Kernel Trick
Definition
The kernel trick enables algorithms to model nonlinear relationships by computing scalar products in an implicit feature space via a kernel function.
This method avoids explicitly calculating high-dimensional features. It is especially associated with Support Vector Machines and Kernel PCA.
Simply explained
How to use complicated additional features without explicitly creating them all as new columns.
Why it matters in practice
Relevant for classical ML methods on medium-sized datasets and for understanding SVMs.
Example from business
An SVM classifier uses an RBF kernel to map a nonlinearly separable quality class.
Limits and pitfalls
- Use any similarity value as a valid kernel; forget feature scaling; choose large datasets despite quadratic memory/computational issues.
Origin & history
The overview by Hofmann, Schölkopf, and Smola (2008) describes, among other things, the kernelization of methods such as Support Vector Machines and PCA.
Use in mid-sized companies
- Possible applications: nonlinear classification, regression, and dimensionality reduction with suitable dataset size.
Frequently asked questions
Is the kernel trick itself a model?
No, it is a computational principle in kernel-based methods. Must the feature space be explicitly computed? That is precisely what is avoided.
Sources
- Schölkopf & Smola (2008), Kernel Methods in Machine Learning · Hofmann, Schölkopf & Smola (2008), Kernel Methods in Machine Learning
- Schölkopf & Smola, Volltext · Hofmann, Schölkopf & Smola, Volltext
Source verification: 10./11.10.2026.
Editorially reviewed on: