Working with Self Organizing Maps - How do I interpret the results? - multidimensional-array

Question

I have this data set that I thought would be a good candidate for making a SOM.
So, I converted it to text thusly:
10
12 1 0 0
13 3 0 0
14 21 0 0
19 1983 15 0
24 5329 48 0
29 4543 50 0
34 3164 32 0
39 1668 22 1
44 459 4 0
49 17 0 0
I'm using Octave, so I transformed the data with these commands:
dataIn = fopen('data.txt','r');
n = fscanf(dataIn,'%d',1);
D = fscanf(dataIn,'%f'); %D is a 1 x n column matrix
D = D'; %Transpose the data D is now an n x 1 matrix
D = reshape(D, 4, []); % give D the shape of a 4 x n/4 matrix
D = D(2:4, :); % the dimensions to be used for the SOM will come from the bottom three rows
Now, I'm applying an SOM script to produce a map using D.
The script is here
and it's using findBMU defined as:
%finds best matching unit in SOM O
function [r c ] = findBMU( iv,O )
dist = zeros(size(O)); for i=1:3
dist(:,:,i) = O(:,:,i)-iv(i);
iv(i);
end
dist = sum(dist.^2,3);
[v r] = min(min(dist,[],2));
[v c] = min(min(dist,[],1));
In the end, it starts with a random map that looks like this:
and it becomes:
The thing is, I don't know what my SOM is saying. How do I read it?

Answer 1

Firstly, you should be aware that Octave provides at best an approximation to the SOM methodology. The main methodological advantage of the SOM is the potential transparent access of (all) the implied parameters, and those cannot be accessed in Octave any more.
Secondly, considering your data, it does not make much sense first to seriously destroy information by summarizing it then feeding a SOM with it. Basically you have four variables in your table shown above: age, total N, single N, twin N. What you have destroyed is the information about the region.
Such you put three distributions into the SOM. The only thing you could expect is clusters. Yet, the SOM is not built for building clusters. Instead, SOM is used for diagnostic and predictive modeling, in order to find the most accurate model and the most relevant variables. Note the term "best matching unit"!
In your example however you find just a distribution in the SOM. Basically, there is no interpretation, as there are neither variables nor is there a predictive/diagnostic purpose.
You could build a model, for instance, determining the similarity of distributions. Yet, for that you should use a goodness-of-fit test (non-parametric, Kolmogorof-Smirnov), not the SOM.