  Despite the recent deep learning (DL) revolution, kernel machines still
remain powerful methods for action recognition. DL has brought the use of large
datasets and this is typically a problem for kernel approaches, which are not
scaling up efficiently due to kernel Gram matrices. Nevertheless, kernel
methods are still attractive and more generally applicable since they can
equally manage different sizes of the datasets, also in cases where DL
techniques show some limitations. This work investigates these issues by
proposing an explicit approximated representation that, together with a linear
model, is an equivalent, yet scalable, implementation of a kernel machine. Our
approximation is directly inspired by the exact feature map that is induced by
an RBF Gaussian kernel but, unlike the latter, it is finite dimensional and
very compact. We justify the soundness of our idea with a theoretical analysis
which proves the unbiasedness of the approximation, and provides a vanishing
bound for its variance, which is shown to decrease much rapidly than in
alternative methods in the literature. In a broad experimental validation, we
assess the superiority of our approximation in terms of 1) ease and speed of
training, 2) compactness of the model, and 3) improvements with respect to the
state-of-the-art performance.
