Kernel-based methods and function approximation

This paper provides a new insight into neural networks by using the kernel theory drawn from the work on support vector machine and related algorithms. The kernel trick is used to extract a relevant data set into the feature space according to a geometrical consideration. Then the data are projected onto the subspace of the selected vectors where classical algorithms are applied without adaptation. This approach covers a wide range of algorithms. In particular, different types of neural network are covered by choosing an appropriate kernel. We investigate the function approximation on a real classification problem and on a regression problem.