Generalization bounds via eigenvalues of the gram matrix

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 Gram matrix of the data. In particular, this makes use of the eigenvalue distribution of the matrix. 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.