A Dynamical Implementation of Self-organizing Maps

The standard learning algorithm for self-organizing maps (SOM) involves the two steps of a search for the best matching neuron and of an update of its weight vectors in the neighborhood of this neuron. In the dynamical implementation discussed here, a competitive dynamics of laterally coupled neurons with diffusive interaction is used to find the best-matching neuron. The resulting neuronal excitation bubbles are used to drive a Hebbian learning algorithm that is similar to the one Kohonen uses. Convergence of the SOM is achieved here by relating time (or number of training steps) to the strength of the diffusive coupling. A standard application of the SOM is used to demonstrate the feasibility of the approach.