Why learning rate is change in SOM with Iterations

Question

Normally learning rate is a value that we decide in the begining and normally it doesn't change with no of iterations. But in SOM learning rate is change with the iteration, what is the idea behind that?

As I understand learning rate should be decrease with the number of iterations. why is that?

Answer 1

Reason is quite simple. SOMs are ill-designed in terms of mathematical models, and one needs to decrease learning rate in order to ensure convergence. In other words, if you do not change this value, learning procedure might not stop at all. This issue is somehow addressed by more mathematical models called "Principal Curves" and "Principal Manifolds", which are much less popular but introduce valid mathematical approach for learning SOM-like representations.