, the new approximation method also has its impact on neural networks. We show how APCA helps to decrease the computation time of feed forward NN.
LA - eng
KW - data smoothing; least squares and related methods; linear regression; approximation by polynomials; neural networks; Autotracking Piecewise Cubic Approximation; data smoothing
UR - http://eudml.org/doc/33879
ER -

References

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  1. Dikoussar N. D., Function parametrization by using 4-point transforms, Comput. Phys. Comm. 99 (1997), 235–254 (1997) Zbl0927.65009
  2. Dikoussar N. D., Török, Cs., Automatic knot finding for piecewise-cubic approximation, Mat. Model. T–18 (2006), 3, 23–40 Zbl1099.65014MR2255951
  3. Kahaner D., Moler, C., Nash S., Numerical Methods and Software, Practice–Hall, Englewood Cliffs, N.J. 1989 Zbl0744.65002
  4. Mallat S., A Wavelet Tour of Signal Processing, Academic Press, New York 1999 Zbl1170.94003MR2479996
  5. Révayová M., Török, Cs., Analysis of prediction with neural networks, In: Prastan 2004, Bratislava, pp. 85–93 
  6. Riplay B. D., Pattern Recognition and Neural Networks, Cambridge University Press, Cambridge 1996 MR1438788
  7. Seber G. A. F., Linear Regression Analysis, Wiley, New York 1977 Zbl1029.62059MR0436482
  8. Török, Cs., 4-Point transforms and approximation, Comput. Phys. Comm. 125 (2000), 154–166 
  9. Török, Cs., Dikoussar N. D., Approximation with discrete projective transformation, Comput. Math. Appl. 38 (1999), 211–220 (1999) Zbl1058.65506MR1718884
  10. Török, Cs., Visualization and data analysis in the MS, NET framework. In: Comm. JINR 2004, E10-2004-136, pp. 1–22 

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