Decay Function Improvements

[BrandonGarciaWx]

• Changed names of decay functions to specify which should be used for learning rate and which should be used for sigma. This avoids confusion where a decay function meant for the learning rate could be used by users to decay sigma and thus potentially lead to overfitting.
• Replaced default sigma value with the hypotenuse of the SOM as this is a common starting sigma value that helps SOMs converge on global minimum. This avoids users picking small sigmas that erroneously converge on local quantization error minima.
• Replaced the asymptotic_decay function with the sigma_inverse_time_decay function. This new function always decays to a value of 1 to avoid overfitting. The asymptotic_decay function struggles to converge on solutions for sigma values greater than 3 due to the sigma at the end of the training being larger than 1 which results in less fine-scale tuning that usually occurs when the sigma value is near a value of 1.
• Updated test decay functions.
• Updated descriptions of decay functions and MiniSom class parameters.

These changes were previously discussed in #184

[JustGlowing]

hi @BrandonGarciaWx , thanks for raising this PR. I'll review it in the following days.

In the meanwhile, can you point out a reference to justify that the hypotenuse of the map is a good initial value for sigma?

[BrandonGarciaWx]

Thank you for the comments, I believe I have addressed them all. I also made some additional minor changes to some decay function descriptions and names.

My justification for the hypotenuse of the SOM being a good initial value for sigma comes from the following paper:
Gervais_etal_2016.pdf. Specifically, the sentence on page 2361 that reads

It is good practice to begin the training with a radius of influence equal to the diameter of the SOM to ensure that all nodes are updated and decrease the value with training time (Kohonen 2001).

I know the lead author personally and confirmed that "diameter" and "hypotenuse" mean the same thing in this context.

The citation for Kohonen (2001) is

Kohonen, 2001: Self-Organizing Maps. 3rd ed. Springer Series in Information Sciences, Vol. 30, Springer, 502 pp.

[BrandonGarciaWx]

In addition to removing the text about custom decay functions, I added a function for sigma to linearly decrease to one.

[JustGlowing]

In addition to removing the text about custom decay functions, I added a function for sigma to linearly decrease to one.

See my comment here: https://github.com/JustGlowing/minisom/pull/185/files#r1572485322

[BrandonGarciaWx]

Decay functions have been moved and function descriptions have been updated.

[JustGlowing]

Thanks for your contribution @BrandonGarciaWx !