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Hilbert space

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Model Perspective
Model Perspective
Aug 6, 2022 · Artificial Intelligence

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.

Hilbert spaceMachine LearningSVM
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How Kernel Functions Enable SVMs to Classify Non‑Linear Data