Boundedness of Input Space and Effective Dimension of Feature Space in Kernel Methods

摘要

Kernel methods such as the support vector machines map input vectors into a high-dimensional feature space and linearly separate them there. The dimensionality of the feature space depends on a kernel function and is sometimes of an infinite dimension. The Gauss kernel is such an example. We discuss the effective dimension of the feature space with the Gauss kernel and show that it can be approximated to a sum of polynomial kernels and that its dimensionality is determined by the boundedness of the input space by considering the Taylor expansion of the kernel Gram matrix.