ABSTRACT
Kernels are the basic ingredients shared by all kernel methods. A kernel’s representation of an object emerges through the object’s relationships to other objects (or data points). The kernel trick has huge practical implications. It is a very convenient way of transforming linear methods, such as linear discriminant analysis or principal component analysis, into nonlinear methods by simply replacing the classic dot product with a more general kernel, such as the Gaussian RBF kernel. Kernel methods can only be applied to vector data. Kernel methods are similar to SBML but do not have the attribute-scaling factors. Since a kernel is the dot product of feature vectors, the selection of appropriate features is essential for constructing a good kernel, and thus requires field knowledge. Many linear models for regression and classification such as support vector machine can be reformulated in terms of a dual representation in which the kernel function arises naturally.
