For a mapping algorithm I'm working on, I'm trying out the effect of sigmoid weightings.
Right now I'm using $$y = \frac{1}{1+x^n}$$ where n is the steepness of the sigmoid function.
This graph shows values of x between 0 and 256 and the following values of n: 2, 4 and 32. X values have been scaled to a range of -10 to 10. Also plotted is equivalent $y=x$ line.
The effect I would like to achieve is a function that lies somewhere between the $y=x$ and the $n=2$ functions. When I set n to be between 1 and 2 however, the location of the asymptotes changes.
How can I use values of n such that $1 < n < 2$ and keep the asymptotes at 0 and 1?
Best Answer
You can also use $y = \frac{1}{1+ax^n}$ to give yourself another parameter to play with. It will still go from 0 to 1 as x goes from -infinity to infinity, but you can change how quickly it gets close.