Asymmetric kernel-based robust classification by ADMM

Correntropy is a locally second-order statistical measure in kernel space. The different kernel functions induce different correntropy with different properties. In this work, we propose an asymmetric mixture kernel and the corresponding correntropy. Then, we propose a new loss function (called RCH-loss) that is induced by the correntropy with the reproducing asymmetric kernel. Some important properties of the proposed kernel and RCH-loss are demonstrated such as non-convexity, boundedness, asymmetry and asymptotic approximation. Moreover, the proposed RCH-loss satisfies Bayes optimal decision rule. With the RCH-loss function, a new robust classification framework is built to handle robust classification. Theoretically, we prove the generalization bound of the proposed model based on the Rademacher complexity. Following that, DC (difference of convex functions) programming algorithm (DCA) is developed to solve the problem iteratively, where ADMM (alternating direction method of multipliers) is used to solve the subproblem at each iteration. Moreover, we analyze the computation complexity of the algorithm and the sensitivity of parameters. Numerical experimentations are carried out on various datasets including benchmark data sets and artificial data sets with different noise levels. The experimental results display the feasibility and effectiveness of the proposed methods.