Complex-valued support vector classifiers

In this paper, we present a family of complex-valued support vector classifiers (CSVCs) based on the definition of the complex sign inspired by the modulation in digital communications and the complex-valued kernel functions. We also propose a theorem to construct the complex-valued Mercer kernels and the corresponding kernel function groups. CSVC algorithms include binary (2-state) CSVC (BCSVC), quadrature (4-state) CSVC (QCSVC) and some multi-state CSVCs. In this paper, we focus on QCSVC. For a quadrature complex-valued classification problem, QCSVC is identical to the 4-quadrature amplitude modulation demodulation methods in digital communications. Finally, the simulated experiments confirm the validity and the efficiency of CSVCs.