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Recently, the minimum error entropy (MEE) criterion has been used as an information theoretic alternative to traditional mean-square error criterion in supervised learning systems. MEE yields nonquadratic, nonconvex performance surface even for adaptive linear neuron (ADALINE) training, which complicates the theoretical analysis of the method. In this paper, we develop a unified approach for mean-square convergence analysis for ADALINE training under MEE criterion. The weight update equation is formulated in the form of block-data. Based on a block version of energy conservation relation, and under several assumptions, we carry out the mean-square convergence analysis of this class of adaptation algorithm, including mean-square stability, mean-square evolution (transient behavior) and the mean-square steady-state performance. Simulation experimental results agree with the theoretical predictions very well.