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The extended piecewise quadratic neural network.

David M. Weber1, David P. Casasent

  • 1Department of Electrical and Electronic Engineering, University of Stellenbosch, Private Bag X1, Matieland 7602, South Africa

Neural Networks : the Official Journal of the International Neural Network Society
|March 29, 2003
PubMed
Summary

We introduce the extended piecewise quadratic neural network (E-PQNN), a novel classifier for detection and classification. This E-PQNN can generate various decision surfaces, including linear and quadratic types, enhancing pattern recognition capabilities.

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Area of Science:

  • Machine Learning
  • Artificial Intelligence
  • Neural Networks

Background:

  • Traditional neural networks often have limitations in generating complex decision boundaries.
  • The need for versatile classifiers capable of handling diverse data distributions is crucial in pattern recognition.

Purpose of the Study:

  • To introduce a new neural network architecture, the extended piecewise quadratic neural network (E-PQNN).
  • To demonstrate the E-PQNN's capability in creating diverse decision surfaces (spherical, elliptical, hyperbolic, linear).
  • To develop methods for optimizing E-PQNN architecture and training.

Main Methods:

  • The proposed E-PQNN utilizes complex-valued weights and a square-law non-linearity.
  • The architecture is proven to generate piecewise quadratic decision surfaces of arbitrary rank.

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  • Weight optimization employs a modified perceptron error criterion and a conjugate gradient optimizer.

    • Main Results:

    • The E-PQNN architecture successfully generates linear, spherical, elliptical, and hyperbolic decision surfaces.
    • New methods for determining the optimal number of hidden-layer neurons were developed.
    • The classifier's performance was validated on a synthetic dataset.

    Conclusions:

    • The extended piecewise quadratic neural network (E-PQNN) offers a flexible and powerful approach for classification tasks.
    • The E-PQNN's ability to form complex decision surfaces makes it suitable for challenging detection and classification problems.
    • Further research can explore E-PQNN applications in various real-world datasets.