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Softmax-network and S-Map-models for density-generating topographic mappings

We propose a neural network model for density-generating topographic mappings. The model consists of two parts: the Softmax-network, and the S-Map. The Softmax-network implements the softmax function, so that each neuron's output is a softmax of the weighted sum of the input to that neuron and to its neighbors. The S-Map, based on the Softmax-network, utilises a Hebbian-like learning scheme for the input-to-neuron weights to minimize the negative log likelihood error function; simulations show that a simplified version of the S-Map with fully Hebbian learning yields qualitatively similar results. The model is related both to the generative topographic mapping (GTM) and the self-organizing map (SOM).