Projection Learning Based Kernel Machine Design Using Series of Monotone Increasing Reproducing Kernel Hilbert Spaces

Abstract

Kernel machines are widely known as powerful tools for various fields of information science. In general, they are designed based on a generalization criterion related to the complexity of the model and intuitive but ad hoc philosophy such as maximal margin principle shown in SVM. On the other hand, the projection learning scheme was proposed in the field of neural networks. In the projection learning, the generalization ability is evaluated by the distance between the unknown target function and the estimated one. In this paper, we construct projection learning based kernel machines and propose a method of making a kernel function that has necessary representability for the task. The method is reduced to a selection of an appropriate reproducing kernel Hilbert space from a series of monotone increasing subspaces. We also verify the efficacy of the proposed method by numerical examples.