One new family of smooth semi-supervised support vector classifier based on Fourier series approximation technique

This article presents a new family of smooth semi-supervised support vector machines based on Fourier series approximation technique (FS-S⁴VMs) for classification. The semi-supervised support vector machine (S³VM) is the powerful tool for coping with quantities of unlabeled data in the real world. However, the symmetric hinge loss function of S³VM is not smooth. It will decrease the classification accuracy and endure heavy burden calculation. To deal with this problem, the Fourier series approximation smooth technique for replacing the non-smooth item have been investigated. One novel family of FS-S⁴VMs classifier is derived. Thus, one fast SAGA algorithm for solving non-convex FS-S⁴VMs can be utilized to decrease the computing scale. The nonlinear case and convergence analysis are presents as well. To attest how the new FS-S⁴VMs can be implemented into practice, experiments on synthetic and real data sets are accessed. In the final, theoretical explanation and simulation comparisons illustrate the FS-S⁴VMs enhance the robustness of S³VM, and increase the classification accuracy at about 1%–3% than other smooth techniques.