Decreasing Neighborhood Revisited in Self-Organizing Maps

Abstract

Decreasing neighborhood has been identified as a necessary condition for self-organization to hold in the self-organizing map (SOM). In the SOM, each best matching unit (BMU) decreases its influence area as a function of time and this area is always radial. Here, we present a model in which the BMU does not reduce its neighborhood, but the rest of the neurons exclude some BMUs from affecting them. In this model, what decreases as a function of time is the number of BMUs that affect each neuron, not the neighborhood of the BMUs. Each neuron identifies, from the set of BMUs that influenced it during each epoch, the farthest one and becomes refractory to it for the rest of the process. This BMU exclusion is not equivalent to the original decreasing neighborhood scheme. Even though the decreasing neighborhood condition is not totally maintained, self-organization remains, as shown by several experiments.