Perceptrons and Classification

Notes about perceptrons and sigmoid neurons

Perceptron

A Perceptron behaves like a classifier. Suppose we have an input $\mathbf{x}$ which we want to classify as either belonging to a category (labeled as 1) or another category (labeled as 0).

Its inner formula is given by

$$\begin{equation} score=\sum w_{i}x_{i}+b=\mathbf{w^{T}\cdot x}+b\label{eq:Perceptron} \end{equation}$$

Given an input $\mathbf{x}$ , for example $\mathbf{x}=\left(x_{1},x_{2}\right)$ , the Perceptron calculates a score: when $\mathbf{w^{T}\cdot x}+b\geq0$ the input belongs to the category labeled as 1, if $\mathbf{w^{T}\cdot x}+b<0$ the input belongs to a category labeled as 0.