For this question from last years Mock exam, why is the first answer correct? I was thinking that unless the point is a support vector, the margin wouldn't change. Many thanks.
Hi Olivier,
the points within the margin as well as the points on the wrong side of the decision boundary impact the decision boundary itself. Therefore, if any of them is removed, the decision boundary will change. We can thus consider them support vectors.
Jan
Hi, sorry it isn't very intuitive to me, I don't get why this for example isn't a working counter example to what you wrote ?
(I mean, in this case, how deleting the pointed circle is going to change the boundary ?)
Hi Shayan,
the slack variables allow the SVM to tolerate some misclassifications, but during the optimization the SVM will still try to find the best trade-off between maximizing the margin and limiting the misclassifications, this is what the formula tells it to do. In your example with one circle on the right, the decision boundary probably would not look like you drew it, but it would rather be slightly rotated and/or shifted. After removing that misclassified point on the right, it would look like you drew it. So the bottomline is that the points within the margin and the misclassified points still affect how the decision boundary looks like.
Jan
Ok I got it. Thank you very much
