A robust classification framework with mixture correntropy

In this paper, we define a mixture correntropy criterion where two different kernel functions are combined. We induce a more general nonconvex robust loss function by this heterogenous mixture correntropy. The proposed mixture correntropy is also a local similarity measure that not only improves the limitations of correntropy under a single kernel, but also handles heterogeneous data more flexibly and stably. The induced loss amalgamates the superiors of the state-of-the-art robust loss functions and is more effective. What’s more, we verify the Fisher consistency of the induced loss and analyze the robustness from the view point of robust estimation. With this induced loss, we propose a robust support vector machine (SVM) framework and adopt half quadratic optimization algorithm to handle the nonconvexity and further improve convergent rate. Furthermore, we generate heterogenous structured artificial datasets and impose different levels of label noise on benchmark datasets. Implements on these two types of datasets show the superior flexibility and effectiveness of the proposed framework.