Is there a function that makes a sigmoid look linear ?? (ie how do you flatten a sigmoid) ??

Question

Is there a function that makes a sigmoid look linear ?? (ie how do you flatten a sigmoid) ??

Answer 1

There is an application to convert an AC current to DC.

Assume that f is a sigmoid function, then integration of

f^2 over one period gives a constant number which is considered as flattened sigmoid and is analogous with converting AC to DC.

Answer 2

Suppose that f(x)=S(x) is your equation for the sigmoidal curve, also known as an ogive, you are interested in. Then, just invert the function if you can. S^(-1)[f(x)] should be x, a linear function.



Examples of sigmoid functions:



1. hyperbolic tangent

2. logistic function

3. error function

4. arctangent function



It is fairly obvious how to compute the inverse for sigmoidal functions 1, 2 and 4. For the inverse error function, there are numerical techniques (see references).

Answer 3

Maybe thisis too obvious but, how about inverting the generating function? I.e.: if the sigmoid is f(x) = sin(x), then g(x) = arcsin(f(x)) = x is a linear function.



Hope thats what you´re looking for.