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In Kohonen's SOM algorithm, the equation to find the collaboration is:

$$ \mathit{Damp}(i,j) = \exp\left(-\frac{\mathit{LDist}(i,j)^2}{2\sigma^2}\right) $$

I know that LDist is the lattice distance and $\sigma$ is the standard deviation. I am just wondering why they are squared? Can anyone help me to visualize the equation or explain to me what is going on in the above equation?

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  • $\begingroup$ Are you familiar with the normal distribution? $\endgroup$ – Yuval Filmus Mar 25 '20 at 19:22
  • $\begingroup$ Yes. I am familiar with normal distribution and I know that the above equation is related to that. I just want a clear explanation why the two terms (sigma and distance) are squared in the equation as I could not find one that explains this phenomenon clearly. $\endgroup$ – Tahseen Adit Mar 25 '20 at 20:23
  • $\begingroup$ The distance function is to some extent an arbitrary choice; there are others you could use. The one you describe is known as Gaussian kernel, and is popular in machine learning. $\endgroup$ – Yuval Filmus Mar 25 '20 at 20:29

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