Random Feature Maps for Dot Product Kernels
This work provides a method to reduce computational costs in kernel-based algorithms, which is incremental as it extends existing feature map techniques to dot product kernels.
The paper tackles the problem of approximating dot product kernels for faster SVM and kernel-based learning by introducing low distortion embeddings into linear Euclidean spaces, achieving high confidence approximations with explicit low-dimensional feature maps.
Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line of work and present low distortion embeddings for dot product kernels into linear Euclidean spaces. We base our results on a classical result in harmonic analysis characterizing all dot product kernels and use it to define randomized feature maps into explicit low dimensional Euclidean spaces in which the native dot product provides an approximation to the dot product kernel with high confidence.