Sigmoid function

Defined as:

s (x) = σ (x) = \frac{1}{1 + \exp (- x)} = \frac{\exp (x)}{1 + \exp (x)}

When used as an activation function, it is used in the output layer of a binary classification model as the output values will be between 0 and 1, and can be interpreted as probability.

Such that:

\forall x, 0 < s (x) < 1

lim_{x \to - \infty} s (x) = 0

lim_{x \to \infty} s (x) = 1

s (0) = 0.5

left=-10; right=10;
top=1; bottom=0;
---
y = \frac{1}{1+e^{-x}}

def s(x):
	return 1/(1 + np.exp(-x))