An approximation of the Gaussian RBF kernel for efficient classification with SVMs
Author(s): Ring M, Eskofier B
Publication year: 2016
Pages range: 107–113
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 kernel’s 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.
FAU Authors / FAU Editors How to cite
APA: Ring, M., & Eskofier, B. (2016). An approximation of the Gaussian RBF kernel for efficient classification with SVMs. Pattern Recognition Letters, 84, 107–113. https://dx.doi.org/10.1016/j.patrec.2016.08.013
MLA: Ring, Matthias, and Björn Eskofier. "An approximation of the Gaussian RBF kernel for efficient classification with SVMs." Pattern Recognition Letters 84 (2016): 107–113.