Modeling Kohonen networks by attributed parallel array systems

摘要

The concept of n-dimensional attributed parallel array systems is introduced and shown to be a useful tool for the formal description of the static as well as the dynamic characteristics of neural networks. Because of the underlying grid structure. Kohonen's model of self-organizing feature maps is especially well suited for being represented by n-dimensional attributed parallel array systems. Using our formal description model we prove that Kohonen's global algorithm for the adaption of the weights of the neurons in a fully connected network can be simulated in a network with locally bounded connections, which can be represented by an n- dimensional attributed parallel array system containing only parallel array productions with a bounded neighborhood. These results show that our model of n-dimensional attributed parallel array systems can be used as a specification language for various models of neural networks and as a formal tool for proving specific characteristic features of these networks.