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I just learned the basics of SVM, and I have 2 questions about the solution for the non-separable case:

  1. In the separable case, the distance of all the support vectors from the hyperplane is the same, and they determine the margin. Now, in the non-separable case, is it possible that no support vector falls on the edge of the margin?

  2. In the separable case the meaning of $\frac{1}{\vert \vert \beta \vert \vert}$ was the distance of the support vectors from the hyperplane (where the hyperplane is defined by $\beta ^T x+\beta _0 = 0$). What is the exact meaning of $\frac{1}{\vert \vert \beta \vert \vert}$ in the non-separable case?

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    $\begingroup$ I would suggest you to look at literature that explaining SVN from hinge loss persopective $\endgroup$
    – Haitao Du
    Jan 16, 2017 at 17:26

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