Robust semi-supervised support vector machines with Laplace kernel-induced correntropy loss functions

The insufficiency and contamination of supervision information are the main factors affecting the performance of support vector machines (SVMs) in real-world applications. To address this issue, novel correntropy loss functions and Laplacian SVM (LapSVM) are utilized for robust semi-supervised classification. It is known that correntropy loss functions have been used in robust learning and achieved promising results. However, the potential for more diverse priors has not been extensively explored. In this paper, a correntropy loss function induced from Laplace kernel function, called LK-loss, is applied to LapSVM for the construction of robust semi-supervised classifier. Properties of LK-loss are demonstrated including robustness, symmetry, boundedness, Fisher consistency and asymptotic approximation behaviors. Moreover, the asymmetric version of LK-loss is introduced to further improve the performance. Concave-convex procedure (CCCP) technique is used to handle the non-convexity of Laplace kernel-induced correntropy loss functions iteratively. Experimental results show that in most cases, the proposed methods have better generalization performance than the comparing ones, which demonstrate the feasibility and effectiveness of the proposed semi-supervised classification framework.