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Generalized multiscale radial basis function networks.

Stephen A Billings1, Hua-Liang Wei, Michael A Balikhin

  • 1Department of Automatic Control and Systems Engineering, The University of Sheffield, Mappin Street, Sheffield, S1 3JD, UK. s.billings@sheffield.ac.uk

Neural Networks : the Official Journal of the International Neural Network Society
|November 13, 2007
PubMed
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This study introduces a novel multiscale radial basis function (RBF) network. This new model offers improved flexibility and generalization for nonlinear dynamical systems compared to traditional RBF networks.

Area of Science:

  • Artificial Intelligence
  • Machine Learning
  • Computational Science

Background:

  • Traditional radial basis function (RBF) networks utilize a single kernel width for all basis functions, limiting representational flexibility.
  • General nonlinear dynamical systems require adaptable models for accurate prediction and analysis.

Purpose of the Study:

  • To propose a novel multiscale radial basis function (RBF) network framework.
  • To enhance model flexibility and generalization properties for nonlinear dynamical systems.
  • To develop a parsimonious and efficient modeling approach.

Main Methods:

  • Development of a novel network architecture employing multiscale Gaussian functions with multiple kernel widths per center.
  • Utilization of k-means clustering for determining basis function centers.

Related Experiment Videos

  • Application of an improved orthogonal least squares (OLS) algorithm for parameter estimation (widths and weights).

    • Main Results:

    • The proposed multiscale RBF network demonstrates superior flexibility in representing nonlinear dynamical systems.
    • Models constructed using the new framework exhibit significantly improved generalization properties.
    • The multiscale RBF network achieves parsimony with comparable or enhanced performance to single-scale networks.

    Conclusions:

    • The multiscale RBF network provides a flexible and parsimonious modeling framework for nonlinear dynamical systems.
    • The proposed method offers enhanced generalization capabilities over traditional single-scale RBF networks.
    • The network is easily implemented and learned using standard algorithms, making it practical for various applications.