I have a distance measure going from 0 to infitiny, where 0 indicates closeness.
I need to perform a transformation in order that the distances sum up to 1. Therefore, softmax seems appropriate, especially that the gap between the values is not constant but increase with the distance, so 1 to 2 is much closer than 9 to 10.
My issue is that I want the opposite to a softmax transformation.
Imagine the following vector x = c(0, 0, 0, 1, 1, 2, 5, 5, 10)
If I apply a softmax transformation (using R)
softmax = round( exp(x) / sum(exp(x)), 2)
I get
0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.01 0.99
But I want the opposite of that, I want the 0 being closest to 1 and so on.
How could I do that?
