Get hextop self-organizing map neuron connections

Question

How do I get a n-by-2 vector that contains the connections of the neurons in an SOM? For example, if I have a simple 2x2 hextop SOM, the connections vector should look like:

[ 1 2 1 3 1 4 ]

This vector indicates that the neuron 1 is connected to neuron 2, neuron 1 is connected to neuron 3, etc.

How can this connections vector be retrieved from any given SOM?

Answer 1

Assuming the SOM is defined with neighbourhood distance 1 (i.e., for each neuron, edges to all neurons within an Euclidian distance of 1), the default option for Matlabs hextop(...) command, you can create your connections vector as follows:

pos = hextop(2,2);

% Find neurons within a Euclidean distance of 1, for each neuron.

% option A: count edges only once
distMat = triu(dist(pos));
[I, J] = find(distMat > 0 & distMat <= 1);
connectionsVectorA = [I J]

% option B: count edges in both directions
distMat = dist(pos);
[I, J] = find(distMat > 0 & distMat <= 1);
connectionsVectorB = sortrows([I J])

% verify graphically
plotsom(pos)

The output from the above follows:

connectionsVectorA =

     1     2
     1     3
     2     3
     2     4
     3     4


connectionsVectorB =

     1     2
     1     3
     2     1
     2     3
     2     4
     3     1
     3     2
     3     4
     4     2
     4     3

If you have a SOM with a non-default neighbourhood distance (!= 1), say nDist, just replace the find(..) commands above with

... find(distMat > 0 & distMat <= nDist);