A novel description of the reproducing kernel support vector machines

Abstract

Support vector machines (SVMs) and related kernel-based algorithms have become one of the most popular approaches for many machine learning problems. but little is known about the structure of their reproducing kernel Hilbert spaces (RKHS). In this work, based on Mercer's Theorem, the relation among reproducing kernel (RK) and Mercer kernel, and their roles in SVMs are discussed, corresponding to some important theorems and consequences are given. Furthermore, a novel framework of reproducing kernel support vector machines (RKSVM) is proposed. The simulation results are presented to illustrate the feasibility of the proposed method. Choosing a proper Mercer kernel for different tasks is an important factor for studying the result of the SVMs.