Finding small sets of random fourier features for shift-invariant kernel approximation

Kernel based learning is very popular in machine learning, but many classical methods have at least quadratic runtime complexity. Random fourier features are very effective to approximate shift-invariant kernels by an explicit kernel expansion. This permits to use efficient linear models with much lower runtime complexity. As one key approach to kernelize algorithms with linear models they are successfully used in different methods. However, the number of features needed to approximate the kernel is in general still quite large with substantial memory and runtime costs. Here, we propose a simple test to identify a small set of random fourier features with linear costs, substantially reducing the number of generated features for low rank kernel matrices, while widely keeping the same representation accuracy. We also provide generalization bounds for the proposed approach.