Generalized RBF feature maps for Efficient Detection

These kernels combine the benefits of two other important classes of kernels: the homogeneous additive kernels (e.g. the χ2 kernel) and the RBF kernels (e.g. the exponential kernel). However, large scale problems require machine learning techniques of at most linear complexity and these are usually limited to linear kernels. Recently, Maji and Berg [2] and Vedaldi and Zisserman [4] proposed explicit feature maps to approximate the additive kernels (intersection, χ2, etc.) by linear ones, thus enabling the use of fast machine learning technique in a non-linear context. An analogous technique was proposed by Rahimi and Recht [3] for the translation invariant RBF kernels. In this paper, we complete the construction and combine the two techniques to obtain explicit feature maps for the generalized RBF kernels. The generalized RBF kernels extend the RBF kernels to use a metric not necessarily Euclidean. Recall that, for any Positive Definite kernel K(x,y), the equation