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Gradient-based adaptation of general gaussian kernels.

Tobias Glasmachers1, Christian Igel

  • 1Institut für Neuroinformatik, Ruhr-Universität Bochum, D-44780 Bochum, Germany. Tobias.Glasmachers@neuroinformatik.rub.de

Neural Computation
|August 18, 2005
PubMed
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This study introduces gradient-based optimization for Gaussian kernel functions, enabling invariance to linear transformations. Controlling kernel size prevents overfitting in machine learning models like support vector machines.

Area of Science:

  • Machine Learning
  • Computational Mathematics

Background:

  • Gaussian kernel functions are crucial in machine learning algorithms.
  • Adapting kernel parameters is essential for model performance and generalization.
  • Invariance to input space transformations improves model robustness.

Purpose of the Study:

  • To develop a gradient-based optimization method for Gaussian kernel functions.
  • To achieve invariance against linear transformations of the input space.
  • To control kernel size for preventing overfitting in machine learning models.

Main Methods:

  • Computing gradients for scaling and rotation adaptation of the input space.
  • Utilizing the exponential map for parameterizing the kernel parameter manifold.
  • Restricting optimization to a constant trace subspace for kernel size control.

Related Experiment Videos

  • Demonstrating concepts via training hard margin support vector machines.

    • Main Results:

    • Successfully computed gradients for kernel adaptation.
    • Demonstrated invariance to linear transformations.
    • Showcased effective kernel size control to prevent overfitting.
    • Validated the approach on toy datasets using support vector machines.

    Conclusions:

    • Gradient-based optimization of Gaussian kernels offers a robust method for enhancing model generalization.
    • The proposed technique effectively manages kernel size, mitigating overfitting risks.
    • This approach advances the development of more invariant and reliable machine learning models.