Efficient Additive Kernels via Explicit Feature Maps

Large scale nonlinear support vector machines (SVMs) can be approximated by linear ones using a suitable feature map. The linear SVMs are in general much faster to learn and evaluate (test) than the original nonlinear SVMs. This work introduces explicit feature maps for the additive class of kernels, such as the intersection, Hellinger's, and χ2 kernels, commonly used in computer vision, and enables their use in large scale problems. In particular, we: 1) provide explicit feature maps for all additive homogeneous kernels along with closed form expression for all common kernels; 2) derive corresponding approximate finite-dimensional feature maps based on a spectral analysis; and 3) quantify the error of the…

• RA
  Royal Academy of Engineering