A novel recursive algorithm used to model hardware programmable neighborhood mechanism of self-organizing neural networks

In this paper we propose a novel recursive algorithm that models the neighborhood mechanism, which is commonly used in self-organizing neural networks (NNs). The neighborhood can be viewed as a map of connections between particular neurons in the NN. Its relevance relies on a strong reduction of the number of neurons that remain inactive during the learning process. Thus it substantially reduces the quantization error that occurs during the learning process. This mechanism is usually difficult to implement, especially if the NN is realized as a specialized chip or in Field Programmable Gate Arrays (FPGAs). The main challenge in this case is how to realize a proper, collision-free, multi-path data flow of activations signals, especially if the neighborhood range is large. The proposed recursive algorithm allows for a very efficient realization of such mechanism. One of major advantages is that different learning algorithms and topologies of the NN are easily realized in one simple function. An additional feature is that the proposed solution accurately models hardware implementations of the neighborhood mechanism.