Nonlinear decision boundaries

With a non-linear kernel, the SVM finds a linear boundary in the feature space, which maps back to a curved boundary in the original space. Circles, spirals and islands become separable.

For the RBF kernel, $\gamma$ sets how far each support vector's influence reaches. Small γ: wide influence, smooth boundary, can underfit. Large γ: very local influence, wiggly boundary that wraps around individual points, overfits.

$C$ and $\gamma$ interact, so tune them together with a grid search on a log scale (e.g. $C,\gamma \in \{10^{-3},\dots ,10^3\}$) and cross-validation. Always standardise features first — the RBF kernel uses distances.