Skip to main content
Interactive 3D/SVM Kernels & Margin
SVM Kernel Explorer
Kernel trick + margin maximization
Dataset
Kernel
K(x,z) = xᵀz
C (soft margin)1.0
0.1 (wide)10 (narrow)
Model Stats
Support vectors0
Margin width0.000
KernelLinear
Legend
Class +1 (indigo)
Class −1 (orange)
Support vector (star)
Decision boundary
Margin lines (±1)
Kernel trick: maps data into a higher-dimensional space where a linear boundary separates classes.

Support vectors are the points closest to the margin - removing all others would give the same boundary.

SVM Kernels & Margin - Interactive Visualization

A Support Vector Machine finds the hyperplane that maximizes the margin between two classes - the widest possible road separating positive from negative examples. When classes are not linearly separable, kernel functions implicitly map data to a higher-dimensional space where a linear boundary does exist. The kernel trick lets SVMs find complex boundaries without ever computing high-dimensional coordinates explicitly.

  • See the maximum-margin hyperplane and the support vectors that define it - only a few points matter
  • Switch between Linear, RBF, and Polynomial kernels and watch the boundary shape transform
  • Adjust the regularization parameter C to trade off between margin width and training error
  • Understand soft-margin SVM: allowing some misclassifications to get a wider, more robust margin
  • Learn why the kernel trick is computationally elegant - it computes dot products in feature space without explicit transformation

Part of the EngineersOfAI Interactive 3D - free interactive visualizations covering every major concept in machine learning and AI engineering. Hover any element for a plain-English explanation. No code required.