Gabriel networks: self-organizing neural networks for adaptive vector quantization

A self-organizing neural network model that resembles Kohonen´s feature map model is presented in this paper. Unlike conventional feature maps which require static neighborhood relations to be defined a priori, our model is characterized by its use of dynamic neighborhood relations which change as learning proceeds. In particular, the neighborhood relations between neurons in a feature map are determined by an underlying Gabriel graph, which represents two neurons as neighbors if and only if the smallest hypersphere enclosing the two corresponding weight vectors encloses no other weight vectors. We show empirically that this network model works consistently well in the vector quantization tasks tested. More importantly, our model can adapt to data manifolds which may not be handled well using conventional self-organizing feature maps