  The minimum error entropy (MEE) criterion has been verified as a powerful
approach for non-Gaussian signal processing and robust machine learning.
However, the implementation of MEE on robust classification is rather a vacancy
in the literature. The original MEE only focuses on minimizing the Renyi's
quadratic entropy of the error probability distribution function (PDF), which
could cause failure in noisy classification tasks. To this end, we analyze the
optimal error distribution in the presence of outliers for those classifiers
with continuous errors, and introduce a simple codebook to restrict MEE so that
it drives the error PDF towards the desired case. Half-quadratic based
optimization and convergence analysis of the new learning criterion, called
restricted MEE (RMEE), are provided. Experimental results with logistic
regression and extreme learning machine are presented to verify the desirable
robustness of RMEE.
