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Related Experiment Videos

Fuzzy function approximation with ellipsoidal rules.

J A Dickerson1, B Kosko

  • 1Dept. of Electr. Eng. & Comput. Eng., Iowa State Univ., Ames, IA.

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
|January 1, 1996
PubMed
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This study introduces a hybrid neural system for accurate function approximation using ellipsoidal fuzzy rules. This approach combines unsupervised and supervised learning for improved performance over traditional methods.

Area of Science:

  • Computational intelligence
  • Machine learning
  • Fuzzy systems

Background:

  • Fuzzy systems approximate functions using rules, which can be represented as ellipsoids in state space.
  • Additive fuzzy systems cover function graphs with ellipsoidal rule patches, averaging overlapping regions.
  • Optimal fuzzy rules often correspond to the extrema or bumps of the function.

Purpose of the Study:

  • To develop a hybrid neural system combining unsupervised and supervised learning for accurate function approximation.
  • To utilize ellipsoidal fuzzy rules for enhanced system performance.
  • To improve upon traditional fuzzy and neural network approaches.

Main Methods:

  • A hybrid neural system integrating unsupervised competitive learning and supervised gradient descent was employed.

Related Experiment Videos

  • Unsupervised learning identified cluster statistics, defining ellipsoidal rules based on covariance matrices.
  • Supervised learning fine-tuned these rules via gradient descent to minimize mean-squared error.

    • Main Results:

    • The hybrid system demonstrated more accurate function approximation compared to standalone unsupervised or supervised methods.
    • A closed-form model for optimal rules was derived when only ellipsoid centroids varied.
    • Numerical techniques were used to determine optimal rules in the general case.

    Conclusions:

    • Hybrid neural systems offer superior function approximation accuracy by leveraging both data clustering and gradient-based optimization.
    • Ellipsoidal fuzzy rules, initialized by unsupervised learning and tuned by supervised learning, provide an effective framework.
    • The findings advance the development of intelligent systems for complex function approximation tasks.