We propose a new formulation for the optimal separation problems. This robust formulation is based on finding the minimum volume ellipsoid covering the points belong to the class. Idea is to separate by ellipsoids in the input space without mapping data to a high dimensional feature space unlike Support Vector Machines. Thus the distance order in the input space is preserved. Hop-field Neural Network is described for solving the optimization problem. The benchmark Iris data is given to evaluate the formulation. © Springer-Verlag Berlin Heidelberg 2006.