In a SOM how does the neighbour distance work?
1- If two nodes are close in the map and their distance is small then they have a similar color, is that right?
2- If two nodes are close in the map but their distance is big then they have a different grey color, is that right?
3- But, what if two nodes that are totally apart have similar grey color, are they close?
4- Another question. In this map link here in some hexagons there is no country and in anoyther hexagons there is more than a country what des it mean?
The grey color is commonly used to indicate the histogram. That is, the number of hits that landed on each neuron. In that case, the color of the node is not influenced by its codebook value, but by how much data was associated with that node.
If one node has more than one label, it just means that the data points associated with those labels most closely matched the codebook value for that node.
Kohonen goes into more detail on the countries map on p. 13 of MATLAB Implementations and Applications of the Self-Organizing Map available from http://docs.unigrafia.fi/publications/kohonen_teuvo/