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Related Experiment Videos

Optimally regularised kernel Fisher discriminant classification.

Kamel Saadi1, Nicola L C Talbot, Gavin C Cawley

  • 1School of Computing Sciences, University of East Anglia, Norwich, Norfolk, UK.

Neural Networks : the Official Journal of the International Neural Network Society
|June 30, 2007
PubMed
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This study presents an efficient method for tuning the regularization parameter in kernel Fisher discriminant analysis. The new approach significantly reduces computational cost, enabling faster model selection for kernel machines.

Area of Science:

  • Machine Learning
  • Pattern Recognition
  • Computational Statistics

Background:

  • Kernel Fisher Discriminant Analysis (KFDA) extends Fisher's linear discriminant using the kernel trick for non-linear classification.
  • Efficient leave-one-out cross-validation (LOO-CV) is crucial for model selection in KFDA.
  • Tuning the regularization parameter in KFDA typically requires computationally intensive methods.

Purpose of the Study:

  • To develop a computationally efficient method for re-estimating the leave-one-out cross-validation error in KFDA after changes to the regularization parameter.
  • To enable faster tuning of the regularization parameter within a model selection strategy for kernel machines.
  • To improve the efficiency of model selection for kernel-based classifiers.

Main Methods:

Related Experiment Videos

  • Extending an existing analytical expression for LOO-CV error in KFDA.
  • Performing discriminant analysis in canonical form to achieve computational efficiency.
  • Developing an O(l^2) algorithm for re-estimating LOO-CV error, significantly faster than the O(l^3) training algorithm.

    • Main Results:

    • The proposed method allows for re-estimation of LOO-CV error with O(l^2) complexity, drastically reducing computational cost.
    • Tuning the regularization parameter can be performed at a negligible computational expense.
    • The method demonstrates competitive generalization performance compared to k-fold cross-validation on benchmark datasets, while being considerably faster.

    Conclusions:

    • The proposed efficient re-estimation of LOO-CV error is a valuable tool for model selection in KFDA.
    • This method facilitates faster and more effective tuning of regularization parameters in kernel machines.
    • The approach offers a significant speed advantage over traditional methods for model selection in KFDA.