  Kernel matrices are crucial in many learning tasks such as support vector
machines or kernel ridge regression. The kernel matrix is typically dense and
large-scale. Depending on the dimension of the feature space even the
computation of all of its entries in reasonable time becomes a challenging
task. For such dense matrices the cost of a matrix-vector product scales
quadratically with the dimensionality N , if no customized methods are applied.
We propose the use of an ANOVA kernel, where we construct several kernels based
on lower-dimensional feature spaces for which we provide fast algorithms
realizing the matrix-vector products. We employ the non-equispaced fast Fourier
transform (NFFT), which is of linear complexity for fixed accuracy. Based on a
feature grouping approach, we then show how the fast matrix-vector products can
be embedded into a learning method choosing kernel ridge regression and the
conjugate gradient solver. We illustrate the performance of our approach on
several data sets.
