A closed form recursive solution for Maximum Correntropy training

This paper presents a closed form recursive solution for training adaptive filters using the Maximum Correntropy Criterion (MCC). Correntropy has been recently proposed as a robust similarity measure between two random variables or signals, when the pdfs involved are heavy tailed and non-Gaussian. Maximizing the cross-correntropy between the output of an adaptive filter and the desired response leads to the Maximum Correntropy Criterion for adaptive systems training. We show that a closed form, recursive solution of the filter weights using this criterion yields a simple weighted least squares like formulation. Our simulations show that training the filter weights using this recursive solution is much faster than gradient based training, and more accurate than the RLS algorithm in cases where the error pdf is non-Gaussian and heavy tailed.