Generalized RBF feature maps for Efficient Detection

Kernel methods yield state-of-the-art performance in certain applications such as image classification and object detection. However, large scale problems require machine learning techniques of at most linear complexity and these are usually limited to linear kernels. This unfortunately rules out gold-standard kernels such as the generalized RBF kernels (e.g. exponential-χ2) . Recently, Maji and Berg 13 and Vedaldi and Zisser-man 20 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 14 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. Furthermore, we investigate a learning method using l1 regularization to encourage sparsity in the final vector representation, and thus reduce its dimension. We evaluate this technique on the VOC 2007 detection challenge, showing when it can improve on fast additive kernels, and the trade-offs in complexity and accuracy.