can a perceptron be used for regression? In machine learning, the perceptron is an algorithm for supervised learning of binary classifiers. A binary classifier is a function which can decide whether or not an input, represented by a vector of numbers, belongs to some specific class.

on wiki page, the problems section includes regression without more explanation.



can a perceptron used for regression?
The deep feedforward neural networks used for regression are nothing but multilayer perceptron architectures.



Originally, perceptrons were used as binary classifiers i.e to classify binary labels ( 0 or 1 ). But, if no non-linear activation function is applied to the dot product of the features and weights, then it is simply a linear regressor.

If the linear function is $f(x) = x$ and $N$ is the number of features then,

$\Large y = \sum_{i=0}^N x_i w_i$

or using vector notation,

$\Large y = \vec{x}.\vec{w} ...(1)$

For multiple regression, we use the below equation with mean-squared error loss function to optimize the $\beta$ parameters,

$\Large y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 ... \beta_n X_n$

Let , 

$\Large 
\vec{W} = [ \beta_1 \ \beta_2 \ \beta_3 \ ... \ \beta_n ] \\
\vec{X} = [ X_1 \ X_2 \ X_3 \ ... \ X_n ]
$ 

Where $N$ is the number of features, $\vec{X}$ is the feature vector and $\vec{W}$ is the weights vector. Then, 

$\Large y = \beta_0 + \beta_1 X_1 + \beta_2 X_2 ... \beta_n X_n = \beta_0 + \vec{W}.\vec{X} ...(2) $

Where, $\beta_0$ is also called as the bias coefficient in Artificial Neural Networks. You can relate equations 1 and 2 and understand the concept.


  Hence, $\Large y = \vec{x}.\vec{w} + bias $ generally represents a hyperplane
  which is used in linear regression.