dm.cs.tu-dortmund.de/en/mlbits/class-svm-kernel-trick/
Non-linear SVM and the Kernel Trick – Lecture Notes
Example:
original space \(\vec{x} = (x_1,x_2) \in \mathbb {R}^2\)
transformation \(\phi (\vec{x})=(1, \sqrt{2}\; x_1, \sqrt{2}\; x_2, x_1^2, x_2^2, \sqrt{2}\; x_1 x_2) \in \mathbb {R}^6\)
Nonlinear SVM [...] \nolimits _{i=1}^{N} \lambda _i \left( y_i \left(\left\langle \vec{w},\vec{x_i}\mathstrut \right\rangle + b\right) - (1-\xi _i) \right) }_{\text{converted constraints}}\]
The dual looks as before, 1 with a simple [...] constraint on \(\lambda _i\) :
\[\begin{align*} L_D & = \sum \nolimits _{i=1}^N \lambda _i - \tfrac {1}{2} \sum \nolimits _{i,j=1}^{N} \lambda _i \lambda _j y_i y_j \left\langle \vec{x_i},\vec{x_j}\mathstrut …
