Circular rows and columns follow a simple premise — the neighbourhood influence effect of training can now wrap around both row and column, allowing for circular, cylindrical and torodial geometries.

Think of it like this, a network with a single row wrapped around allows for a network to learn a circular topology. A nice, simple example of this is the Travelling Salesman Problem as you need one continuous, circular route to be determined. Below there is an example of a Kohonen network run over 350 iterations. The initial phase starts to spread the nodes out over the map, with the second phase making more localized adjustments:

It is worth noting that the Kohonen-based solver isn’t perfect, sometimes choosing interim junctions where there is no city, but it is an interesting, reasonably practical use of a different kind of Kohonen topology. Continue reading “Kohonen Neural Network Experimentations”