Using Correntropy as a cost function in linear adaptive filters

Correntropy has been recently defined as a localised similarity measure between two random variables, exploiting higher order moments of the data. This paper presents the use of correntropy as a cost function for minimizing the error between the desired signal and the output of an adaptive filter, in order to train the filter weights.We have shown that this cost function has the computational simplicity of the popular LMS algorithm, along with the robustness that is obtained by using higher order moments for error minimization. We apply this technique for system identification and noise cancellation configurations. The results demonstrate the advantages of the proposed cost function as compared to LMS algorithm, and the recently proposed minimum error entropy (MEE) cost function.