1
$\begingroup$

How to show that solution for the maximum margin hyperplane for hard-margin SVM is unchanged when w.x + b = (+/-) 1 is replaced by arbitrary constant $\gamma$?

In the derivation for the SVM, we generally assume that the margin boundaries are given by w.x + b = +1 and w.x+b = −1.

Can we show that if the +1 and -1 on the right-hand side were replaced by some arbitrary constants +$\gamma$ and −$\gamma$ where $\gamma$ > 0, the solution for the maximum margin hyperplane will remain unchanged?

$\endgroup$
1
  • $\begingroup$ Here's a hint - Let $S_\gamma = \left\{(w_\gamma, b_\gamma)\right\}$ be the solution set when solving with a given $\gamma > 0$. Prove that $S_\gamma = \gamma S_1$ by contradiction. $\endgroup$
    – MotiNK
    Commented Oct 10, 2021 at 7:08

0

Your Answer

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

Browse other questions tagged or ask your own question.