Influence of radius in neighborhood function of SOM Reference document: here
In section 3.3 of the referenced document, discussion regarding neighborhood function in SOM is provided. What I am not being able to understand is what influence radius has on the neighborhood function since I do not see it being used in the actual function formula. In the first screenshot below, different neighborhood functions are shown, and in the second screenshot, the images of different neighborhood functions with different radius values are shown. Could anyone please help me understand how they are related?


Looking at how the step/bubble function is formulated and drawn, my guess is that $\sigma$(k) is the radius. Is my guess correct?

Yes, $(k)$ is the radius at step $k$.
I'd say this is the reference that will give the most assistance. The article above provides a good summary of Kohonen's work (and extends it to a new dataset); more details are here.
Kohonen, T. MATLAB Implementations and Applications of the Self-Organizing Map. Unigrafia Oy, Helsinki, Finland, 2014.
See p. 48 for a different representation of the four neighbourhood functions:


*

*case ’bubble’, H = (Ud<=radius(t));

*case ’gaussian’, H = exp(-Ud/(2*radius(t)));

*case ’cutgauss’, H = exp(-Ud/(2radius(t))) . (Ud<=radius(t));

*case ’ep’, H = (1-Ud/radius(t)) .* (Ud<=radius(t));


