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The minimum error entropy (MEE) criterion in information theoretic learning is an efficient way to deal with non-Gaussian signal processing. And the minimum dispersion (MD) criterion has been widely applied in stable signal processing. In this letter, we show that there exists an equivalence between the MD criterion and the MEE criterion where symmetric α-stable (SαS) random variables are considered as the errors of the adaptive signal processing. As an application, we propose an algorithm with the MEE criterion for the time delay estimation (TDE) problem which was solved by the MD criterion. [ABSTRACT FROM AUTHOR]