I'm a little confused about how scaling w^Tx + b = 0 by 1/||w|| results in an equation in the normal form. Can anyone explain this to me? Thank you so much!
motoole2
We didn't quite get to this in lecture yet; we'll be finishing up image classification next time.
To answer your question though, note that the vector $[cos(\theta), sin(\theta)]$ always has unit norm for all values $\theta$. Hence it is in normal form. As a result, we can put our expression $w\cdot x + b = 0$ in normal form by making sure $w$ also has unit norm, i.e., by rescaling the entire expression by $1 / |w|$.
I'm a little confused about how scaling w^Tx + b = 0 by 1/||w|| results in an equation in the normal form. Can anyone explain this to me? Thank you so much!
We didn't quite get to this in lecture yet; we'll be finishing up image classification next time.
To answer your question though, note that the vector $[cos(\theta), sin(\theta)]$ always has unit norm for all values $\theta$. Hence it is in normal form. As a result, we can put our expression $w\cdot x + b = 0$ in normal form by making sure $w$ also has unit norm, i.e., by rescaling the entire expression by $1 / |w|$.