Nonlinear Combination of Multiple Kernels for Support Vector Machines

Support vector machines (SVMs) are effective kernel methods to solve pattern recognition problems. Traditionally, they adopt a single kernel chosen beforehand, which makes them lack flexibility. The recent multiple kernel learning (MKL) overcomes this issue by optimizing over a linear combination of kernels. Despite its success, MKL neglects useful information generated from the nonlinear interaction of different kernels. In this paper, we propose SVMs based on the nonlinear combination of multiple kernels (NCMK) which surmounts the drawback of previous MKL by the potential to exploit more information. We show that our method can be formulated as a semi-definite programming (SDP) problem then solved by interior-point algorithms. Empirical studies on several data sets indicate that the presented approach is very effective.