A robust semi-supervised regressor with correntropy-induced manifold regularization and adaptive graph

For semi-supervised regression tasks, most existing methods ignore the impact of noise. However, the data inevitably contain noise. Therefore, this study proposes a novel correntropy-induced semi-supervised regression (CSSR) method that mitigates the adverse effects of noise. To implement the robustness of CSSR, a novel correntropy-induced manifold regularization (CMR) and a correntropy-induced adaptive graph (CAG) are designed. Specifically, CMR is inspired by the principles of correntropy and aims to learn a graph representation, whereas CAG inherits the robust characteristics of the correntropy metric and adaptively constructs an adjacency matrix. Finally, by incorporating CMR, CAG, and the correntropy-induced loss seamlessly, CSSR demonstrates the ability to deliver promising joint performance. The final solution of CSSR is achieved through an iterative process. Moreover, we validated the convergence of CSSR through a combination of theoretical analyses and empirical experiments. The experimental evaluation encompassed three synthetic, 15 benchmark, and two image datasets. The findings demonstrate that CSSR surpasses similar methods in the realm of semi-supervised regression tasks, demonstrating its effectiveness and robustness.