In this paper, we discuss an important problem of the selection of the neighborhood radius in the learning schemes of the Winner Takes Most Kohonen neural network. The optimization of this parameter is essential in case of hardware realization of the network given that the lower values of the radius can result in significant reduction of both the power dissipation and the chip area, even by 40-60% that is important in application of such networks in low power devices. The simulation studies reveal that using large initial values of the neighborhood radius usually is not the most optimal. For a wide range of the training parameters some optimal values, usually small, of the neighborhood radius may be indicated that allow for the minimization of the quantization error.