# Why goal of PLA can ignore the norm of normal vector

Define hyperplane $$w*x+b=0$$, the goal of PLA(Perceptron Learning Algorithm) is minimizing the distance of misclassified points to the decision boundary, i.e. $$-\frac{1}{||w||}\sum_{i\in M} y_i(w*x_i + b)$$ But actual algorithm is $$\min_{w,b} -\sum_{i\in M} y_i(w*x_i + b)$$