A survey of the state of the art in learning the kernels

In recent years, the machine learning community has witnessed a tremendous growth in the development of kernel-based learning algorithms. However, the performance of this class of algorithms greatly depends on the choice of the kernel function. Kernel function implicitly represents the inner product between a pair of points of a dataset in a higher dimensional space. This inner product amounts to the similarity between points and provides a solid foundation for nonlinear analysis in kernel-based learning algorithms. The most important challenge in kernel-based learning is the selection of an appropriate kernel for a given dataset. To remedy this problem, algorithms to learn the kernel have recently been proposed. These methods formulate a learning algorithm that finds an optimal kernel for a given dataset. In this paper, we present an overview of these algorithms and provide a comparison of various approaches to find an optimal kernel. Furthermore, a list of pivotal issues that lead to efficient design of such algorithms will be presented.