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Gradient-Based Adaptation of General Gaussian Kernels

Tobias.Glasmachers{at}neuroinformatik.rub.de, Institut für Neuroinformatik, Ruhr-Universität Bochum, D-44780 Bochum, Germany

Christian Igel

Christian.Igel{at}neuroinformatik.rub.de, Institut für Neuroinformatik, Ruhr-Universität Bochum, D-44780 Bochum, Germany

Gradient-based optimizing of gaussian kernel functions is considered. The gradient for the adaptation of scaling and rotation of the input space is computed to achieve invariance against linear transformations. This is done by using the exponential map as a parameterization of the kernel parameter manifold. By restricting the optimization to a constant trace subspace, the kernel size can be controlled. This is, for example, useful to prevent overfitting when minimizing radius-margin generalization performance measures. The concepts are demonstrated by training hard margin support vector machines on toy data.

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				T. Glasmachers and C. Igel Second-Order SMO Improves SVM Online and Active Learning Neural Comput., February 1, 2008; 20(2): 374 - 382. [Abstract] [Full Text] [PDF]