1
$\begingroup$

In a video lecture (MIT 6.034 Artificial Intelligence, Fall 2010 lecture 16)

It was mentioned that the dot product here is taking the projection of $\vec u$ onto $\vec w$ and it should be greater than some constant. $\vec w$ is the normal to the decision boundary

$\vec w.\vec u>c$

and to generalize it if $\vec w.\vec u+b>0$ positive sample negative otherwise

but as far as I remember length of the projection is

$\frac{|\vec w.\vec u|}{|\vec w|}$

but here a different equation is used

$\endgroup$
2
$\begingroup$

It is correct that $|\vec w \cdot \vec u|/|\vec w|$ is the length of the projection of $\vec u$ onto $\vec w$. If $\vec{w}$ is a unit vector, i.e. $|\vec{w}| = 1$, then this becomes simply $|\vec w \cdot \vec u|$. In general, if $\vec{w}$ is not a unit vector, then you are right to point out that $|\vec w \cdot \vec u|$ is not exactly the length of the projection of $\vec u$ onto $\vec w$, since it differs by a factor of $|\vec w|$. However, you could think of this factor as being absorbed into $c$ on the right side of the inequality $\vec w \cdot \vec u > c$, so in the end the discrepancy does not matter.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.