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Abstract:
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The Gaussian RBF kernel functions are widely used for many kernel methods, including classification. The bandwidth parameter is often selected by some data driven tuning methods. One of the most popular tuning methods is cross validation, which is known to be subjective to sampling variation and also computationally expensive. We propose a new method for bandwidth selection, based on the geometrical understanding of kernel based classification: a nonlinear classification that is actually a linear one in the embedded feature space. Thus we find the bandwidth that makes this linear classification task the "easiest". This method empirically turns out to be remarkably robust to sampling variation, for both SVM and the nearest centroid method. It also yields highly competitive misclassification rates, especially compared to GACV and Xi-alpha method.
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