Mercer Large-Scale Kernel Machines from Ridge Function Perspective

TL;DR

This paper explores the theoretical foundations of large-scale kernel machines through ridge functions, analyzing kernel approximation via cosine sums and applying findings to image processing tasks.

Contribution

It provides a ridge function perspective on Mercer kernel machines, examines approximation obstacles, and connects theory to practical image processing applications.

Findings

Identifies kernels approximable by cosine product sums

Highlights obstacles in kernel approximation methods

Applies theoretical insights to image processing

Abstract

To present Mercer large-scale kernel machines from a ridge function perspective, we recall the results by Lin and Pinkus from {\it Fundamentality of ridge functions}. We consider the main result of the recent paper by Rachimi and Recht, 2008, {\it Random features for large-scale kernel machines} from the Approximation Theory point of view. We study which kernels could be approximated by a sum of products of cosine functions with arguments depending on $x$ and $y$ and present the obstacles of such an approach. The results of this article are applied to Image Processing by procedure "one-vs-rest".