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.

[1]  Deniz Erdoğmuş.  INFORMATION THEORETIC LEARNING: RENYI'S ENTROPY AND ITS APPLICATIONS TO ADAPTIVE SYSTEM TRAINING , 2002 .

[2]  T. Ajdler,et al.  The Plenacoustic Function and Its Sampling , 2006, IEEE Transactions on Signal Processing.

[3]  Allan Kardec Barros,et al.  Using non-linear even functions for error minimization in adaptive filters , 2006, Neurocomputing.

[4]  Weifeng Liu,et al.  Correntropy: Properties and Applications in Non-Gaussian Signal Processing , 2007, IEEE Transactions on Signal Processing.

[5]  Deniz Erdogmus,et al.  Generalized information potential criterion for adaptive system training , 2002, IEEE Trans. Neural Networks.

[6]  J. Príncipe,et al.  The Correntropy Mace Filter for Image Recognition , 2006, 2006 16th IEEE Signal Processing Society Workshop on Machine Learning for Signal Processing.

[7]  José Carlos Príncipe,et al.  Nonlinear Component Analysis Based on Correntropy , 2006, The 2006 IEEE International Joint Conference on Neural Network Proceedings.

[8]  José Carlos Príncipe,et al.  Correntropy as a Novel Measure for Nonlinearity Tests , 2006, The 2006 IEEE International Joint Conference on Neural Network Proceedings.

[9]  J. Príncipe,et al.  A family of minimum renyi's error entropy algorithm for information processing , 2007 .

[10]  Bernard Widrow,et al.  The least mean fourth (LMF) adaptive algorithm and its family , 1984, IEEE Trans. Inf. Theory.

[11]  Weifeng Liu,et al.  A unifying criterion for instantaneous blind source separation based on correntropy , 2007, Signal Process..

[12]  José Carlos Príncipe,et al.  Generalized correlation function: definition, properties, and application to blind equalization , 2006, IEEE Transactions on Signal Processing.

[13]  José Carlos Príncipe,et al.  Correntropy based Granger causality , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.