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.