Kernel construction via generalized eigenvector decomposition

Abstract

Kernel construction is one of the key issues both in current research and application of kernel methods. In this paper, we present an effective kernel construction method, in which we reduce the construction of kernel function to the solutions of generalized eigenvalue problems. Specifically, we first obtain a primal kernel function based on the similarity of instances, and refine it with the conformal transformation. Then we determine the parameters of kernel function by simply solving the generalized eigenvalue problems according to the kernel alignment and Fisher criteria. Our method can avoid local maxima and insure positive semidefinite of the constructed kernel. Experimental results show that our kernel construction method is effective and robust. © 2011 Springer-Verlag Berlin Heidelberg.