Episode 01 · Support Vector Machines

Learn ML by
playing it.

You are a field botanist sorting two species of specimens scattered across a meadow. Your tool? A hyperplane — the razor-sharp decision boundary at the heart of Support Vector Machines, one of the most elegant algorithms in all of machine learning.

🌿 5 Levels 📏 Maximize the Margin 🌀 3 Kernel Types 🧠 Real ML Theory
Hyperplane ← Margin →
The Science

What is a Support Vector Machine?

An SVM finds the optimal hyperplane that separates two classes with the widest possible gap — called the margin.

Key Concepts

① Hyperplane — the decision boundary: w·x + b = 0

② Support Vectors — nearest points, they define the boundary

③ Margin — gap = 2 / ‖w‖ — SVM maximises this

④ Objective — minimise ‖w‖ subject to correct classification

Watch the diagram → dots appear, then the optimal hyperplane draws itself, and the support vectors glow.

Hyperplane ← margin → support vector
Advanced Concept

When a straight line isn't enough

Some data is non-linearly separable — no straight line can divide the classes. The kernel trick solves this by mapping data into a higher-dimensional feature space where a linear hyperplane can separate them.

Three Kernels You'll Use

📏 Linear — straight line, works for simple data

🌀 RBF — circular boundary, great for ring clusters
K(x,y) = exp(−γ‖x−y‖²)

〰️ Polynomial — curved boundary, d=2 gives parabola
K(x,y) = (xᵀy + c)ᵈ

The "trick": computing K(x,y) is cheap, but it's equivalent to working in an infinite-dimensional space.

Original Space → Kernel transform Feature Space
Your Mission

Ready to step into the field?

Five levels, three kernel types, and a whole field journal of ML theory waiting. Here's how to play:

🖱️

Drag to Position

Click and drag the hyperplane boundary to place it between the two specimen groups on the canvas.

🔄

Rotate to Align

Use the rotation slider or scroll wheel to find the ideal angle. On mobile, pinch with two fingers.

📏

Maximise Margin

The wider the gap between the boundary and the nearest points, the higher your score. Watch the margin bar!

🌀

Switch Kernels

When data can't be split linearly, switch to RBF or Polynomial kernels. The sidebar tells you when and why.

Press → or click Enter the Field to begin. Good luck, Botanist!