Kernel-dependent support vector error bounds
Bernhard Schölkopf · 1999
Model selection in Support Vector machines is usually carried out by minimizing the quotient of the radius of the smallest enclosing sphere of the data and the observed margin on the training set. We provide a new criterion taking the distribution within that sphere into account by considering the eigenvalue distribution of the Gram matrix of the data. Experimental results on real world data show that this new criterion provides a good prediction of the shape of the curve relating generalization error to kernel width. 1 Introduction Support Vector (SV) machines traditionally carry out model selection by minimizing the ratio between the radius of the smallest sphere enclosing the data in feature space and the width of the margin 1=kwk since this corresponds to a classifier with minimal fat shattering dimension [4]. Whilst in general capturing the correct scaling behaviour in terms of the weight vector w, this approach has the shortcoming that it completely ignores the information abo...