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August  2020, 19(8): 4159-4177. doi: 10.3934/cpaa.2020186

## Kernel-based maximum correntropy criterion with gradient descent method

 School of Mathematics and Statistics, Wuhan University, Wuhan, China

Received  September 2019 Revised  December 2019 Published  May 2020

Fund Project: The author is supported by NSFC grant 11671307 and 11571078

In this paper, we study the convergence of the gradient descent method for the maximum correntropy criterion (MCC) associated with reproducing kernel Hilbert spaces (RKHSs). MCC is widely used in many real-world applications because of its robustness and ability to deal with non-Gaussian impulse noises. In the regression context, we show that the gradient descent iterates of MCC can approximate the target function and derive the capacity-dependent convergence rate by taking a suitable iteration number. Our result can nearly match the optimal convergence rate stated in the previous work, and in which we can see that the scaling parameter is crucial to MCC's approximation ability and robustness property. The novelty of our work lies in a sharp estimate for the norms of the gradient descent iterates and the projection operation on the last iterate.

Citation: Ting Hu. Kernel-based maximum correntropy criterion with gradient descent method. Communications on Pure & Applied Analysis, 2020, 19 (8) : 4159-4177. doi: 10.3934/cpaa.2020186
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