Sparse kernel approximations for efficient classification and detection

Efficient learning with non-linear kernels is often based on extracting features from the data that “linearise” the kernel. While most constructions aim at obtaining low-dimensional and dense features, in this work we explore high-dimensional and sparse ones. We give a method to compute sparse features for arbitrary kernels, re-deriving as a special case a popular map for the intersection kernel and extending it to arbitrary additive kernels. We show that bundle optimisation methods can handle efficiently these sparse features in learning. As an application, we show that product quantisation can be interpreted as a sparse feature encoding, and use this to significantly accelerate learning with this technique. We demonstrate these ideas on image classification with Fisher kernels and object detection with deformable part models on the challenging PASCAL VOC data, obtaining five to ten-fold speed-ups as well as reducing memory use by an order of magnitude.