On Generalization Error of Self-Organizing Map

Self-organizing map is usually used for estimation of a low dimensional manifold in a high dimensional space. The main purpose of applying it is to extract the hidden structure from samples, hence it has not been clarified how accurate the estimation of the low dimensional manifold is. In this paper, in order to study the accuracy of the statistial estimation using the self-organizing map, we define the generalization error, and show its behavior experimentally. Based on experiments, it is shown that the learning curve of the self-organizing map is determined by the order that are smaller than dimensions of parameter. We consider that the topology of self-organizing map contributed to abatement of the order.