Correntropy-based metric for robust twin support vector machine.

• Propose a robust distance metric based on correntropy. • A robust twin SVM is built with the proposed metric. • The metric satisfies the conditions of distance metric. • Demonstrate important properties for the metric. • Experiments show the robustness of the proposed method. This work proposes a robust distance metric that is induced by correntropy based on Laplacian kernel. The proposed metric satisfies the properties that distance metric must have. Moreover, we demonstrate important properties of the proposed metric such as robustness, boundedness, non-convexity and approximation behaviors. The proposed metric includes and extends the traditional metrics such as L 0 -norm and L 1 -norm metrics. Following that we apply the proposed metric to twin support vector machine classification (TSVM), and then a new robust TSVM algorithm (called RCTSVM) is built to reduce the influence of noise and outliers. The proposed RCTSVM inherits the advantages of TSVM and improves the robustness. However, the non-convexity of the proposed model makes it difficult to optimize. A continuous optimization method is developed to solve the RCTSVM. The problem is converted into difference of convex (DC) programming, and the corresponding DC algorithm (DCA) converges linearly. Compared with the traditional algorithms, numerical experiments under different noise setting and evaluation criteria show that the proposed RCTSVM has robustness to noise and outliers in most cases, which demonstrates the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]