Designing Kernel Functions Using the Karhunen-Loève Expansion

In recent years, a number of kernel-based learning algorithms such as the regularization networks [1], the support vector machines [7, 4, 5], and the Gaussian process regression [8] have been investigated. These kernel machines are shown to work very well on real-world problems, given appropriate kernel functions. For general purposes, the Gaussian kernel is widely used and seems to work well [5]. On the other hand, a lot of attention have been paid recently to designing kernel functions using the problem-dependent prior knowledge. Various methods for constructing suitable kernels have been proposed [7, 3, 9, 6, 4]. In this contribution, we propose a framework for designing kernel functions for regression.