The neighborhood function Θ(u, v, s) (also called "function of lateral interaction") depends on the grid-distance between the BMU (neuron "u") and neuron "v". In the simplest form, it is 1 for all neurons close enough to BMU and 0 for others, but the Gaussian and mexican-hat functions are common choices, too. Regardless of the functional form, the neighborhood function shrinks with time. At the beginning when the neighborhood is broad, the self-organizing takes place on the global scale. When the neighborhood has shrunk to just a couple of neurons, the weights are converging to local estimates. In some implementations, the learning coefficient α and the neighborhood function Θ decrease steadily with increasing s, in others (in particular those where t scans the training data set) they decrease in step-wise fashion, once every T steps.