Complex support vector regression

We present a support vector regression (SVR) rationale for treating complex data, exploiting the notions of widely linear estimation and pure complex kernels. To compute the Lagrangian and derive the dual problem, we employ the recently presented Wirtinger's calculus on complex RKHS. We prove that this approach is equivalent with solving two real SVR problems exploiting a specific real kernel, which it is induced by the chosen complex kernel.