Answer: (i) Map data to higher-dimensional space for linear separation

Explanation:

SVM finds optimal linear hyperplane $w^T x + b =0$ maximizing margin. Data not linearly separable in original space can be made separable by mapping $\phi: \mathcal{X} \rightarrow \mathcal{H}$ to higher dimension where linear separation is possible (Cover's theorem).

• Kernel trick: Avoids explicit $\phi(x)$ computation; computes inner products in $\mathcal{H}$ via kernel $K(x_i,x_j)=\phi(x_i)^T\phi(x_j)$. Examples: Polynomial $K=(x^T y +c)^d$, RBF $K=\exp(-\gamma||x-y||^2)$.

• (ii) Compute probabilities — not kernel purpose (Platt scaling does, but not trick)

• (iii) Reduce dimensions — opposite; it increases dimension implicitly (PCA reduces, kernel doesn't)

• (iv) Normalize features — preprocessing, unrelated.

Thus (i) correct.