Let $w$ be the decision boundary of a linear SVM trained on the dataset $D=\{(x_i, y_i)_{i=1}^N\}$. Suppose we apply a linear transformation A to examples $x_i$s and obtain a new dataset $D'=\{(z_i, y_i)_{i=1}^N\}$ where $z_i = Ax_i$. And let $w_2$ denote the decision boundary of the linear SVM trained on $D'$.

Can we say anything about the relationship between $w$ and $w_2$? Depending on the properties of $A$, would it be possible to cheaply obtain $w_2$ from $w$?

  • $\begingroup$ We're assuming $A$ is a unitary transformation matrix, right? $\endgroup$ Mar 29, 2014 at 3:20
  • $\begingroup$ OK, that's not a bad assumption. $\endgroup$
    – emrea
    Mar 29, 2014 at 16:27


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