A New Algorithm for Solving Multiple Kernel Problem as SILP

Abstract

The need to consider multiple kernels being emphasized in recent development in the literature on the support vector machines has lead to the development of Multiple Kernel Learning (MKL) problems. Lanckriet et al. (2004) considered conic combinations of kernel matrices for support vector machines; latterly quadratically-constrained quadratic program is developed to solve the Multiple Kernel Learning problem. Sonnenburg et al. (2006) rewrote multiple kernel problem as a semi-infinite linear program that be solved by recycling the standard SVM implementations. In this paper we follow the new way in which MKL problem is reformulated as a semiinfinite linear program, compute parameters of the MKL dual using a globally convergent method. Our experiments show that the new algorithm has good scaling ability and could be more efficient solving multiple kernel problems.