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Slides polynomial kernel #109

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Adding missing Transpose
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patriciomassaro committed Mar 5, 2023
commit 6ca36980713bd2145976a03c65f11cb768a3f9d0
Binary file modified slides-pdf/slides-nonlinsvm-kernel-poly.pdf
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2 changes: 1 addition & 1 deletion slides/nonlinear-svm/slides-nonlinsvm-kernel-poly.tex
Original file line number Diff line number Diff line change
@@ -53,7 +53,7 @@
& \ \ \ \ \ \ (x_1 \xt_1 + x_1 \xt_2 + x_2 \xt_1 + x_2 \xt_2 + b) \\[10pt]
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  • same as line above => remove the two summands in the middle
  • why not use proper alignment here instead of \\\\\\? :)

&= x_1^2 \xt_1^2 + x_2^2 \xt_2^2 + 2 x_1 \xt_1 x_2 \xt_2 + 2 b x_1 \xt_1 + 2 b x_2 \xt_2 + b^2 \\[10pt]
&= ( x_1^2 , x_2^2 , \sqrt{2} x_1 x_2 , \sqrt{2b} x_1 , \sqrt{2b} x_2 , b ) \cdot \\
& \ \ \ \ \ \ ( \xt_1^2 , \xt_2^2 ,\sqrt{2} \xt_1 \xt_2 , \sqrt{2b} \xt_1 , \sqrt{2b} \xt_2 , b ) \\[10pt]
& \ \ \ \ \ \ ( \xt_1^2 , \xt_2^2 ,\sqrt{2} \xt_1 \xt_2 , \sqrt{2b} \xt_1 , \sqrt{2b} \xt_2 , b )^T \\[10pt]
&= \phix \cdot \phixt
\end{aligned}
\end{equation*}