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The robustness problem of the classical proximal support vector machine for regression estimation (PSVR) when confronting with samples in the presence of outliers is addressed in this paper. Correntropy is a local similarity measure between two arbitrary variables and has been proven the insensitivity to noises and outliers. Based on the maximum correntropy criterion (MCC), a correntropy-based robust PSVR framework is proposed, named as RPSVR-MCC. The half-quadratic optimization method is employed to solve the resultant optimization, and an iterative algorithm is developed to solve RPSVR-MCC. In each iteration, the complex optimization can be converted to a linear system of equations which can be easily solved by the widely popular optimization techniques. The experimental results on synthetic datasets and real-world benchmark datasets demonstrate that the effectiveness of the proposed method. Moreover, the superiority of the proposed algorithm is more evident in noisy environment, especially in the presence of outliers.

Robust Proximal Support Vector Regression Based on Maximum Correntropy Criterion