Mercer Large-Scale Kernel Machines from Ridge Function Perspective
Karol Dziedziul Sergey Kryzhevich
To present Mercer large-scale kernel machines from a ridge function
perspective, we recall the results by Lin and Pinkus from Fundamentality of
ridge functions. We consider the main theorem of the recent paper by Rachimi
and Recht, 2008, Random features for large-scale kernel machines in terms of
the Approximation Theory. We study which kernels can be approximated by a sum
of cosine function products with arguments depending on $x$ and $y$ and present
the obstacles of such an approach. The results of this article may have various
applications in Deep Learning, especially in problems related to Image
Processing.