Classification via explicit feature lift: 2D points → (φ₁(x), φ₂(x), φ₃(x)) in 3D
Left: click to add labeled 2D points (x₁,x₂). Right: see their lifted coordinates in 3D feature space
(φ₁(x₁,x₂), φ₂(x₁,x₂), φ₃(x₁,x₂)). Click “Fit linear classifier” to fit a halfspace in feature space via
logistic regression (gradient descent). The induced decision boundary is drawn on the left, and the corresponding
separating plane is drawn on the right.
class +1
class −1
boundary
Tip: The XOR example is not linearly separable in (x₁,x₂). Try a lift like
φ₁=x₁, φ₂=x₂, φ₃=x₁*x₂ (or x₁²+x₂²) to help.