How Kernel Functions Enable SVMs to Classify Non‑Linear Data
When training data from two classes overlap heavily, linear SVMs fail, so we map inputs into a high‑dimensional Hilbert (feature) space using kernel functions—such as linear, polynomial, radial basis, and Fourier kernels—to make the data linearly separable, formulate a quadratic programming problem, solve its convex dual, and construct a classifier for unknown samples.