0
$\begingroup$

Suppose you are given $6$ one-dimensional points: $3$ with negative labels $x_1 = −1$, $x_2 = 0$, $x_3 = 1$ and $3$ with positive labels $x_4 = −3$, $x_5 = −2$, $x_6 = 3$. In this question, we first compare the performance of linear classifier with or without kernel. Then we solve for the maximum margin classifier using SVM.

Consider a linear classifier of form $f(x) = sign(w_1x+w_0)$. Write down the optimal value of $w$ and its classification accuracy on the above 6 points. There might be more than one optimal solution, writing down one of them is enough.

My attempt:
I understand that the data isn't linearly separable and that there will be some error, but I don't get how to get the optimal value of $w$. Do I minimize $f(x)$? But how do I take the derivative of $f(x)$? Any guidance would be appreciated, I'm a little lost.

$\endgroup$

1 Answer 1

0
$\begingroup$

The best that we can do is to classify $5$ points correctly and sacrifice one point.

We want to classify $-1,0,1$ as negative and $-3,-2$ as positivie. (we have to sacrifice $3$).

The boundary with maximum margin would be in the middle of $-2$ and $-1$. That is $-\frac32$.

$$sign(-(2x+3))=sign(-2x-3).$$

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

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