5 ) ( x w ⋅ denotes the dot product of the weight vector n R w ∈ and a given instance The well-known perceptron algorithm, as shown in Figure 1, belongs to online learning of linear classifiers, where the learning algorithm represents its t -th hyposthesis by a weight vector received at trial t .
the perceptron algorithm updates the hypothesis by adding a scalar multiple of the instance, as shown in Equation 1 of Figure 1, when there is an error.