Effects of kernel function on nu support vector machines in extreme cases

How we should choose a kernel function in support vector machines (SVMs), is an important but difficult problem. In this paper, we discuss the properties of the solution of the nu-SVM's, a variation of SVM's, for normalized feature vectors in two extreme cases: All feature vectors are almost orthogonal and all feature vectors are almost the same. In the former case, the solution of the nu-SVM is nearly the center of gravity of the examples given while the solution is approximated to that of the nu-SVM with the linear kernel in the latter case. Although extreme kernels are not employed in practice, analyzes are helpful to understand the effects of a kernel function on the generalization performance.