Complex support vector machines for quaternary classification

We present a support vector machines (SVM) rationale suitable for quaternary classification problems that use complex data, exploiting the notions of widely linear estimation and pure complex kernels. The recently developed Wirtinger´s calculus on complex RKHS is employed in order to compute the Lagrangian and derive the dual optimization problem. We show that this approach is equivalent with solving two real SVM tasks exploiting a specific real kernel, which is induced by the chosen complex kernel.