An approximation of the Gaussian RBF kernel for efficient classification with SVMs

Gaussian RBF kernels are approximated to speed up SVM classifications.An upper bound for the relative approximation error is given.Error decreases with factorial growth if approximation quality is linearly increased.Experiments showed an average 18-fold speed-up without losing accuracy. In theory, kernel support vector machines (SVMs) can be reformulated to linear SVMs. This reformulation can speed up SVM classifications considerably, in particular, if the number of support vectors is high. For the widely-used Gaussian radial basis function (RBF) kernel, however, this theoretical fact is impracticable because the reproducing kernel Hilbert space (RKHS) of this kernel has infinite dimensionality. Therefore, we derive a finite-dimensional approximative feature map, based on an orthonormal basis of the kernels RKHS, to enable the reformulation of Gaussian RBF SVMs to linear SVMs. We show that the error of this approximative feature map decreases with factorial growth if the approximation quality is linearly increased. Experimental evaluations demonstrated that the approximative feature map achieves considerable speed-ups (about 18-fold on average), mostly without losing classification accuracy. Therefore, the proposed approximative feature map provides an efficient SVM evaluation method with minimal loss of precision.