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Design of wavelet neural networks based on symmetry fuzzy C-means for function approximation

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Abstract

Specifying the number and locations of the translation vectors for wavelet neural networks (WNNs) is of paramount significance as the quality of approximation may be drastically reduced if initialization of WNNs parameters was not done judiciously. In this paper, an enhanced fuzzy C-means algorithm, specifically the modified point symmetry–based fuzzy C-means algorithm (MPSDFCM), was proposed, in order to determine the optimal initial locations for the translation vectors. The proposed neural network models were then employed in approximating five different nonlinear continuous functions. Assessment analysis showed that integration of the MPSDFCM in the learning phase of WNNs would lead to a significant improvement in WNNs prediction accuracy. Performance comparison with the approaches reported in the literature in approximating the same benchmark piecewise function verified the superiority of the proposed strategy.

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Abbreviations

ANNs:

Artificial neural networks

DSL:

Distance symmetry level

FCM:

Fuzzy C-means

GA:

Genetic algorithm

KM:

K-means

MLPs:

Multilayer perceptrons

MPSDFCM:

Modified point symmetry–based fuzzy C-means

MS:

Minkowski

MSE:

Mean-squared error

OSL:

Orientation symmetry level

PSD:

Point symmetry distance

PSDFCM:

Point symmetry–based fuzzy C-means

SSL:

Symmetry similarity level

SVMs:

Support vector machines

WNNs:

Wavelet neural networks

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Acknowledgment

The second author is grateful to Universiti Sains Malaysia, which supplied a generous Post-Doctoral Fellowship and made it possible to undertake this research.

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Authors and Affiliations

  1. School of Mathematical Sciences, Universiti Sains Malaysia (USM), 11800, Penang, Malaysia

    Zarita Zainuddin & Pauline Ong

  2. Faculty of Mechanical and Manufacturing Engineering, Universiti Tun Hussein Onn Malaysia (UTHM), Parit Raja, 86400, Batu Pahat, Johor, Malaysia

    Pauline Ong

Authors
  1. Zarita Zainuddin
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  2. Pauline Ong
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Correspondence to Zarita Zainuddin.

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Zainuddin, Z., Ong, P. Design of wavelet neural networks based on symmetry fuzzy C-means for function approximation. Neural Comput & Applic 23 (Suppl 1), 247–259 (2013). https://doi.org/10.1007/s00521-013-1350-x

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  • DOI: https://doi.org/10.1007/s00521-013-1350-x

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