Explicit Approximations of the Gaussian Kernel

We investigate training and using Gaussian kernel SVMs by approximating the kernel with an explicit finite- dimensional polynomial feature representation based on the Taylor expansion of the exponential. Although not as efficient as the recently-proposed random Fourier features [Rahimi and Recht, 2007] in terms of the number of features, we show how this polynomial representation can provide a better approximation in terms of the computational cost involved. This makes our "Taylor features" especially attractive for use on very large data sets, in conjunction with online or stochastic training.