Editing Perceptron (section)

=== Steps===
{{Ordered list 
| Initialize the weights. Weights may be initialized to 0 or to a small random value. In the example below, we use 0.
| For each example {{mvar|j}} in our training set {{mvar|D}}, perform the following steps over the input <math>\mathbf{x}_j </math> and desired output <math>d_j </math>:
{{Ordered list |list_style_type=lower-alpha
|Calculate the actual output:
:<math>\begin{align}
y_j(t) &= f[\mathbf{w}(t)\cdot\mathbf{x}_j] \\
&= f[w_0(t)x_{j,0} + w_1(t)x_{j,1} + w_2(t)x_{j,2} + \dotsb + w_n(t)x_{j,n}]
\end{align}</math>
|Update the weights:
:<math>w_i(t+1) = w_i(t) \; \boldsymbol{+} \; r\cdot(d_j - y_j(t)) x_{j,i} </math>, for all features <math>0 \leq i \leq n</math>, <math>r</math> is the [[learning rate]].
}}
| For [[offline learning]], the second step may be repeated until the iteration error <math>\frac{1}{s} \sum_{j=1}^s |d_j - y_j(t)| </math> is less than a user-specified error threshold <math>\gamma </math>, or a predetermined number of iterations have been completed, where ''s'' is again the size of the sample set. 
}}
The algorithm updates the weights after every training sample in step 2b.