# Clustered Regions by Each Neuron in Self Organizing Map (SOM)

I was given a question about SOM.

There is a SOM which have 4x4 neurons and each neuron's x1 and x2 values (coordinates) given. Also neighborhood function and weight update rule given. How can i find and show the regions which are clustered by each neuron?

In other words, for an input $$v$$ and a set of neurons $$N$$ (in your case $$|N| = 16$$ ) the cluster is:
$$\text{Cluster}(v)=\arg \min_{i\in A}(||w_i-v||_2)$$