Kernel Path for Semisupervised Support Vector Machine

Semisupervised support vector machine ((SVM)-V-3) is a powerful semisupervised learning model that can use large amounts of unlabeled data to train high-quality classification models. The choice of kernel parameters in the kernel function determines the mapping between the input space and the feature space and is crucial to the performance of the (SVM)-V-3. Kernel path algorithms have been widely recognized as one of the most efficient tools to trace the solutions with respect to a kernel parameter. However, existing kernel path algorithms are limited to convex problems, while (SVM)-V-3 is nonconvex problem. To address this challenging problem, in this article, we first propose a kernel path algorithm of (SVM)-V-3 ((KPSVM)-V-3), which can track the solutions of the nonconvex (SVM)-V-3 with respect to a kernel parameter. Specifically, we estimate the position of the breakpoint by monitoring the change of the sample sets. In addition, we also use an incremental and decremental learning algorithm to deal with the Karush-Khun-Tucker violating samples in the process of tracking the solutions. More importantly, we prove the finite convergence of our (KPSVM)-V-3 algorithm. Experimental results on various benchmark datasets not only validate the effectiveness of our (KPSVM)-V-3 algorithm but also show the advantage of choosing the optimal kernel parameters.