Kernel Method
Last Updated: July 29, 2026 | By Mihail Sebastian | AI Dictionary
A technique that lets linear algorithms learn non-linear patterns by computing similarities in a high-dimensional space without ever mapping the data into it.
What is a Kernel Method?
A kernel method lets a linear algorithm learn non-linear patterns by computing similarities between data points as if they had been mapped into a much higher-dimensional space, without ever performing the mapping. The shortcut is called the kernel trick, and it turns algorithms that draw straight lines into algorithms that draw curves.
The best-known customer is the support vector machine, but the trick applies to any algorithm whose math touches the data only through inner products.
How Kernel Methods Work
Mapping data into more dimensions makes tangled classes separable by a flat plane, but computing that mapping directly is expensive or impossible. A kernel function \(K\) delivers the inner product of the mapped points straight from the original ones:
\[ K(x, x') = \langle \phi(x), \phi(x') \rangle \]The algorithm never sees the mapping \(\phi\). It only asks the kernel “how similar are these two points?” and works with the answers.
Types of Kernel Functions
- Linear kernel: the plain inner product, with no transformation. Sufficient when the data is already separable.
- Polynomial kernel: raises the inner product to a power, which captures feature interactions up to that degree.
- RBF (Gaussian) kernel: rates points by proximity, with similarity fading exponentially with distance. It is the default choice for SVMs and also defines the covariance in a Gaussian process.
Kernels extend other algorithms too: kernel PCA performs non-linear dimensionality reduction by applying the same substitution inside principal component analysis.
Example of a Kernel Method
Picture a dataset of points in a plane: one class forms a tight inner disc, the other a ring around it. No straight line separates them, so a linear classifier fails no matter how long it trains.
An SVM with an RBF kernel treats each point’s similarity to the training points as its new coordinates. In that implicit space, a flat plane splits the two classes cleanly.
Projected back onto the original plane, the flat plane becomes a circle drawn between the disc and the ring. The algorithm still only ever drew a line – the kernel supplied the curvature.
Related AI terms: Support Vector Machine · Gaussian Process · Principal Component Analysis · Dimensionality Reduction
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Mihail Sebastian — Writes about AI governance, regulation, and the technology behind them. Placeholder bio — replace with a real credential line. About