Learning rate schedules for self-organizing maps

Kohonen maps have been successfully applied for data reduction and density approximation. Unfortunately, the choice of the neighborhood function and the learning rate in the Kohonen model remains empirical. We present a new statistically motivated approach to determine the contribution of each data presentation during training on the final position of the units of the trained map. Experimental results show that employing the commonly used learning rates leads to unit locations which are overly influenced by the later presentations (i.e., last 20% of data points in the finite training set). Better learning rate schedules and neighborhood functions are men determined which allow more uniform contributions of the training data on the unit locations. These improved rates are shown to be a suitable generalization of the standard rates given by stochastic approximation theory for a self-organizing map of units.