Hi.

I saw that the margin in the perceptron algorithm is defined as min{(w*x)/||x||}. (See rec6 theorem 6.1).

My question is: Why do we divide by the norm of x?

As I understand it, w*x is |w||x|cos(a) where "a" is the angle between w and x. so dividing this by ||w|| should give us the distance of x from the seperating hyperplane.

As I understand it, by this you have also decided the creteria in the "Margin Perceptron Algorithm" presented in rec6.

(I assume this is why we calculate there (w*x)/||w|| and compare it to (gamma)/2.

Thanks in advance.