SELF-ORGANIZATION OF A ONE-DIMENSIONAL KOHONEN NETWORK WITH QUANTIZEDWEIGHTS AND INPUTS

If a self-organizing neural network has to be implemented on a digital (or mixed analog and digital) circuit realization, with on-chip learn ing, all the input signals and the weight values halle to be quantized . It is therefore crucial to study whether this quantization does not annihilate the self-organization property of the weights. This paper p rovides necessary and sufficient conditions on the parameters of a one -dimensional network, which ensure the organization of the weights for any one-dimensional input probability distribution. These results are rigorously proved using the Markovian formulation of Kohonen's algori thm.