Support Vector Classi er with Asymmetric Kernel Functions

In support vector classi er, asymmetric kernel functions are not used so far, although they are frequently used in other kernel classi ers. The applicable kernels are limited to symmetric semipositive de nite ones because of Mercer's theorem. In this paper, SVM is extended to be applicable to asymmetric kernel functions. It is proven that, when a positive de nite kernel is given, the extended SVM is identical with the conventional SVM. In the 3D object recognition experiment, the extended SVM with asymmetric kernels performed better than the conventional SVM.