On quantization error of self-organizing map network

In this paper, we analyze how neighborhood size and number of weights in the self-organizing map (SOM) effect quantization error. A sequence of i.i.d. one-dimensional random variable with uniform distribution is considered as input of the SOM. First obtained is the linear equation that an equilibrium state of the SOM satisfies with any neighborhood size and number of weights. Then it is shown that the SOM converges to the unique minimum point of quantization error if and only if the neighborhood size is one, the smallest. If the neighborhood size increases with the increasing number of weights at the same ratio, the asymptotic quantization error does not converge to zero and the asymptotic distribution of weights differs from the distribution of input samples. This suggests that in order to achieve a small quantization error and good approximation of input distribution, a small neighborhood size must be used. Weight distributions in numerical evaluation confirm the result. (C) 2000 Elsevier Science B.V. All rights reserved.