پرسپترون

${\displaystyle \mathrm{\forall }i\in \{1,...,n\}:f(x_i)=y_i.}$

${\displaystyle w\cdot x=w_0{x}_0+\sum _{i=1}^m{w}_i{x}_i=b+\sum _{i=1}^m{w}_i{x}_i}$

${\displaystyle \mathrm{\forall }i\in \{1,...n\}:f(x^{(i)})=y^{(i)}}$

input: A training set ${\displaystyle D}$

initialize: ${\displaystyle w^{(1)}=(0,...,0)}$

 for t = 1,2 ,...
 if(${\displaystyle \mathrm{\exists }is.t{y}^{(i)}\times (w^{(t)}\cdot x^{(i)})\le 0}$
)
   ${\displaystyle w^{(t+1)}=w^{(t)}+y^{(i)}{x}^{(i)}}$

 else
   ${\displaystyle w^{(t+1)}=w^{(t)}}$

${\displaystyle \mathrm{\forall }i\in \{1,...,n\}\to y^{(i)}\times (w^{(T)}\cdot x^{(i)})>0.}$

${\displaystyle \mathrm{\forall }i\in \{1,...,n\}\to f(x^{(i)})=y^{(i)}>0.}$