### alphas in SVMs

Hi,

I was reading over the conditions for alpha in SVM. I understand if it is correctly classified alpha is 0, if it is on the margin is its [0,1] and if it is misclassified then alpha is 1. I was thus wondering if alpha is 1 how do we know if the vector is a misclassified vector or a support vector. I also don't quite understand the subtlety between the bound and essential support vector.

TAs please correct me if I'm wrong.

The way I understand it is:
When alpha is 1 three things are possible:

1. The point is on the correct side but just on the margin.
2. The point is on the correct side but inside the margin.
3. The point is on the wrong side.

For these three examples, it does not matter whether the point is correctly classified or not. What the alpha is indicating is that all of those points could be better classified and thus should be taken into account to move the hyperplane that is separating both groups.

Recall that there are many hyperplanes that can separate groups of point (for example, shift the hyperplane by 1 degree). The hyperplane we are interested in is the hyperplane that maximizes the distance between the points. The idea behind this is to find a robust classifier and the more spacing to the left and right the more separated the classes are and the more likely the classifier is to classify correctly new points.

The reason why alpha is one for the three cases is that we do not want to have points on the margin or inside the margin and these points can help find the hyperplane with maximal spacing.

Difference between bound and essential support-vector.

1. [essential] The point is on the correct side but just on the margin.
2. [bound] The point is on the correct side but inside the margin.
3. [bound] The point is on the wrong side.

I hope this helps...

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