the Kohonen algorithm for SOMs says how to adjust the input weights of the best responsive neuron and its neighbours for each training example.
When it comes to plotting I am left with (number of map neurons)-many vectors of feature space Dimension. How is this reduced to get the 2D-plots shown everywhere?
Kind regards!
The SOM is a non-supervised clustering algorithm. As such it represent similar samples, closer on the feature map (this is, similar samples will fire nodes that are closer together).
So lets assume you have 10000 samples with 10 features each, and a 2d-SOM of 20x20x10 (400 nodes with 10 features). After training you therefore clustered 10000 samples into 400 nodes. Further, you can try to identify similar regions on the SOM feature map through for example the U-Matrix (map representing the average distance between the node's weight vector and its closest neighbours), or eliminate non-useful nodes through the Hit-Map (map representing the number of times the node was chosen as the best matching unit - BMU for the training data).
So without any preprocessing you achieved a reduction of 25 times, and with some you may even achieve more.
EDIT: An for a more elaborated answer see Interpreting a Self Organizing Map as indicated by @lejlot
