Learning With Multiple Kernels

Abstract

Over the last decades, learning methods using kernels have become very popular. The main reason is that real data analysis often requires nonlinear methods to detect the dependencies that allow successful predictions of properties of interest. Gaussian kernels have been used in many studies such as learning algorithms and data analysis. Most of these studies have shown that the parameter chosen for a Gaussian kernel could have a huge impact on the desired results. Therefore, it is essential to understand this impact on a theoretical level. The main contribution of this paper is to study the effect of the Gaussian kernel bandwidth parameter on how well an empirical operator defined from data approximates its continuous counterpart. Some results in spectral approximations are provided as well as some examples.

Keywords

• Gaussian kernel
• radial kernels
• kernel principal component analysis
• reproducing kernel
• support vector machine