An equivalence between two error criteria (Corresp.)

Two different criteria used in supervised learning detectors are shown to be equivalent. One criterion is of the "least mean-square error" form, and the other is of the "maximum signal-to-noise ratio" type. The minimization (or maximization) of these two criteria yields the same weight matrices when the decision functions are of quadratic form. The probability distributions of signal and noise are assumed to be unknown to the detectors.