# The Sigmoid

The

elsewhere).

\[\begin{aligned}

\sigma(z) &= \frac{1}{1+e^{-z}}\\

\sigma(0) &= \frac{1}{2}\\

\lim_{z \to \infty} \sigma(z) &= 1\\

\lim_{z \to -\infty} \sigma(z) &= 0\\

\end{aligned}\]

*sigmoid*is a function with an s shape that's used in*logistic regression*(andelsewhere).

#### The Equation

\sigma(z) &= \frac{1}{1+e^{-z}}\\

\sigma(0) &= \frac{1}{2}\\

\lim_{z \to \infty} \sigma(z) &= 1\\

\lim_{z \to -\infty} \sigma(z) &= 0\\

\end{aligned}\]

#### Applying to a Linear Regression Classifier

- Apply the Sigmoid to z multiplied by a weight learned by the classifier.
- Classify using round(Sigmoid(z))