Logistic Function

The logistic function which is defined in $[0,1]$ looks like this

L(x)=\frac{1}{1+e^{-F(x)}}

f(x)=\frac{1}{1+e^{-x}}

In a Classification task the function $F(x)$ is also called the Decision Boundary.

One interesting property of the logistic function is its derivative:

g(x)(1-g(x))

This derivative is useful as we need it to compute the Gradient Descent update rules.

By adding a coefficient $a$ to the $x$ we can rearange probabilites of class membership.