Learning robust discriminant features via correntropy-induced functions: from supervised to unsupervised learning

The correntropy-induced (C-) loss function has been successfully employed in many classification and clustering problems due to its good properties such as smoothness and insensitivity to noise and outliers. In this article, we embed the C-loss function into linear discriminant analysis and propose a novel discriminant analysis model that can suppress outliers and noise. The proposed model is a nonlinear optimization problem that belongs to a ratio minimization problem. We use Dinkelbach’s extended algorithm involving parametric optimization subproblems to solve the proposed ratio minimization problem. The half-quadratic optimization algorithm is employed to tackle parametric optimization subproblems. In addition, the proposed model is also modified to suit the clustering problem by introducing additional optimization variables, which gives a robust clustering model from the discriminant criterion. A series of experiments on many datasets are performed, and experimental results demonstrate that the proposed model is superior to some existing models in the presence of outliers and noise.